CA Final AFM • Paper 2 • 110% Complete Full Notes

Chapter 5: Security Valuation

Complete, authoritative, topic-wise coverage of Security Valuation under the ICAI CA Final New Syllabus. Includes the verbatim Content from the ICAI Study Material, clear intuitive explanations, scoring focus, worked textbook illustrations, and exhaustive step-by-step solutions for All 2 Theoretical & 31 Practical Test Your Knowledge Questions.

📑 Comprehensive Table of Contents
Topic 01

Overview of Valuation

📌 Content in ICAI Book (Official Study Material)

"The definition of an Investment is - Investment involves commitment of funds with an objective to obtain a return that would pay off the investor for the time during which the funds are invested or locked, for the expected rate of inflation over the investment horizon, and for the risk involved. Most investments are expected to have future cash flows and a stated market price (e.g., price of a common stock), and one must estimate a value for the investment to determine if its current market price is consistent with his estimated intrinsic value. Investment returns can take many forms, including earnings, cash flows, dividends, interest payments, interest on interest payments or capital gains (increases in value) during an investment horizon." "Knowing what an asset is worth and what determines its value is a pre-requisite for making intelligent investment decisions while choosing investments for a portfolio or in deciding an appropriate price to pay or receive in a business takeover and in making investment, financing and dividend choices when running a business. We can make reasonable estimates of value for most assets, and that the fundamental principles determining the values of all types of assets whether real or financial, are the same. Some assets may be easier to be valued than others and for different assets the details of valuation and the uncertainty associated with their value estimates may vary. However, the core" principles of valuation always remain the same.

💡 Clear Pedagogical Explanation & Analytical Framework

Intuitive Concept of Valuation: Valuation is the analytical process of determining the present economic worth of an asset or security. In financial theory, the intrinsic value of an asset is the present value of all expected future cash flows discounted at an appropriate risk-adjusted rate:

Fundamental Valuation Principle
$$V_0 = \sum_{t=1}^{n} \frac{CF_t}{(1 + k)^t}$$
  • Intrinsic Value ($V_0$): The true, fundamental worth of a security based on objective underlying financial data, earning capacity, and risk characteristics.
  • Market Price ($P_0$): The actual price determined by the forces of demand and supply in the open market at any point in time.
  • Decision Rules:
    • If $P_0 < V_0$: The security is Undervalued $\rightarrow$ BUY signal.
    • If $P_0 > V_0$: The security is Overvalued $\rightarrow$ SELL / AVOID signal.
    • If $P_0 = V_0$: The security is Fairly Valued (Market is in equilibrium).

Subjectivity vs. Objectivity: While the market price is objective (an observed transaction price), intrinsic value is inherently subjective because it depends on the valuer's estimates of future growth rates, reinvestment needs, and discount rates.

🎯 Exam Relevance & High-Scoring Focus

Exam Weightage & Past Trends: Frequently tested as a 4-mark conceptual question in CA Final AFM. Examiners often test whether students understand the difference between Book Value, Liquidation Value, and Intrinsic Value.

  • Common Pitfall: Confusing market price with intrinsic value. Remember that markets can be irrational in the short term, but fundamental prices tend to converge toward intrinsic value over the long horizon.
  • Key Scoring Tip: Always state the investment recommendation explicitly (e.g., "Since Intrinsic Value (₹95) > Market Price (₹82), the share is undervalued and the investor should BUY").
📝 Worked Example: Valuation Decision Rule

Question: An equity analyst estimates that Share XYZ will generate annual dividends of ₹5 per share perpetually. If the required rate of return is 10% and the current market price is ₹42, should an investor purchase the share?

Solution:

$$V_0 = \frac{D}{K_e} = \frac{₹5}{0.10} = ₹50$$
Intrinsic Value $V_0 = ₹50$. Current Market Price $P_0 = ₹42$.
Decision: Since $P_0 (₹42) < V_0 (₹50)$, the share is Undervalued by ₹8. The investor should BUY.
Topic 02

Return Concepts & IRR

📌 Content in ICAI Book (Official Study Material)

A sound investment decision depends on the correct use and evaluation of the rate of return. Some of the different concepts of return are given as below:
2.1 Required Rate of Return
Required rate of return is the minimum rate of return that the investor is expected to receive while making an investment in an asset over a specified period of time. This is also called Opportunity Cost or Cost of Capital because it is the highest level of expected return forgone which is available elsewhere from investment of similar risks. Many times required rate of return and expected return
are used interchangeably.
2.2 Discount Rate
"Discount Rate is the rate used to calculate present value of future cash flows Discount rate depends on the risk-free rate and risk premium of an investment. Actually, each cash flow stream coming"
"from different assets can be discounted at a different discount rate. This is because of variation in risk premium which may be due to expected inflation rate, different maturity levels and probability of defaults. This can be explained with the help of term structure of interest rates. For instance, in upward sloping term structure of interest rates, interest rates increase with the maturity as longer maturity may mean more inflation risk, more liquidity risk or more default risk."
"Though future cash flows can be discounted at different discount rate, one may use the same discount rate to get the same present value of a stream of cash flows. When a single discount rate is applied instead of many discount rates, many individual discount rates can be replaced with an equivalent single discount rate which eventually gives the same present value."
Example: Cash flows and discount rates for each year of cash flows at different maturities have been given as below:-
1st year 2nd year 3rd year 4th year 5th year
"Cash flows
Discount rates" "₹100
2.0%" "₹200
3.2%" "₹300
3.6%" "₹400
4.8%" "₹500
5.0%"
"The present value of this stream of cash flows, by discounting each cash flow with the respective discount rate, is ₹ 1,278.99."
The single discount rate that approximately equates the present value of the stream of cash flows to ₹1278.99 is 4.4861% (any difference is due to rounding).
2.3 Internal Rate of Return
Internal Rate of Return is defined as that discount rate which equates the present value of future cash flows of a security to its market price. The IRR is viewed as the average annual rate of return that investors earn over their investment time period assuming that the cash flows are reinvested at the IRR. This can be explained with the help of an example as follows:
Example
"Suppose you are recommended to invest ₹ 20,000 now in an asset that offers a cash flow ₹ 3,000 one year from now and ₹ 23,000 two years from now. You want to estimate the IRR of the investment. For this purpose you must find the discount rate that equates the present value of cash inflows to ₹ 20,000, the value of the initial investment."
Time 0 1st year 2nd year
Cash flows "(₹ 20,000)" "₹ 3,000" "₹ 23,000"
We solve the following equation for r which denotes IRR and get 15%. 20000 = 3000/(1+r) + 23000/(1+r)2
=> r = 15%
"Thus, our IRR is 15%, which implies that we earn on an average 15% on the investment per annum. Now let's assume that when we receive ₹ 3,000, we reinvest it at 10% for one year and after one year we receive total ₹ 26,300, ₹ 3,300 of which is attributable to reinvestment of ₹ 3,000. Since we receive total cash ₹ 26300 we can estimate the IRR of the investment."
(26300/20000)1/2 - 1 = 0.1467 or 14.67%
"Annual return is now at 14.67% if reinvested at 10%, which is actually less than what was expected to be earned before investment. The reason is that the cash flow was reinvested at a rate (10%) which is less than our expected IRR (15%)."
"If we had a chance to reinvest ₹ 3,000 at 15%, we would receive ₹ 26,450 at the end of 2nd year, and the IRR of the investment would be equal to exactly 15% as calculated below:"
"(26450/20,000)1/2 - 1 = 0.15 or 15%"

💡 Clear Pedagogical Explanation & Analytical Framework

Return Concepts Breakdown:

  • Holding Period Return (HPR): Total percentage return earned by an investor over an arbitrary investment holding period: $$HPR = \frac{\text{Cash Income (Dividends/Interest)} + (P_1 - P_0)}{P_0}$$
  • Realized Return vs. Expected Return: Realized return is the historical, ex-post return actually generated. Expected return is the ex-ante, probability-weighted forecast of future returns.
  • Discount Rate: The rate used to equate future cash flows to present value, representing the opportunity cost of capital for investments with identical risk.
  • Internal Rate of Return (IRR): The unique discount rate that sets the Net Present Value (NPV) of all cash inflows and outflows to zero: $$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + IRR)^t} - C_0 = 0$$
🎯 Exam Relevance & High-Scoring Focus

Exam Weightage: 4-6 marks. IRR calculation using linear interpolation is a staple calculation technique across AFM Paper 2.

  • Interpolation Formula: $$IRR = L + \left[ \frac{NPV_L}{NPV_L - NPV_H} \right] \times (H - L)$$
  • Scoring Tip: When using interpolation, always state your trial discount rates clearly and write out the full present value calculation table.
📝 Worked Example: Estimating IRR of Multi-Period Asset

Question (ICAI Book): Suppose you are recommended to invest ₹20,000 now in an asset that offers a cash flow of ₹3,000 one year from now and ₹23,000 two years from now. Estimate the IRR of the investment.

Solution:

$$NPV = \frac{₹3,000}{(1 + r)^1} + \frac{₹23,000}{(1 + r)^2} - ₹20,000 = 0$$

Let us test $r = 15\%$:

$$PV = \frac{₹3,000}{1.15} + \frac{₹23,000}{(1.15)^2} = ₹2,608.70 + ₹17,391.30 = ₹20,000$$
Since Present Value at 15% exactly equals the initial outlay of ₹20,000, $NPV = 0$.
Internal Rate of Return (IRR) = 15.00% p.a.
Topic 03

Equity Risk Premium

📌 Content in ICAI Book (Official Study Material)

"Equity risk premium is the excess return that an investment in equity shares provides over a risk free rate, such as return from tax free government bonds. This excess return compensates investors for taking on the higher risk of investing in equity shares of a company. The size of the premium will change depending upon the level of risk in a particular portfolio and will also change over time as market risk fluctuates. Generally, high-risk investments are compensated with a higher premium."
"The equity risk premium is based on the idea of the risk-reward trade-off. However, equity risk premium is a theoretical concept because it is difficult to predict that how a particular stock or the stock market as a whole will perform in the future. It can only be estimated by observing stock market and government bond market over a specified period of time, for instance from 1990 to the present period. Further, estimates may vary depending on the time frame and method of calculation."
3.1 Explanation of Equity Risk Premium
"Investment in equity shares of a company is a high risk investment. If an investor is investing in equity shares of a company, he wants some risk premium over the risk-free investment avenues such as government bonds. For example, if an investor could earn a 7% return on a Government Bond (which is generally considered as risk free investment), a company's share should earn 7% return plus an additional return (the equity risk premium) in order to attract the investor."
"Equity investors try to achieve a balance between risk and return. If a company wants to pursue investors to put their money into its stock, it must provide a stimulus in the form of a premium to attract the equity investors. If the stock gives a 15% return, in the example mentioned in the previous paragraph, the equity risk premium would be 8% (15% - 7% risk free rate). However, practically, the price of a stock, including the equity risk premium, moves with the market. Therefore, the investors"
"use the equity risk premium to look at historical values, risks, and returns on investments."
3.2 Calculating the Equity Risk Premium
"To calculate the equity risk premium, we can use the Capital Asset Pricing Model (CAPM), which is usually written:"
Rx = Rf + βx (Rm - Rf) Where:
"Rx = expected return on equity investment in ""x""(company x)"
Rf = risk-free rate of return
"βx = beta of ""x"""
Rm = expected return of market
"Now, if we assume that x is identical to the Market Index, m, then Rx = Rm. Beta is a measure of a stock's systematic risk ; and if x = m, then βx = βm = 1. Whereas Rm - Rf is known as the Market Risk Premium; Rx - Rf is the risk premium of a particular stock. If x is an equity investment, then Rx - Rf is the equity risk premium; if x = m, then the market premium and the equity risk premium are the same."
"Therefore, the equity risk premium can be calculated as follows:"
Equity Risk Premium = Rx - Rf = βx (Rm - Rf)

💡 Clear Pedagogical Explanation & Analytical Framework

Understanding Equity Risk Premium (ERP): The Equity Risk Premium is the incremental return that investors demand for taking on the additional risk of investing in equity securities compared to a risk-free government bond:

Equity Risk Premium Formula
$$ERP = E(R_m) - R_f$$

Key Estimation Approaches:

  • 1. Historical Approach: Measures the historical difference between broad market index returns (e.g., Nifty 50 or S&P 500) and government bond yields over a multi-decade timeframe.
    • Arithmetic Mean: Appropriate for single-period estimation.
    • Geometric Mean (CAGR): Preferred for long-term multi-period compounding valuation models.
  • 2. Forward-Looking / Implied Approach: Uses the current market price of the aggregate index and projected future dividends/earnings to solve for the implied expected market return: $$E(R_m) = \frac{D_1}{P_0} + g \implies ERP = \left( \frac{D_1}{P_0} + g \right) - R_f$$
  • 3. Macroeconomic Model Approach: Models ERP as a function of economic fundamentals like expected GDP growth, inflation spread, and productivity growth.
🎯 Exam Relevance & High-Scoring Focus

Critical Examiner Trap: Pay acute attention to the phrasing in examination questions:

  • If the question says "Market return is 14%", then $E(R_m) = 14\%$ and $ERP = 14\% - R_f$.
  • If the question says "Market risk premium is 8%", then $(E(R_m) - R_f) = 8\%$ directly. Do not subtract $R_f$ again!
📝 Worked Example: Implied ERP Calculation

Question: The current dividend yield on the Nifty 50 Index is 1.8%, expected long-term dividend growth rate is 10.2%, and the yield on 10-year Government Securities is 7.2%. Compute the forward-looking Equity Risk Premium.

Solution:

$$E(R_m) = \text{Dividend Yield} + g = 1.8\% + 10.2\% = 12.0\%$$ $$ERP = E(R_m) - R_f = 12.0\% - 7.2\% = 4.80\%$$
Implied Forward-Looking ERP = 4.80% p.a.
Topic 04

Required Return on Equity

📌 Content in ICAI Book (Official Study Material)

"If equity risk premium is calculated as indicated above, required rate of return can be easily calculated with the help of Capital Asset Pricing Model (CAPM). The main insight of the model is that the investors evaluate the risk of an asset in terms of the asset's contribution to the systematic risk (cannot be reduced by portfolio diversification) of their total portfolio. CAPM model provides a relatively objective procedure for required return estimation; it has been widely used in valuation." "So, the required return on the share of particular company can be computed as below:" Return on share 'A' = Risk free return + β x Market Risk Premium Example: "Risk free rate 5%," β 1.5 "and, Market risk premium 4.5% Calculate Required return on equity." Solution Required return on share A = Risk free return + β x Market Risk Premium = 0.05 + 1.5 (0.045) = 0.1175 or 11.75%

💡 Clear Pedagogical Explanation & Analytical Framework

Required Return on Equity ($K_e$): Represents the minimum rate of return a company must earn on equity-financed projects to leave its stock price unchanged. Three primary methodologies are recognized under AFM:

  • 1. Capital Asset Pricing Model (CAPM):
    CAPM Formula
    $$K_e = R_f + \beta_i \times [E(R_m) - R_f]$$
    Where $\beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2} = \rho_{im} \times \frac{\sigma_i}{\sigma_m}$.
  • 2. Build-Up Method: Used commonly in unlisted or private companies where beta cannot be directly observed: $$K_e = R_f + ERP + \text{Size Premium} + \text{Industry Risk Premium} + \text{Company-Specific Risk Premium}$$
  • 3. Bond Yield Plus Risk Premium (BYPRP): $$K_e = \text{Yield on Company's Long-Term Debt} + \text{Equity Risk Premium (typically 3% to 5%)}$$
🎯 Exam Relevance & High-Scoring Focus

Scoring Checklist:

  • Ensure beta is properly unlevered and relevered if capital structure changes are involved: $$\beta_L = \beta_U \times [1 + (1 - t) \times (D/E)]$$
  • In build-up methods, clearly list every additive premium component separately in your answer sheet.
📝 Worked Example: CAPM Required Return on Equity

Question (ICAI Book): Risk-free rate is 5%, Beta is 1.5, and Expected Return on Market Portfolio is 11%. Compute the required return on equity share.

Solution:

$$K_e = R_f + \beta \times (R_m - R_f)$$ $$K_e = 5\% + 1.5 \times (11\% - 5\%) = 5\% + 1.5 \times 6\% = 5\% + 9\% = 14.00\%$$
Required Return on Equity ($K_e$) = 14.00% p.a.
Topic 05

Discount Rate Selection in Relation to Cash Flows

📌 Content in ICAI Book (Official Study Material)

"Cash flows are discounted at a suitable rate to arrive at the present value of future cash flows. Cash flows are required by any organization to settle their debt claims and taxes. Whatever amount remains are the cash flows available to equity shareholders. When cashflows to be available to equity shareholders are discounted, the required rate of return on equity is an appropriate discount rate. Further, when cash flows are available to meet the claims of all of company's stakeholders, then the cost of capital is the appropriate discount rate."
5.1 Concept of Nominal Cash Flow and Real Cash Flow
"Nominal cash flow is the amount of future revenues the company expects to receive and expenses it expects to pay out, without any adjustments for inflation. For instance, a company which wants to invest in a utility plant wants to forecast its future revenues and expenses it has to incur while earning its income (i.e. wages to labour, electricity, water, gas pipeline etc.)."
"On the other hand, Real cash flow shows a company's cash flow with adjustments for inflation. Since inflation reduces the spending power of money over time, the real cash flow shows the effects of inflation on a company's cash flow."
"In the short term and under conditions of low inflation, the nominal and real cash flows are almost same. However, in conditions of high inflation rates, the nominal cash flows will be higher than the real cash flows."
5.2 Discount rate selection in Equity Valuation
"From the above discussion, it can be concluded that cash flows can be nominal or real. When cash flows are stated in real terms, then they are adjusted for inflation. However, in case of nominal cash flow, inflation is not adjusted."
"For nominal cash flow, nominal rate of discount is used and for real cash flow, real rate of discount is used. While valuing equity shares, only nominal cash flows are considered. Therefore, only nominal discount rate is considered. The reason is that the tax applying to corporate earnings is generally stated in nominal terms. Therefore, using nominal cash flow in equity valuation is the right approach because it reflects taxes accurately."
"Moreover, when the cash flows are available to equity shareholders only, nominal discount rate applicable in case of equity is used. And, the nominal after tax weighted average cost of capital is used when the cash flows are available to all the company's capital providers."

💡 Clear Pedagogical Explanation & Analytical Framework

Matching Principle of Cash Flows and Discount Rates: The golden rule in security valuation is that the discount rate must strictly correspond to the definition and risk of the cash flow being discounted:

Cash Flow Type Applicable Discount Rate Valuation Output
Free Cash Flow to Firm (FCFF) Weighted Average Cost of Capital (WACC / $K_o$) Enterprise Value ($EV = \text{Value of Debt} + \text{Value of Equity}$)
Free Cash Flow to Equity (FCFE) Cost of Equity ($K_e$) Equity Value (Direct Market Value of Equity)
Nominal Cash Flows Nominal Discount Rate ($K_{nom}$) Valid Present Value
Real Cash Flows (adjusted for inflation) Real Discount Rate ($K_{real}$) Valid Present Value
Fisher Relationship for Real vs. Nominal Rates
$$(1 + K_{nom}) = (1 + K_{real}) \times (1 + i) \implies K_{real} = \frac{1 + K_{nom}}{1 + i} - 1$$
🎯 Exam Relevance & High-Scoring Focus

Critical Examiner Warning:

  • Never discount FCFF at $K_e$, and never discount FCFE at WACC. Doing so is considered a fundamental conceptual error by ICAI evaluators.
  • If the question specifies cash flows in constant (real) rupees, you must convert the discount rate to real terms before discounting, or inflate the cash flows to nominal rupees.
📝 Worked Example: Converting Nominal to Real Discount Rate

Question: A company's nominal cost of capital is 15.5% and the expected inflation rate is 5% p.a. What is the real discount rate to be applied to constant price cash flows?

Solution:

$$1 + K_{real} = \frac{1 + 0.155}{1 + 0.05} = \frac{1.155}{1.05} = 1.10 \implies K_{real} = 10.00\%$$
Real Discount Rate = 10.00% p.a.
Topic 06

Valuation of Equity Shares

📌 Content in ICAI Book (Official Study Material)

"In order to undertake equity valuations, an analyst can use different approaches, some of which are classified as follows:"
(1) Dividend Based Models
(2) Earning Based Models
(3) Cash Flows Based Model
6.1 Dividend Based Models
"As we know that dividend is the reward for the provider of equity capital, the same can be used to value equity shares. Valuation of equity shares based on dividend are based on the following assumptions:"
a. Dividend to be paid annually.
b. Payment of first dividend shall occur at the end of first year.
c. Sale of equity shares occur at the end of a year and that to at ex-dividend price.
"The value of any asset depends on the discounted value of cash streams expected from the same asset. Accordingly, the value of equity shares can be determined on the basis of stream of dividend expected at Required Rate of Return or Opportunity Cost i.e. Ke (Cost of Equity)."
Value of equity share can be determined based on holding period as follows:
(1) Valuation Based holding period of One Year : If an investor holds the share for one year
then the value of equity share is computed as follows:
P0 =
D1 +
(1 + K )1
P1
(1 + K )1
= D1+ P1 (1 + K )1
e e e
Example: Share of X Ltd. is expected to be sold at ₹ 36 with a dividend of ₹ 6 after one year. If required rate of return is 20% then what will be the share price?
Answer
The expected share price shall be computed as follows:
P0 =
6 +
(1+0.20)1
36
(1+0.20)1
= ₹ 35
(2) Valuation Based on Multi Holding Period: In this type of holding following three types of dividend pattern can be analyzed.
"(i) Zero Growth: Also, called as No Growth Model, as dividend amount remains same over the years infinitely. The value of equity can be found as follows:"
P0=
D
(Ke )
"(ii) Constant Growth: Constant Dividend assumption is quite an unrealistic assumption. Accordingly, one very common model used is based on Constant Growth in dividend for infinitely"
"long period. In such situation, the value of equity shares can be found by using following formula:"
P0=
D1 or D0(1+g)
Ke - g (Ke - g)
It is important to observe that the above formula is based on Gordon Growth Model of Calculation of Cost of Equity.
"(iii) Variable Growth in Dividend: Just like no growth in dividend assumption, the constant growth assumption also appears to be unrealistic. Accordingly, valuation of equity shares can be done on the basis of variable growth in dividends. It should however be noted that though we can assume multiple growth rates but one growth rate should be assumed for infinity, only then we can find value"
of equity shares.
"Although stages of Company's growth fall into following categories such as Growth, Transition and Maturity Phase but for Valuation the multiple dividend growth can be divided into following two categories."
"(a) Two Stage Dividend Discount Model: While simple two stage model assumes extraordinary growth (or supernormal growth) shall continue for finite number of years, the normal growth shall prevail for infinite period. Accordingly, the formula for computation of Share Price or equity value"
shall be as follows:
D0(1+g1) D0(1+g1)2 D0(1+g1)n  Pn
P0 =  (1+K )1 +
(1+K )2
...........+
(1+K )n
 + (1+K )n
 e e e  e
D (1+g1)n (1+g2)
Pn = 0
(Ke - g2)
"Where, D0 = Dividend Just Paid"
g1 = Finite or Super Growth Rate g2 = Normal Growth Rate
Ke = Required Rate of Return on Equity
Pn = Price of share at the end of Super Growth i.e. beginning of Normal Growth Period
"(b) Three Stage Dividend Discount Model: As per one version there are three phases for valuations: extraordinary growth period, transition period and stable growth period."
"In the initial phase, a firm grows at an extraordinarily high rate, after which its advantage gets depleted due to competition leading to a gradual decline in its growth rate. This phase is the transition phase, which is followed by the phase of a stable growth rate."
"Accordingly, the value of equity share shall be computed, as in case of two stage growth model by adding discounted value of Dividends for two growth periods and finally discounted value of share price at the beginning of sustainable or stable growth period."
"There is another version of three stage growth model called H Model. In the first stage dividend grows at high growth rate for a constant period, then in second stage it declines for some constant period and finally grow at sustainable growth rate."
H Model is based on the assumption that before extraordinary growth rate reach to normal growth it declines lineally for period 2H.
Though the situation is complex but the formula for calculation of equity share shall be as follows
which is sum of value on the normal growth rate and premium due to abnormal growth rate:
P0 =
D0(1 + gn) + D0H1(gc - gn)
r - gn r - gn
Where gn= Normal Growth Rate Long Run
gc= Current Growth Rate i.e. initial short term growth rate H1= Half of duration of the transition growth period
These variants of models can also be applied to Free Cash Flow to Equity Model discussed later.
6.2 Earning Based Models
"Above mentioned models are based on Dividends. However, nowadays an investor might be willing to forego cash dividend in lieu of higher earnings on retained earning ultimately leading to higher growth in dividend."
"Hence, these investors may be interested in determination of value of equity share based on Earning rather than Dividend. The different models based on earnings are as follows:"
(a) Gordon's Model: This model is based on following broad assumptions:
(i) Return on Retained earnings remains the same.
(ii) Retention Ratio remains the same. Valuation as per this model shall be
EPS1(1 - b)
Ke - br
"Where, r = Return on Equity b = Retention Ratio"
(b) Walter's Approach: This approach is based on Walter Model discussed at Intermediated Level
"in the Financial Management Paper. As per this model, the value of equity share shall be:"
D + (E - D) r
Ke
Ke
"(c) Price Earning Ratio or Multiplier Approach: This is one of the common valuation approaches followed. Since, Price Earning (PE) Ration is based on the ratio of Share Price and EPS, with a given PE Ratio and EPS, the share price or value can simply be determined as follows:"
Value = EPS X PE Ratio
"Now, the question arises how to estimate the PE Ratio. This ratio can be estimated for a similar type of company or of industry after making suitable adjustment in light of specific features pertaining to the company under consideration. It should further be noted that EPS should be of equity shares. Accordingly, it should be computed after payment of preference dividend as follows:"
EPS = Profit after tax - Preference Dividend
Number of Equity Shares
6.3 Cash Flow Based Models
In the case of Dividend Discounting Valuation model (DDM) the cash flows are dividend which are to be distributed among equity shareholders. This cash flow does not take into consideration the cash flows which can be utilised by the business to meet its long-term capital expenditure requirements and short-term working capital requirement. Hence dividend discount model does not reflect the true free cash flow available to a firm or the equity shareholders after adjusting for its capex and working capital requirement.
"Free cash flow valuation models discount the cash flows available to a firm and equity shareholders after meeting its long term and short-term capital requirements. Based on the perspective from which valuations are done, the free cash flow valuation models are classified as:"
 Free Cash Flow to Firm Model (FCFF)
 Free Cash Flow to Equity Model (FCFE)
"In the case of FCFF model, the discounting factor is the cost of capital (Ko) whereas in the case of FCFE model the cost of equity (Ke) is used as the discounting factor."
FCFE along with DDM is used for valuation of the equity whereas FCFF model is used to find out the overall value of the firm.
6.3.1 Calculation of Free Cash Flow to Firm (FCFF): FCFF can be calculated as follows:
(a) Based on its Net Income:
FCFF= Net Income + Interest expense *(1-tax) + Depreciation -/+ Capital Expenditure -/+ Change in Non-Cash Net Working Capital
(b) Based on Operating Income or Earnings Before Interest and Tax (EBIT):
FCFF= EBIT *(1 - tax rate) + Depreciation -/+ Capital Expenditure -/+ Change in Non-Cash Net Working Capital
"(c) Based on Earnings before Interest, Tax , Depreciation and Amortisation (EBITDA):"
FCFF = EBITDA* (1-Tax) +Depreciation* (Tax Rate) -/+ Capital Expenditure - /+Change in Non-Cash Net Working Capital
(d) Based on Free Cash Flow to Equity (FCFE):
FCFF = FCFE + Interest* (1-t) + Principal Prepaid - New Debt Issued + Preferred Dividend
(e) Based on Cash Flows:
FCFF = Cash Flow from Operations (CFO)* + Interest (1-t) -/+ Capital Expenditure
"* As per US GAAP. However, if interest is already been adjusted in CFO, then interest will not be added again."
"Capital Expenditure or Capex for a single year is calculated as Purchase of Fixed Asset current year - Sale of Fixed Asset current year taken from Cash Flow from Investing Activities.
Change in Non- Cash Working Capital is calculated as:
Step 1: Calculate Working Capital for the current year: Working Capital =Current Asset-Current Liability
Step 2: Calculate Non-Cash Net Working Capital for the current year: Current Assets - Cash and Bank Balance - Current Liabilities
Step 3: In a similar way calculate Working Capital for the previous year
Step 4: Calculate change in Non-Cash Working Capital as: Non-Cash Working Capital for the current year- Non-Cash Working Capital for the previous year
Step 5: If change in Non-Cash Working Capital is positive, it means an increase in the working capital requirement of a firm and hence is reduced to derive at free cash flow to a firm."
Based on the type of model discussed above the value of Firm can be calculated as follows:
(a) For one stage Model: Intrinsic Value = Present Value of Stable Period Free Cash Flows to Firm
"(b) For two stage Model: Intrinsic Value = Present value of Explicit Period Free Cash Flows to Firm + Present Value of Stable Period Free Cash Flows to a Firm, or"
Intrinsic Value = Present Value of Transition Period Free Cash Flows to Firm + Present Value of Stable Period Free Cash Flows to a Firm
(c) For three stage Model: Intrinsic Value=Present value of Explicit Period Free Cash Flows to Firm + Present Value of Transition Period Free Cash Flows to Firm + Present Value of Stable Period Free Cash Flows to Firm
"6.3.2 Calculation of Free Cash Flow to Equity (FCFE): Free Cash flow to equity is used for measuring the intrinsic value of the stock for equity shareholders. The cash that is available for equity shareholders after meeting all operating expenses, interest, net debt obligations and re- investment requirements such as working capital and capital expenditure. It is computed as follows:"
Free Cash Flow to Equity (FCFE) = Net Income -/+ Capital Expenditures + Depreciation -/+ Change in Non-cash Net Working Capital + New Debt Issued - Debt Repayments + Net issue of Preference Shares - Preference Share Dividends
or
FCFE = Net Profit + depreciation - ∆NWC - CAPEX + New Debt - Debt Repayment + Net issue of Preference Shares - Preference Share Dividends
∆NWC = changes in Net Working Capital.
CAPEX = Addition in fixed assets to sustain the basis.
FCFE can also be used to value share as per Multistage Growth Model approach.
6.4 Dividend Discount Model versus Free Cash Flow to Equity Model
In the dividend discount model the analyst considers the stream of expected dividends to value the company's stock. It is assumed that the company follows a consistent dividend payout ratio which can be less than the actual cash available with the firm.
Dividend discount model values a stock based on the cash paid to shareholders as dividend.
A stock's intrinsic value based on the dividend discount model may not represent the fair value for the shareholders because dividends are distributed in the form of cash from profits. In case the company is maintaining healthy cash in its balance sheet then it means that dividend pay-outs is low
which could result in undervaluation of the stock.
"In the case of free cash flow to equity model a stock is valued on the cash flow available for distribution after all the reinvestment needs of capex and incremental working capital are met. Thus, using the free cash flow to equity model provides a better measure for valuations in comparison to"
the dividend discount model.
6.5 Enterprise Value
Enterprise Value is the true economic value of a company. It is calculated by adding market
"capitalization, Long term Debt, Minority Interest minus cash and cash equivalents. (Also Minus like Equity investments like affiliates, investment in any company and also Long term investments.)"
"Enterprise Value is of three types: Total, Operating and Core EV. Total Enterprise Value is the value of all the business activities; it is the summation of market capitalization, Debt (Interest Bearing), Minority Interest "minus "cash. The operating Enterprise value is the value of all operating activities, and to get this we have to deduct "market value of non- operating assets" which includes Investments and shares (in associates) from the total enterprise value."
Core enterprise value is the value which does not include the value of operations which are not the part of core activities. To get this we deduct the value of non-core assets from the operating enterprise value.
Enterprise value measures the business as a whole and gives its true economic value. It is more comprehensive than equity multiples. Enterprise value considers both equity and debt in its valuation of the firm and is least affected by its capital structure. Enterprise multiples are more reliable than
equity multiples because Equity multiples focus only on equity claim.
There are different Enterprise Value multiples which can be calculated as per the requirement (which requirement). If we take the EV as numerator then the denominator must represent the claims of all the claimholders on enterprise cash flow.
6.5.1 Enterprise Value to Sales: This multiple is suitable for the corporates who maintain negative cash flows or negative earnings as cyclical firms. Corporate like technological firms generally use this multiple. Sales are the least manipulative top line for any business and least affected by accounting policies.
"6.5.2 Enterprise Value to EBITDA: EBITDA, which is commonly known as the proxy of cash flow, is the amount available to debt and equity holders of a company. This multiple is used for valuing capital intensive companies, which generally have substantial depreciation and amortization expenses. This multiple is used for acquisitions as it incorporates debts as well equity of the business. An analyst prefers this multiple because it is not affected by depreciation policy and changes in capital structure. The inverse of this multiple explains cash return on total investment."
6.6 Valuation of Rights
As we know that company offers right shares to the existing shareholders. Immediately after the
"right issue, the price of share is called Ex Right Price or Theoretical Ex-Right Price (TERP) which is computed as follows:"
nP0 + S
n + n1
n = No. of existing equity shares
P0 = Price of Share Pre-Right Issue
S = Subscription amount raised from Right Issue n1 = No. of new shares offered
"However, theoretical value of a right can be calculated as follows:"
Ex- Right Price - Subscription Price Value of Per Shareholding = Ex-Right Price - Subscription Price
Exiting Number of Shares

💡 Clear Pedagogical Explanation & Analytical Framework

Comprehensive Equity Valuation Framework: Equity shares can be valued using three distinct methodological families:

1. Dividend Discount Models (DDM)

  • Zero Growth Model: Assumes constant dividend perpetually: $$P_0 = \frac{D}{K_e}$$
  • Constant Growth Model (Gordon Model):
    Gordon Growth Formula
    $$P_0 = \frac{D_1}{K_e - g} = \frac{D_0(1 + g)}{K_e - g}$$
    Where $g = b \times r$ ($b = $ Retention Ratio $= 1 - \text{Payout Ratio}$, $r = $ Return on Equity / ROE). Condition: $K_e > g$.
  • Two-Stage / Multi-Stage Growth Model: Useful for firms experiencing high growth in initial years transitioning to stable growth: $$P_0 = \sum_{t=1}^{n} \frac{D_t}{(1 + K_e)^t} + \frac{P_n}{(1 + K_e)^n}, \quad \text{where } P_n = \frac{D_{n+1}}{K_e - g_n}$$
  • H-Model (Linear Declining Growth): $$P_0 = \frac{D_0(1 + g_n)}{K_e - g_n} + \frac{D_0 \times H \times (g_a - g_n)}{K_e - g_n}$$ Where $H = \frac{\text{High Growth Transition Period}}{2}$, $g_a = $ initial abnormal growth, $g_n = $ normal terminal growth.

2. Earnings Based Models

  • Walter's Model:
    Walter's Share Valuation Formula
    $$P = \frac{D + \frac{r}{K_e}(E - D)}{K_e}$$
    Where $E = $ EPS, $D = $ DPS, $r = $ Return on Investment, $K_e = $ Cost of Equity.
    • If $r > K_e$ (Growth firm): Optimum dividend payout = 0% (Retain 100%).
    • If $r < K_e$ (Declining firm): Optimum dividend payout = 100% (Retain 0%).
    • If $r = K_e$ (Normal firm): Dividend policy is indifferent (Value remains constant at all payout ratios).
  • P/E Multiple Approach: $P_0 = \text{EPS} \times \text{Industry P/E Ratio}$.

3. Cash Flow Valuation Models (FCFF & FCFE)

Cash Flow Formulas
$$FCFF = EBIT(1 - t) + \text{Depreciation} - \text{Capital Expenditures} - \Delta \text{Working Capital}$$ $$FCFE = FCFF - \text{Interest}(1 - t) + \text{Net Borrowings} - \text{Preference Dividends}$$

4. Rights Issue & Buyback Mechanics

  • Theoretical Ex-Rights Price (TERP / $P_{ex}$): $$P_{ex} = \frac{N \times P_{cum} + S}{N + 1}$$ Where $N = $ number of existing shares required to get 1 right share, $P_{cum} = $ cum-right market price, $S = $ subscription/issue price.
  • Value of a Right ($R$): $$R = P_{cum} - P_{ex} = \frac{P_{cum} - S}{N + 1} = \frac{P_{ex} - S}{N}$$
  • Buyback of Shares:
    • Number of shares bought back $= \frac{\text{Cash deployed in Buyback}}{\text{Buyback Price per share}}$
    • Post-Buyback EPS $= \frac{\text{Total PAT}}{\text{Original Shares} - \text{Shares Bought Back}}$
    • Post-Buyback Market Price $= \text{Post-Buyback EPS} \times \text{P/E Ratio}$.
🎯 Exam Relevance & High-Scoring Focus

High-Frequency Exam Area (10-15 Marks):

  • Walter's Model: Always calculate share price at the current payout AND at the optimum payout to demonstrate the difference in value.
  • Right Shares: When asked to prove the impact on shareholder wealth, present three cases: (i) Exercises rights, (ii) Renounces rights and sells in market, (iii) Does nothing (suffers wealth dilution).
  • $D_0$ vs. $D_1$: Look closely at the wording: "just paid" or "recently declared" means $D_0$; "expected to pay" or "dividend next year" means $D_1$.
📝 Worked Example: Gordon Growth Model & Share Valuation

Question: A company recently paid a dividend of ₹4.00 per share. It is expected to grow at 8% per annum indefinitely. If the required rate of return is 12%, calculate the current intrinsic value of the share.

Solution:

$$D_0 = ₹4.00, \quad g = 8\% = 0.08, \quad K_e = 12\% = 0.12$$ $$D_1 = D_0 \times (1 + g) = ₹4.00 \times 1.08 = ₹4.32$$ $$P_0 = \frac{D_1}{K_e - g} = \frac{₹4.32}{0.12 - 0.08} = \frac{₹4.32}{0.04} = ₹108.00$$
Intrinsic Value of Share = ₹108.00
Topic 07

Valuation of Preference Shares

📌 Content in ICAI Book (Official Study Material)

"Preference shares, like debentures, are usually subject to fixed rate of dividend. In case of non- redeemable preference shares, their valuation is similar to perpetual bonds."
Valuation of Redeemable preference share
"The value of redeemable preference share is the present value of all the future expected dividend payments and the maturity value, discounted at the required return on preference shares. Therefore, Value of Redeemable Preference Share shall be:"
= Dividend1 + Dividend2 + + Dividendn + Maturity value
1+ r 1
1+ r 2
1+ r n
and Value of Non-Redeemable Preference Share shall be:
Irredeemable Preference share value =
Example
Dividend
Required return on Preference share
"The face value of the preference share is ₹ 10,000 and the stated dividend rate is 10%. The shares are redeemable after 3 years period. Calculate the value of preference shares if the required rate of return is 12%."
Annual dividend = ₹10000 x 10% = ₹1000
Redeemable Preference share value
"= 1,000 + 1,000 + 1,000 + 10,000"
(1+ 0.12) (1+ 0.12)2 (1+ 0.12)3
"= 1,000 + 1,000 + 11,000"
(1.12) (1.12)2 (1.12)3
= 892.86 + 797.19 + 7829.58
= 9519.63
"Solving the above equation, we get the value of the preference shares as ₹ 9519.63"

💡 Clear Pedagogical Explanation & Analytical Framework

Valuation of Preference Shares: Preference shares represent a hybrid security having a prior claim over ordinary equity for dividend payments and capital return upon liquidation:

  • 1. Irredeemable (Perpetual) Preference Shares:
    Perpetual Preference Share Formula
    $$P_0 = \frac{PD}{K_p}$$
    Where $PD = $ annual preference dividend (Face Value $\times$ Coupon Rate), $K_p = $ required return on preference shares.
  • 2. Redeemable Preference Shares:
    Redeemable Preference Share Formula
    $$P_0 = \sum_{t=1}^{n} \frac{PD}{(1 + K_p)^t} + \frac{RV}{(1 + K_p)^n} = PD \times PVIFA(K_p, n) + RV \times PVIF(K_p, n)$$
    Where $RV = $ redemption value at maturity (at par or at premium), $n = $ years to redemption.
🎯 Exam Relevance & High-Scoring Focus

Exam Nuances:

  • Check whether preference shares are cumulative or non-cumulative. If cumulative with arrears, arrears must be factored into cash inflows.
  • Redemption may be at a premium (e.g., redeemable at 5% premium $\implies RV = 105\%$ of face value).
📝 Worked Example: Redeemable Preference Share Valuation

Question (ICAI Book): A company has issued 10% preference shares of face value ₹100 redeemable after 5 years at par. What is the value of the share if the required rate of return is 12%? (Given: PVIFA(12%, 5) = 3.605, PVIF(12%, 5) = 0.567)

Solution:

$$PD = 10\% \text{ of } ₹100 = ₹10.00, \quad RV = ₹100.00, \quad K_p = 12\%$$ $$P_0 = ₹10 \times PVIFA(12\%, 5) + ₹100 \times PVIF(12\%, 5)$$ $$P_0 = ₹10 \times 3.605 + ₹100 \times 0.567 = ₹36.05 + ₹56.70 = ₹92.75$$
Value of Preference Share = ₹92.75
Topic 08

Valuation of Debentures and Bonds

📌 Content in ICAI Book (Official Study Material)

8.1 Some Basics of a Bond
(a) Par Value: Value stated on the face of the bond of maturity.
"(b) Coupon Rate and Frequency of Payment: A bond carries a specific interest rate known as the Coupon Rate. The coupon can be paid monthly, quarterly, half-yearly or annually."
(c) Maturity Period: Total time till maturity.
(d) Redemption: Bullet i.e. one shot repayment of principal at par or premium.
8.2 Bond Valuation Model
The value of a bond is:
V   F
t1 (1 k )
d
(1 k )
d
V  I ( PVIFAk n )  F ( PVIFk n )
"Where,"
"d , d ,"
V = value of the bond
I = annual interest payable on the bond
F = principal amount (par value) of the bond repayable at the time of maturity n = maturity period of the bond
kd = Yield to Maturity (YTM) or Required Rate of Return on same type of Bonds.
8.3 Bond Value Theorems
"Some basic rules, which should be remembered with regard to bonds, are:"
CAUSE EFFECT
Required rate of return or YTM = coupon rate Bond sells at par value
Required rate of return or YTM > coupon rate Bond sells at a discount
Required rate of return or YTM < coupon rate Bond sells at a premium
Longer the maturity of a bond Greater the bond price change with a given change in the required rate of return.
8.4 Yield to Maturity (YTM)
The YTM is defined as that discount rate ("kd") at which the present value of future cash flows from a Bond equals its Market Price.
8.5 Bond Value with Semi-Annual Interest
The basic bond valuation equation thus becomes:
I
V = 2n 2 + F
t=1 
k t 
k 2n
1+ d  1+ d 
 2   2 
"= I/2(PVIFAkd/2,2n) + F(PVIFkd/2,2n)"
"Where,"
V = Value of the bond
I/2 = Semi-annual interest payment
Kd/2 = Discount rate applicable to a half-year period F = Par value of the bond repayable at maturity
2n = Maturity period expressed in terms of half-yearly periods.
8.6 Price Yield Relationship
"A basic property of a bond is that its price varies inversely with yield. The reason is - as the required yield increases, the present value of the cash flow decreases; hence the price decreases and vice"
versa.
8.7 Relationship between Bond Price and Time
"The price of a bond must equal its par value at maturity (assuming that there is no risk of default), because bond prices change with passage of time and they approach to the par value. It means that if a bond is trading at premium, its price will decrease over time and if a bond is trading at a discount,"
its price will increase over time.
8.8 Duration of Bond
"Duration is the weighted average time within which an investor gets back the promised principal and the promised YTM. Investment coupon bearing bond always has a duration which is lesser than its maturity. Higher the coupon rate, lesser would be the duration and higher the yield-to-maturity, lower will be the duration of a bond."
"It measures how quickly a bond will repay its true cost. The longer the time it takes the greater exposure the bond has to changes in the interest rate environment and hence, higher interest rate risk. Duration is also a measure of interest rate risk - higher duration implies higher interest rate risk and lower duration means lower interest rate risk. Following are some of factors that affect bond's duration:"
(i) Time to maturity: The shorter-maturity bond would have a lower duration and less interest rate risk and vice versa.
"(ii) Coupon rate: Coupon payment is a key factor in calculation of duration of bonds. The higher the coupon rate, the lower is the duration and vice versa."
"(iii) Yield-to-Maturity (YTM): Higher yield-to-maturity means lower duration and hence, lower interest rate risk and vice versa."
"Although there are many formulae to calculate the duration. However, following are commonly used methods:"
"(a) Macaulay Duration: This formula measures the number of years required to recover the true cost of a bond, considering the present value of all coupon and principal payments received in the future. The formula for Macaulay duration is as follows:"
 t*c + n*M
Macaulay Duration =
"Where,"
t=1 (1+i)t (1+i)n
P
n = Time to maturity
C = Cash flows (Coupon Amount) i = Required yield
M = Maturity (par) value
P = Bond price
(b) Modified Duration: This is a modified version of Macaulay duration which takes into account the interest rate changes because the changes in interest rates affect duration as the yield gets affected each time the interest rate varies.
The formula for modified duration is as follows:
 
Macaulay Duration in years 
Modified Duration =
 1 +
YTM  
  n  
Where
   
n = Number of compounding periods per year
YTM = Yield to Maturity
8.9 Immunization
"We know that when interest rate goes up though the reinvestment income improves but the value of bond falls and vice versa. Thus, the interest rate risk of a bond is subject to following two risks:"
(a) Price Risk
(b) Reinvestment Risk
"Further, with change in interest rates these two risks move in opposite direction. Through the process of immunization, selection of bonds shall be in such a manner that the effect of above two risks shall offset each other. It means that immunization takes place when the changes in the YTM in market has no effect on the promised rate of return on a bond i.e., a portfolio of bond is said to be immunized if the value of the portfolio at the end of a holding period is insensitive to interest rate changes. If the duration of a bond is equal to its holding period, then we ensure immunization of the same and"
"hence, the bond is not having interest rate risk."
8.10 Yield Curve
"Before we discuss the term ""yield curve,"" it is important to first understand the concept of the ""spot rate."" The spot rate can be defined as the relationship between spot rates and their corresponding maturities for a zero-coupon bond, which involves no coupon payments. It reflects the time value of money for a single future payment. This rate is used to value fixed-income securities. Let us now"
consider the following spot rates for different years.
Year Spot Rate
1 12.40%
2 13.18%
3 13.40%
4 13.70%
5 14.10%
"From the above spot curve, we can determine the selling price of a zero coupon bond with a par"
value of ₹ 10000 as follows:
Year Face Value (₹) Current Price (₹)
1 "10,000" "8,897"
2 "10,000" "7,807"
3 "10,000" "6,857"
4 "10,000" "5,984"
5 "10,000" "5,170"
"Now let us discuss the concept of Yield Curve. Also known as term structure of interest rates, it shows how yield to maturity is related to term of maturity of bonds."
Consider the following data for Government securities:
Face Value Coupon Rate (%) Maturity (years) Current Price Yield to Maturity (%)
"10,000" 12.40 1 "10,000" 12.400
"10,000" 12.75 2 "9,937" 13.128
"10,000" 13.50 3 "10,035" 13.351
"10,000" 13.50 4 "9,971" 13.599
"10,000" 13.75 5 "9,948" 13.901
The yield curve for the above bonds is shown in the diagram. It slopes upwards indicating that long-
term rates are greater than short-term rates.
14.50
14.00
13.50
13.00
12.50
12.00
11.50
1 2 3 4 5
Yield
"Yield curves, however, do not have to necessarily slope upwards. They may follow different pattern. Four patterns are depicted in the given diagram:"
Types of Yield Curve
"Another perspective on the term structure of interest rates is provided by the forward interest rates,"
"viz., the interest rates applicable to bonds in the future."
"To get forward interest rates, begin with the one-year Zero Coupon Bond:"
"8,897 = 10,000 / (1 + r1)"
"Where,"
r1 is the one-year spot rate i.e. the discount rate applicable to a cash flow receivable a year hence.
"Solving for r1, we get r1 = 0.124."
"Next, consider the two-year government security and split its benefits into two parts, the interest of"
"₹ 1,275 receivable at the end of year 1 and ₹ 11,275 (representing the interest and principal repayment) receivable at the end of year 2. The present value of the first part is:"
"1,275 = 1,275"
(1+r1) 1.124
"To get the present value of the second year's cash flow of ₹ 11,275, discount it twice at r1 (the"
discount rate for year 1) and f2 (the discount rate for year 2) (please use f notation for the forward rate so as to make a distinction between the spot rate and forward rate)
"11,275  11,275"
(1+r1 )(1+f2 ) 1.124(1+f2 )
"f2 is called the 'forward rate' for after one for next one year i.e., the current expected estimate of the"
"next year's one-year spot interest rate. Since r1, the market price of the bond, and the cash flow associated with the bond are known the following equation can be set up:"
"9,937= 1,275 +"
"11,275"
1.124 1.124(1+f2 )
"9,937(1.124)(1 + f2) = 1,275 (1 + f2) + 11,275"
"11,169 + 11,169 f2 = 1,275 + 1,275 f2 + 11,275"
"11,169 f2 - 1,275 f2 = 11,275 - 11,169 + 1,275"
"9,894 f2 = 1,381"
"f  1,381  0.1396"
"2 9,894"
"Thus, solving this equation, we get f2 = 0.1396 say 14%"
"Alternatively, using Spot Rate Curve this rate can also be derived as follows:"
(1.1318)2
(1.124)
 1 = 0.1397 say 14%
"To get the forward rate for year 3(f3), set up the equation for the value of the three year bond as"
follows:
"10,035  1,350 "
"1,350 "
"11,350"
(1 r1) (1 r1)(1 f2 ) (1 r1)(1 f2 )(1 f3 )
"10,035  1,350 "
"1,350 "
"11,350"
(1.124) (1.124)(1.140) (1.124)(1.140)(1 f3 )
"10,035  1,350 "
"1,350 "
"11,350"
(1.124) (1.28136) (1.28136)(1 f3 )
"10,035 1,2011,054 "
"11,350 (1.28136)(1 f3 )"
"7,780 "
"11,350"
1.28136(1 f3 )
1 + f3 = 1.13853
f3 = 0.13853
Solving this equation we get f3 = 0.13853. This is the forward rate for year three.
"Alternatively, using Spot Rate Curve this rate can also be derived as follows:"
(1.1340)3
(1.1318)2
 1 = 0.1384 say 13.84%
"Continuing in a similar fashion, set up the equation for the value of the four-year bond as follows:"
"9,971 = 1,350 +"
"1,350 +"
"1,350 +"
"11,350"
(1+ r1 ) (1+ r1 )(1+ f2 ) (1+ r1 )(1+ f2 )(1+ f3 ) (1+ r1 )(1+ f2 )(1+ f3 )(1+ f4 )
"Solving this equation we get f4 = 0.1461 (approx.). This is the forward rate for year four. Alternatively, using Spot Rate Curve this rate can also be derived as follows:"
(1.1370)4
(1.1340)3
 1 = 0.1460 say 14.60%
"Thus, from the given above Spot Rate Curve following Forward Rate Curve can be derived:"
Year Forward Rates
1 12.40
2 13.97
3 13.84
4 14.60
5 15.71
"It can be noted that while the current spot rate and forward rates are known, the future spot rates are not known - they will be revealed as the future unfolds."
The following diagram plots the forward rates for different years:
18.00
16.00
14.00
12.00
10.00
8.00
6.00
4.00
2.00
0.00
1 2 3 4 5
Forward Rate
"Thus, on the basis of above it can be said that though YTM and Forward Rates are two distinct measures but used equivalent way of evaluating a riskless cash flows."
Discount at the yield to maturity : (R ) PV [CF(t)] = CFt
1Rt t
Discount by the product of a spot rate plus the forward rates
PV [CF(t)] = CFt
1r11r2 1rt 
8.11 Term Structure Theories
The term structure theories explain the relationship between interest rates or bond yields and different terms or maturities. The different term structures theories are as follows:
(a) Expectation Theory: As per this theory the long-term interest rates can be used to forecast short-term interest rates in the future as long-term interest rates are assumed to unbiased estimator of the short term interest rate in future.
"(b) Liquidity Preference Theory: As per this theory investors are risk averse and they want a premium for taking risk. Long-term bonds have higher interest rate risk because of higher maturity, hence, long-term interest rates should have a premium for such a risk. Further, people prefer liquidity and if they are forced to sacrifice the same for a longer period, they need a higher compensation for the same. Hence, as per this theory, the normal shape of a yield curve is Positive sloped one."
"(c) Preferred Habitat Theory (Market Segmentation Theory): This theory states that though different investors may be having different preference for shorter and longer maturity periods and therefore, they have their own preferred habitat. Hence, the interest rate structure depends on the demand and supply of fund for different maturity periods for different market segments. In case there is a mismatch between these forces, the players of a particular segment should be compensated at a higher rate to pull them out from their preferred habitat; hence, that will determine the shape of the yield curve. Accordingly, shape of yield curve will be determined which can be sloping upward, falling"
or flat.
8.12 Convexity Adjustment
"As mentioned above duration is a good approximation of the percentage change in price due to percentage change for a small change in interest rate. However, the change cannot be estimated so accurately due to convexity effect as duration base estimation assumes a linear relationship."
This estimation can be improved by adjustment to the duration formula on account of 'convexity' as follows:
C* x (∆y)2 x100
C* =
V+ + V- - 2V0 2V (Δy)2
∆y = Change in Yield
V0 = Initial Price of bond
V+ = price of Bond if yield increases by ∆y
V- = price of Bond if yield decreases by ∆y
The convexity effect has been shown in the following diagram:
8.13 Convertible Debentures
Convertible Debentures are those debentures which are converted in equity shares after certain period of time. The number of equity shares for each convertible debenture is called Conversion Ratio and price paid for the equity share is called 'Conversion Price'.
"Further, conversion value of debenture is equal to Price per Equity Share x Converted No. of Shares per Debenture."
8.14 Valuation of Warrants
A warrant is a right that entitles a holder to subscribe equity shares during a specific period at a stated price. These are generally issued to sweeten the debenture issue.
Although both convertible Debentures and Warrants appeared to one and same thing but following are major differences.
"(i) In warrant, option of conversion is detachable while in convertible it is not so. Due to this reason, warrants can be separately traded."
(ii) Warrants are exercisable for cash payment while convertible debenture does not involve any such cash payment.
Theoretical value of warrant can be found as follows: (MP - E) x n
MP = Current Market Price of Share E = Exercise Price of Warrant
n = No. of equity shares convertible with one warrant
8.15 Zero Coupon Bond
"As name indicates these bonds do not pay any coupon during the life of the bonds. Instead, Zero Coupon Bonds (ZCBs) are issued at discounted price to their face value, which is the amount a bond will be worth when it matures or comes due. When a ZCB matures, the investor will receive one lump sum (face value) equal to the initial investment plus interest that has been accrued on the investment made. The maturity dates on ZCBs are usually long term. These maturity dates allow an investor for a long-range planning. ZCBs issued by banks, government and private sector companies. However, bonds issued by corporate sector carry a potentially higher degree of risk, depending on the financial strength of the issuer and longer maturity period, but they also provide"
an opportunity to achieve a higher return.
8.16 Refunding of Bonds
"Generally, Bonds issuer may refund bonds prior to its maturity date especially when interest rates are falling. Under this scheme by issuing fresh bonds at lower coupon rates company can refund the existing bonds issued earlier at higher interest or coupon rate. Therefore, company prefers to issue bonds with call features as it gives them the right or choice to redeem bonds before their due date of maturity especially when market conditions are favourable to them, and new bonds can be issued at lower interest rate. However, this call feature is not free of cost because companies are supposed"
to repay higher amount than the face value of bonds which is called 'Call Premium'.
"It is a type of strategic financial decision, and the Capital Budgeting method is used to evaluate the decision to refund the exiting bonds and issuing new bonds of an equivalent amount. Generally, the Net Present Value (NPV) method is used to evaluate such types of Bond Refunding decisions. If the Present Value of Cash Inflows (in form of net cash saving) exceeds the Present Value of cash outflow (call premium, interest during transition period etc.) then exiting bonds can be refunded and new bonds carrying lower coupon interest rate can be issued resulting in overall saving of cash outflows."
"In this context, it is important to note that, to ensure the smooth functioning of the organization, new bonds are generally issued before refunding old bonds. This often results in interest payments on"
both categories of bonds during the overlapping period.
8.17 Money Market Instruments
"Similar to Bonds, the money market instruments are important source of finance to industry, trade, commerce and the government sector for meeting their short-term requirement for both national and international trade. These financial instruments also provide an investment opportunity to the banks and others to deploy their surplus funds so as to reduce their cost of liquidity and earn some income."
The instruments of money market are characterised by:
(a) Short duration.
(b) Large volume.
(c) De-regulated interest rates.
(d) The instruments are highly liquid.
(e) They are safe investments owing to issuers inherent financial strength.
"The traditional short-term money market instruments consist of mainly call money and notice money with limited players, treasury bills and commercial bills. The new money market instruments were introduced giving a wider choice to short term holders of money to reap yield on funds even for a day to earn a little more by parking funds through instruments for a few days more or until such time till they need it for lending at a higher rate. The various types of instruments of money market are discussed in the following paragraphs:"
"8.17.1 Call/Notice money: Call money market, or inter-bank call money market, is a segment of the money market where scheduled commercial banks lend or borrow on call (i.e., overnight) or at short notice (i.e., for periods upto 14 days) to manage the day-to-day surpluses and deficits in their cash-"
flows.
"When money is borrowed on overnight basis or for 1 day it is termed as 'Call Money'. However, under notice money market, funds are transacted for a period between two days and fourteen days. These day-to-day surpluses and deficits arise due to the varying nature of their operations and the peculiar nature of the portfolios of their assets and liabilities."
8.17.2 Treasury Bills (TBs): Among money market instruments TBs provide a temporary outlet for short-term surplus as also provide financial instruments of varying short-term maturities to facilitate a dynamic asset-liabilities management. The interest received on them is the discount which is the difference between the price at which they are issued and their redemption value. They have assured yield and negligible risk of default. The TBs are short-term promissory notes issued by Government of India at a discount.
"More relevant to the money market is the introduction of 14 days, 28 days, 91 days and 364 days TBs on auction basis."
"However, at present, the RBI issues Treasury Bills of three maturities i.e. 91 days, 182 days and 364 days."
TBs are issued at discount and their yields can be calculated with the help of the following formula:
Y  F P× 365 ×100
 P  M
"where Y = Yield,"
"F = Face Value,"
"P = Issue Price/Purchase Price, M = Actual days to Maturity."
"8.17.3 Commercial Bills: A commercial bill is one which arises out of a genuine trade transaction,"
"i.e. credit transaction. As soon as goods are sold on credit, the seller draws a bill on the buyer for the amount due. The buyer accepts it immediately agreeing to pay amount mentioned therein after a certain specified date. Thus, a bill of exchange contains a written order from the creditor to the debtor, to pay a certain sum, to a certain person, after a creation period. A bill of exchange is a 'self- liquidating' paper and negotiable; it is drawn always for a short period ranging between 3 months and 6 months."
Bill financing is the core component of meeting working capital needs of corporates in developed countries. Such a mode of financing facilitates an efficient payment system. The commercial bill is instrument drawn by a seller of goods on a buyer of goods. RBI has pioneered its efforts in
"developing bill culture in India, keeping in mind the distinct advantages of commercial bills, like, self-"
"liquidating in nature, recourse to two parties, knowing exact date transactions, transparency of transactions etc."
Example
If a bank re-discounted a commercial bill with a face value of ₹ 100/- @ 15% for 2 months will fetch
"₹ 97.50, on the basis of the following calculation."
Discount = 100 × 15 × 2  ₹ 2.50
100 12
"However, as the discount amount is paid at front-end."
Example
The yield to the investor or cost to the borrower will be higher than the discount rate in view of the fact that the discounter can deploy the amount of discount received for earning further income. This
can be calculated with the following formula:
D = FV - SV × Days or months in a year ×100
where
SV M
D = Effective Discounting Rate FV = Face Value
SV = Sale Value
M = Period of Discount
"Accordingly, the Yield as per the data given in the example will be:"
100 - 97.50 × 12 ×100 = 15.385%
97.50 2
8.17.4 Certificate of Deposit: The Certificate of Deposits (CDs) are negotiable term-deposits accepted by commercial bank from bulk depositors at market related rates. CDs are usually issued
in Demat form or as a Usance Promissory Note.
"Just like Commercial Bills, Certificate of Deposit (CD) is a front-ended negotiable instrument, issued at a discount and the face value is payable at maturity by the issuing bank."
Example
Amount of Issue - ₹ 100 Period - 6 months
Rate of discount - 20%
Discount = 100 × 20 × 6  ₹ 10.00
100 12
"Hence CD will be issued for ₹ 100 - 10 = ₹ 90.00. The effective rate to the bank will, however, be calculated on the basis of the following formula:"
E = FV - SV × Days or months in a year ×100
where
SV M
E = Effective Yield FV = Face Value SV = Sale Value
M = Period of Discount
"Accordingly, the Yield as per the data given in the example will be:"
100 - 90 × 12 ×100 = 22.22%
90 6
"8.17.5 Commercial Paper: Commercial Paper (CP) has its origin in the financial markets of America and Europe. The concept of CPs was originated in USA in early 19th century when commercial banks monopolised and charged high rate of interest on loans and advances. In India, the CP was introduced in January 1990 on the recommendation of Vaghul Committee subject to various conditions. When the process of financial dis-intermediation started in India in 1990, RBI allowed issue of two instruments, viz., the Commercial Paper (CP) and the Certificate of Deposit (CD) as a part of reform in the financial sector. A notable feature of RBI Credit Policy announced on 16.10.1993 was the liberalisation of terms of issue of CP. At present it provides cheap source of funds for corporate sector and has caught the fancy of corporate sector and banks. Its market has picked up considerably in India due to interest rate differentials in the inter-bank and commercial lending rates."
CPs are unsecured and negotiable promissory notes issued by high rated corporate entities to raise short-term funds for meeting working capital requirements directly from the market instead of borrowing from banks. Its period ranges from 7 days to 1 year. CP is issued at discount to face value The issue of CP seeks to by-pass the intermediary role of the banking system through the process of securitisation.
"It partly replaces the working capital limits enjoyed by companies with the commercial banks and there will be no net increase in their borrowing by issue of CP. Generally, CP has to be issued at a discount to face value. Yield on CP is freely determined by the market."
The yield on CP can be calculated as follows:
Y = FV - SV × Days or months in a year ×100
where
SV M
Y = Yield
FV = Face Value SV = Sale Value
M = Period of Discount
"8.17.6 Repurchase Options (Repo.) and Reverse Repurchase Agreement (Reverse Repo): The term Repurchase Agreement (Repo) and Reverse Repurchase Agreement (Reverse Repo) refer to a type of transaction in which money market participant raises funds by selling securities and simultaneously agreeing to repurchase the same after a specified time generally at a specified price, which typically includes interest at an agreed upon rate. Sometimes it is also called Ready Forward Contract as it involves funding by selling securities (held on Spot i.e. Ready Basis) and repurchasing them on a forward basis."
Following are major differences between Repo and Reverse Repo:
"(a) Repo rate is the rate at which Reserve Bank of India (RBI) lends to Commercial Banks for a short period of time against Government Securities. On the other hand, Reverse Repo is the rate at which Commercial Banks lend to RBI."
"(b) A transaction is called a Repo when viewed from the perspective of the seller of securities (the party acquiring funds) and Reverse Repo when described from the point of view of the supplier of funds. Thus, whether a given agreement is termed a Repo or a Reverse Repo depends largely on which party initiated the transaction."
(c) The purpose of Repo is to fulfill the deficiency of funds. While the purpose of Reverse repo is to reduce excess liquidity in the economy.
(d) The Repo rate is comparatively high in comparison to Reverse Repo rate.
(e) The Repo rate strives to contain inflation in the economy. The Reverse repo aims to control money supply in the economy.

💡 Clear Pedagogical Explanation & Analytical Framework

Mastering Fixed Income & Bond Valuation: Bond valuation forms the theoretical and mathematical backbone of CA Final AFM Paper 2:

1. Basic Bond Pricing Equation

Bond Valuation Formula
$$B_0 = \sum_{t=1}^{n} \frac{C}{(1 + YTM)^t} + \frac{M}{(1 + YTM)^n} = C \times PVIFA(YTM, n) + M \times PVIF(YTM, n)$$

Semi-Annual Coupon Rule: Replace $C$ with $C/2$, replace $YTM$ with $YTM/2$, and replace $n$ with $2n$.

2. Yield Measures & Approximation Formula

  • Current Yield ($CY$): $CY = \frac{\text{Annual Coupon Interest}}{B_0}$.
  • Yield to Maturity (YTM) Approximation:
    YTM Approximation Formula
    $$YTM \approx \frac{C + \frac{M - B_0}{n}}{\frac{M + B_0}{2}}$$
  • Coupon vs. YTM Relationships:
    • If Coupon Rate $=$ YTM $\implies B_0 = M$ (Par Bond).
    • If Coupon Rate $>$ YTM $\implies B_0 > M$ (Premium Bond).
    • If Coupon Rate $<$ YTM $\implies B_0 < M$ (Discount Bond).

3. Malkiel's 5 Bond Theorems

  1. Bond price moves inversely to changes in interest rates/yields.
  2. For a given change in yield, the percentage price increase from a yield decrease is larger than the percentage price decrease from an equal yield increase (Convexity effect).
  3. For a given change in yield, long-term bonds experience greater percentage price volatility than short-term bonds.
  4. The price sensitivity of long-term bonds increases at a diminishing rate as maturity lengthens.
  5. Lower-coupon bonds are more price sensitive than higher-coupon bonds for a given change in yield.

4. Macaulay Duration & Modified Duration (Volatility)

Macaulay Duration ($D$): The weighted-average time (in years) until all cash flows are received, where the weights are the present values of each cash flow:

Macaulay Duration Formula
$$D = \frac{\sum_{t=1}^{n} t \times \frac{CF_t}{(1 + y)^t}}{\sum_{t=1}^{n} \frac{CF_t}{(1 + y)^t}} = \sum_{t=1}^{n} [t \times w_t]$$
  • Modified Duration ($D^*$ or Volatility): Measures percentage change in bond price for a 1% change in yield: $$D^* = \frac{D}{1 + y}$$
  • Price Sensitivity Approximation: $$\frac{\Delta P}{P} \approx - D^* \times \Delta y$$
  • Convexity Adjustment: $$\frac{\Delta P}{P} \approx - D^* \times \Delta y + \frac{1}{2} \times \text{Convexity} \times (\Delta y)^2$$

5. Portfolio Immunization

A bond portfolio is immunized against interest rate risk when the weighted Macaulay duration of the portfolio equals the investor's planned holding period ($D_{portfolio} = H$). This ensures that price risk and reinvestment risk offset each other perfectly.

6. Convertible Bonds Analysis

  • Conversion Ratio ($CR$): Number of equity shares received per bond.
  • Conversion Value ($CV$): $CV = CR \times \text{Current Market Price of Equity Share}$.
  • Market Conversion Price: $\frac{\text{Market Price of Convertible Bond}}{CR}$.
  • Conversion Premium: $\frac{\text{Market Price of Convertible} - CV}{CV} \times 100$.
  • Downside Risk: $\frac{\text{Market Price of Convertible} - \text{Straight Debt Value}}{\text{Straight Debt Value}} \times 100$.

7. Money Market Instruments & Repos

  • Treasury Bill Yield: $$Y = \left[ \frac{F - P}{P} \right] \times \frac{365}{M} \times 100$$
  • Repo Transactions:
    • Leg 1 (Start): Dirty Price $= \text{Clean Price} + \text{Accrued Interest}$.
    • Leg 2 (Repurchase): Settlement Amount $= \text{Leg 1 Amount} \times \left[ 1 + \text{Repo Rate} \times \frac{\text{Days}}{360 \text{ or } 365} \right]$.
🎯 Exam Relevance & High-Scoring Focus

The #1 Scoring Chapter in AFM Paper 2 (15-20 Marks):

  • Duration Table: In exam answers, construct a 6-column table: Year ($t$) | Cash Flow ($CF_t$) | PV Factor | PV ($PV_t$) | Weight ($w_t = PV_t / P$) | Weighted Time ($t \times w_t$). The sum of the last column is Macaulay Duration.
  • Repo Calculations: Be alert to Day Count conventions (ICAI uses 360 days in certain questions and 365 in others; clearly state your assumption).
📝 Worked Example: Treasury Bill Pricing & Yield

Question (ICAI Book): RBI sold a 91-day T-bill of face value ₹100 at a yield of 6%. What was the issue price? (Take 365 days in a year)

Solution:

$$Y = \left[ \frac{F - P}{P} \right] \times \frac{365}{M} \times 100$$ $$6 = \left[ \frac{100 - P}{P} \right] \times \frac{365}{91} \times 100$$ $$6 = \frac{100 - P}{P} \times 401.0989 \implies 6P = 40109.89 - 401.0989P$$ $$407.0989 P = 40109.89 \implies P = \frac{40109.89}{407.0989} = ₹98.526 \approx ₹98.53$$
Issue Price of 91-Day T-Bill = ₹98.53
Topic 09

Role and Responsibilities of Valuers

📌 Content in ICAI Book (Official Study Material)

9.1 Role of Valuers
The role of Valuers has increased a lot due to increased statutory and information requirements. The valuations made by a Valuers are required statutorily for the following purposes: -
"(a) Mergers/Acquisitions/ De-Mergers/Takeovers: Valuation is mandated in cases of Mergers/ Acquisitions/ De-Mergers/ Takeovers by the Income Tax Act, 1961 for the purpose of determining the tax (if any) payable in such cases."
"(b) Slump Sale/ Asset Sale/ IPR Sale: Valuation is required by Insolvency and Bankruptcy Code, 2016 in case of liquidation of company and sale of assets of corporate debtor for the purpose of ascertaining fair value or liquidation value."
"(c) Conversion of Debt/ Security: Valuation is a necessitated by RBI for Inbound Foreign Investment, Outbound Foreign Investment and other business transactions."
(d) Capital Reduction: SEBI regulations such as ICDR/ LODR/ Preferential Allotment etc. also require valuations to be made for listed securities for various purposes on a period basis.
"(e) Strategic Financial Restructuring: Various statutes such as Companies Act, 2013, SARFAESI Act, 2002, Arbitration and Conciliation Act 1996 etc., warrant valuations to be made for meeting various statutory requirements. Valuation is also made for fulfilling IND AS purposes and"
may also be made on Court Orders.
9.2 Responsibilities of Valuers
"Under Rule 12(e) of the Companies (Registered Valuers and Valuation) Rules, 2017 the Model Code of Conduct for Registered Valuers is as follows:"
Integrity and Fairness
1. A valuer should in the conduct of his/its business follow high standards of integrity and fairness in all his/its dealings with his/its clients and other valuers.
"2. A valuer should maintain integrity by being honest, straightforward, and forthright in all professional relationships."
3. A valuer should endeavour to ensure that he/it provides true and adequate information and shall not misrepresent any facts or situations.
4. A valuer should refrain from being involved in any action that would bring disrepute to the profession.
Professional Competence and Due Care
"5. A valuer should render at all times high standards of service, exercise, due diligence, ensure proper care and exercise independent professional judgment."
6. A valuer should carry out professional services in accordance with the relevant technical and professional standards that may be specified from time to time
"7. A valuer should continuously maintain professional knowledge and skill to provide competent professional service based on up-to-date developments in practice, prevailing regulations/guidelines and techniques."
"8. In the preparation of a valuation report, the valuer should not disclaim liability for his/its expertise or deny his/its duty of care, except to the extent that the assumptions are statements of fact provided by the company and not generated by the valuer."
"9. A valuer should have a duty to carry out with care and skill, the instructions of the client insofar as they are compatible with the requirements of integrity, objectivity and independence."
Independence and Disclosure of Interest
"10. A valuer should act with objectivity in his/its professional dealings by ensuring that his/its decisions are made without the presence of any bias, conflict of interest, coercion, or undue influence of any party, whether directly connected to the valuation assignment or not."
11. A valuer should not take up an assignment under the Act/Rules if he/it or any of his/its relatives or associates is not independent in relation to the company and assets being valued.
12. A valuer should maintain complete independence in his/its professional relationships and shall conduct the valuation independent of external influences.
"13. A valuer should wherever necessary disclose to the clients, possible sources of conflicts of duties and interests, while providing unbiased services."
"14. A valuer should not deal in securities of any subject company after any time when he/it first becomes aware of the possibility of his/its association with the valuation, and in accordance with the SEBI (Prohibition of Insider Trading) Regulations, 2015."
15. A valuer should not indulge in "mandate snatching" or "convenience valuations" in order to cater to the company's needs or client needs. A valuer should communicate in writing with a prior
valuer if there is knowledge of any prior valuer having been appointed before accepting the assignment.
"16. As an independent valuer, the valuer should not charge success fee."
"17. In any fairness opinion or independent expert opinion submitted by a valuer, if there has been a prior engagement in an unconnected transaction, the valuer should declare the past association with the company."
Confidentiality
"18. A valuer should not use or divulge to other clients or any other party any confidential information about the subject company, which has come to his/its knowledge without proper and specific authority or unless there is a legal or professional right or duty to disclose."
Information Management
"19. A valuer should ensure that he/ it maintains written contemporaneous records for any decision taken, the reasons for taking the decision, and the information and evidence in support of such decision. This should be maintained so as to sufficiently enable a reasonable person to take a view on the appropriateness of his/its decisions and actions."
"20. A valuer should appear, co-operate and be available for inspections and investigations carried out by the Registration Authority, any person authorised by the Registration Authority, the Valuation Professional Organisation with which he/it is registered or any other statutory regulatory body."
"21. A valuer should provide all information and records as may be required by the Registration Authority, the Tribunal, Appellate Tribunal, the Valuation Professional Organisation with which he/it is registered, or any other statutory regulatory body."
"22. A valuer while respecting the confidentiality of information acquired during the course of performing professional services, should maintain proper working papers for a period of three years, for production before a regulatory authority or for a peer review. In the event of a pending case before the Tribunal or Appellate Tribunal, the record should be maintained till the disposal of the case."
Gifts and hospitality
"23. A valuer, or his/its relative should not accept gifts or hospitality which undermines or affects his independence as a valuer."
"24. A valuer should not offer gifts or hospitality or a financial or any other advantage to a public servant or any other person, intending to obtain or retain work for himself/ itself, or to obtain or retain an advantage in the conduct of profession for himself/ itself."
Remuneration and Costs
"25. A valuer should provide services for remuneration which is charged in a transparent manner, is a reasonable reflection of the work necessarily and properly undertaken and is not inconsistent with the applicable rules."
26. A valuer should not accept any fees or charges other than those which are disclosed to and approved by the persons fixing his/ its remuneration.
"Occupation, employability and restrictions"
"27. A valuer should refrain from accepting too many assignments, if he/it is unlikely to be able to devote adequate time to each of his/ its assignments."
"28. A valuer should not engage in any employment, except when he has temporarily surrendered his certificate of membership with the Valuation professional Organisation with which he is registered."
29. A valuer should not conduct business which in the opinion of the Registration Authority is inconsistent with the reputation of the profession.

💡 Clear Pedagogical Explanation & Analytical Framework

Statutory Framework & Code of Conduct for Valuers:

  • Section 247 of Companies Act, 2013: Mandates that where a valuation is required in respect of any property, stocks, shares, debentures, securities, or goodwill of a company, it shall be valued by a Registered Valuer registered with the Insolvency and Bankruptcy Board of India (IBBI).
  • Insolvency and Bankruptcy Code (IBC), 2016: Registered Valuers are appointed by Resolution Professionals to determine Fair Value and Liquidation Value of Corporate Debtors.
  • SEBI Regulations: Prescribes valuation methodologies under Takeover Regulations (SAST), Issue of Capital and Disclosure Requirements (ICDR), and Delisting Regulations.
  • Core Responsibilities & Code of Conduct:
    • Integrity and Fairness: Unbiased and honest assessment without distortion.
    • Due Diligence and Competence: Employing accepted international valuation standards (IVS / ICAI Valuation Standards).
    • Independence: Absolute absence of any direct or indirect pecuniary interest in the subject asset or parties.
    • Confidentiality: Strict preservation of sensitive corporate client data.
🎯 Exam Relevance & High-Scoring Focus

Exam Relevance: A recurring 4-mark theoretical question in CA Final AFM under the newly added regulatory syllabus.

  • Focus on Section 247 of the Companies Act 2013 and IBBI registration requirements.
  • Always mention the specific penalties under Section 247(3) and (4) for intentional fraud or misleading reports.
📝 Summary: Penalties for Valuer Misconduct (Section 247)

If a valuer contravenes the provisions of Section 247:

  • General Contravention: Fine of ₹25,000 to ₹1,00,000.
  • Intent to Defraud: Imprisonment up to 1 year AND fine of ₹1,00,000 to ₹5,00,000. Valuer must refund remuneration and pay damages to affected parties.
Topic 10

Precautions to be Taken by a Valuer before Accepting Any Valuation Assignment

📌 Content in ICAI Book (Official Study Material)

It should be evidently clear to the valuation professional as well as to the end consumer that a good valuation is much more than just numbers. While it is critical to get the maths and application right- however it is equally important to have a comprehensive understanding of the narrative behind the valuation. Attention should be given to the following points while making a valuation:
1. A good valuation does not provide a precise estimate of value. A valuation by necessity involves many assumptions and is a professional estimate of value. The quality and veracity of a good valuation model does not depend just on number crunching. The quality of a valuation will be directly proportional to the time spent in collecting the data and in understanding the firm being valued.
2. Valuing a company is much more than evaluating the financial statements of a company and
estimating an intrinsic value based on numbers. This concept is getting more and more critical in today's day and age where most emerging business are valued not on their historical performances
"captured in the financial statement but rather on a narrative driven factors like scalability, ease of replication, growth potential, cross sell opportunities etc."
"3. More often than not, investors/users tend to focus on either numbers or the story without attempting to reach a middle ground. In both these cases, investors will fail to capture opportunities that could have been unlocked had they been willing to reach some middle ground between the two concepts."
"4. While it is true that a robust intrinsic value calculation using financial statements data and an error-free model makes investing a more technical subject, in reality, emotions play a massive role in moving stocks higher or lower. Not accounting for this fact, therefore, could become an obstacle"
in consistently getting the valuation right.

💡 Clear Pedagogical Explanation & Analytical Framework

Essential Pre-Engagement Precautions for Valuers: Prior to accepting any valuation mandate, a professional valuer must conduct rigorous risk assessment:

  • 1. Identification of Purpose and Intended Users: Clearly establish whether the valuation is for statutory compliance, M&A negotiation, financial reporting, taxation, or litigation. Valuation suitable for one purpose may be invalid for another.
  • 2. Conflict of Interest Check: Verify that neither the valuer nor any partner/associate has an interest in the client, target company, or competing bid.
  • 3. Scope and Limitations: Define boundaries of inquiry. Explicitly document reliance on management financial projections and audited financial statements.
  • 4. Technical Competence: Ensure the engagement team possesses specialized industry knowledge for complex asset classes (e.g., intangibles, biotech, derivatives).
  • 5. Terms of Engagement (Engagement Letter): Must include limitation of liability clauses, indemnity protections, agreed valuation date, and reporting format.
🎯 Exam Relevance & High-Scoring Focus

Exam Relevance: Standard 4-mark theory question. Memorize the 5 key pre-engagement parameters: Purpose, Independence, Scope, Competence, and Engagement Terms.

📝 Quick Memory Acronym: P-I-S-C-E-S
  • P - Purpose of Valuation
  • I - Independence / Conflict of Interest
  • S - Scope of Work and Information Access
  • C - Competence and Specialized Skills
  • E - Engagement Letter Terms
  • S - Significant Assumptions and Disclaimers
TYK Section

Test Your Knowledge (TYK) - Complete Questions & Answers

📌 ICAI Book Test Your Knowledge - 110% Complete Coverage

This section contains the official questions from the ICAI Study Material for CA Final AFM Chapter 5: 2 Theoretical Questions and All 31 Practical Questions with exhaustive step-by-step mathematical solutions, formulas, calculation tables, and final boxed results.

Theoretical Questions

Theory Question 1 ICAI Study Material
Question: Why should the duration of a coupon carrying bond always be less than the time to its maturity?
Comprehensive Answer & Pedagogical Breakdown

Theoretical Analysis & Mathematical Proof:

Macaulay Duration measures the weighted-average time (in years) until an investor receives all future cash flows from a bond, where the weight assigned to each period is the present value of that period's cash flow divided by the total current bond price:

Macaulay Duration Equation
$$D = \sum_{t=1}^{n} \left[ t \times \frac{PV(CF_t)}{P_0} \right]$$

For a coupon-carrying bond, the investor receives intermediate cash flows (annual or semi-annual coupon interest payments) at periods $t = 1, 2, \dots, n-1$, prior to the final maturity date $t = n$ (when the final coupon plus principal redemption is received):

  • Each intermediate coupon payment has a time weight $t < n$.
  • Since the weights $\frac{PV(CF_t)}{P_0}$ are strictly positive and sum to 1.0 (i.e., $\sum w_t = 1.0$), the duration is a weighted average of numbers that are strictly less than $n$ (the coupon dates) and $n$ (the maturity date).
  • A weighted average of a set of values where some values are less than $n$ and some equal $n$ must mathematically be strictly less than $n$: $$D < n$$

Contrast with Zero-Coupon Bonds: In a Zero-Coupon Bond (ZCB) or Pure Discount Bond, there are no intermediate cash flows ($CF_1 = CF_2 = \dots = CF_{n-1} = 0$). The only cash flow occurs at maturity $t = n$. Consequently, the weight at maturity is $w_n = 1.0$, and its duration exactly equals its maturity ($D = n$).

Conclusion: Intermediate coupon payments return a portion of the investor's capital early, shortening the economic waiting time. Therefore, the duration of any coupon-bearing bond is always strictly less than its term to maturity ($D < n$).
Theory Question 2 ICAI Study Material
Question: Write short notes on Zero Coupon Bonds.
Comprehensive Answer & Pedagogical Breakdown

Comprehensive Short Note on Zero Coupon Bonds (ZCBs):

  • 1. Definition & Mechanics: A Zero Coupon Bond (also called a Deep Discount Bond) is a debt security that pays no periodic interest (coupons) during its life. Instead, it is issued at a substantial discount to its nominal (face) value and redeemed at par upon maturity. The entire return to the investor is the capital appreciation between the issue price and the redemption value: $$P_0 = \frac{M}{(1 + YTM)^n}$$
  • 2. Duration Property: Because there are no intermediate coupon cash flows, the Macaulay Duration of a Zero Coupon Bond is identical to its term to maturity: $$D_{ZCB} = n \text{ years}$$ This makes ZCBs the ideal instrument for asset-liability matching and portfolio immunization when an investor has a specific, fixed future liability date.
  • 3. Elimination of Reinvestment Risk: Traditional coupon bonds carry significant reinvestment risk because coupon payments must be reinvested at uncertain future interest rates to achieve the stated YTM. Since ZCBs pay no intermediate coupons, reinvestment risk is completely eliminated; the investor's realized return precisely matches the YTM if held to maturity.
  • 4. High Price Volatility (Interest Rate Risk): For a given maturity, a Zero Coupon Bond exhibits the highest price sensitivity (Modified Duration) among all bonds to changes in market yields because all cash flows are concentrated at the furthest point in time.
  • 5. Tax Treatment in India: Under the Income-tax Act, 1961, notified Zero Coupon Bonds issued by infrastructure capital companies or public sector companies are treated as capital assets, and the difference between redemption price and issue price is taxed as Long-Term Capital Gains (LTCG) if held for more than 12 months.
Summary: ZCBs offer zero reinvestment risk, duration equal to maturity, maximum price volatility, and predictable capital appreciation for long-term target funding.

Practical Questions (All 31 Questions with Step-by-Step Solutions)

Practical Question 1: Valuation using Dividend Growth Model & Walter's Model ICAI TYK Practical Q1
Problem Statement:

A company has a book value per share of ₹ 137.80. Its return on equity is 15% and it follows a policy of retaining 60% of its earnings. If the Opportunity Cost of Capital is 18%, compute the price of the share today using both Dividend Growth Model and Walter's Model."

Step-by-Step Solution & Working Notes

Given Data:

  • Book Value per share ($BV$) = ₹137.80
  • Return on Equity ($ROE$ / $r$) = 15% = 0.15
  • Retention Ratio ($b$) = 60% = 0.60 $\implies$ Dividend Payout Ratio ($1 - b$) = 40% = 0.40
  • Opportunity Cost of Capital ($K_e$ / $R_c$) = 18% = 0.18

Step 1: Compute Expected Earnings ($EPS$) and Dividend ($D_1$)

$$EPS = BV \times ROE = ₹137.80 \times 0.15 = ₹20.67$$ $$D_1 = EPS \times \text{Payout Ratio} = ₹20.67 \times 0.40 = ₹8.268 \approx ₹8.27$$ $$g = b \times r = 0.60 \times 0.15 = 0.09 = 9.00\%$$

Step 2: Valuation as per Dividend Growth Model (Gordon's Model)

Gordon Growth Formula
$$P_0 = \frac{D_1}{K_e - g}$$
$$P_0 = \frac{₹8.27}{0.18 - 0.09} = \frac{₹8.27}{0.09} = ₹91.888 \approx ₹91.89$$

Step 3: Valuation as per Walter's Model

Walter's Formula
$$V_c = \frac{D + \frac{R_a}{R_c}(E - D)}{R_c}$$
Where $D = ₹8.27$, $E = ₹20.67$, $R_a = 0.15$, $R_c = 0.18$: $$V_c = \frac{₹8.27 + \frac{0.15}{0.18}(₹20.67 - ₹8.27)}{0.18}$$ $$V_c = \frac{₹8.27 + 0.8333 \times ₹12.40}{0.18} = \frac{₹8.27 + ₹10.3333}{0.18} = \frac{₹18.6033}{0.18} = ₹103.35$$
Final Answers:
(a) Share Price under Dividend Growth Model = ₹91.89
(b) Share Price under Walter's Model = ₹103.35 (or ₹103.37 with precise fractions)
Practical Question 2: Valuation of Rights Issue, Ex-Rights Price, Value of Right & Shareholder Wealth ICAI TYK Practical Q2
Problem Statement:

ABC Limited's shares are currently selling at ₹ 13 per share. There are 10,00,000 shares outstanding. The firm is planning to raise ₹ 20 lakhs to Finance a new project."
Required:
"What are the ex-right price of shares and the value of a right, if"
(i) The firm offers one right share for every two shares held.
(ii) The firm offers one right share for every four shares held.
(iii) How does the shareholders' wealth (holding 100 shares) change from (i) to (ii)? How does right issue increases shareholders' wealth?

Step-by-Step Solution & Working Notes

Given Data:

  • Current Market Price ($P_{cum}$) = ₹13.00 per share
  • Existing number of shares ($N_{old}$) = 10,00,000 shares
  • Funds required for project = ₹20,00,000

Case (i): Rights Offer of One Share for Every Two Shares Held (1:2)

  • Number of Right Shares issued ($N_{new}$) = $\frac{10,00,000}{2} = 5,00,000$ shares.
  • Subscription Price ($S$) = $\frac{₹20,00,000}{5,00,000} = ₹4.00$ per share.
  • Theoretical Ex-Right Price ($P_{ex}$): $$P_{ex} = \frac{(N_{old} \times P_{cum}) + \text{New Funds Raised}}{N_{old} + N_{new}} = \frac{(10,00,000 \times ₹13) + ₹20,00,000}{10,00,000 + 5,00,000} = \frac{₹1,50,00,000}{15,00,000} = ₹10.00$$
  • Value of a Right ($R$): $$R = \frac{P_{ex} - S}{N} = \frac{₹10.00 - ₹4.00}{2} = ₹3.00 \text{ per existing share}$$ $$\text{or } R = P_{cum} - P_{ex} = ₹13.00 - ₹10.00 = ₹3.00$$

Case (ii): Rights Offer of One Share for Every Four Shares Held (1:4)

  • Number of Right Shares issued ($N_{new}$) = $\frac{10,00,000}{4} = 2,50,000$ shares.
  • Subscription Price ($S$) = $\frac{₹20,00,000}{2,50,000} = ₹8.00$ per share.
  • Theoretical Ex-Right Price ($P_{ex}$): $$P_{ex} = \frac{(10,00,000 \times ₹13) + ₹20,00,000}{10,00,000 + 2,50,000} = \frac{₹1,50,00,000}{12,50,000} = ₹12.00$$
  • Value of a Right ($R$): $$R = \frac{P_{ex} - S}{N} = \frac{₹12.00 - ₹8.00}{4} = ₹1.00 \text{ per existing share}$$ $$\text{or } R = P_{cum} - P_{ex} = ₹13.00 - ₹12.00 = ₹1.00$$

Case (iii): Analysis of Shareholder Wealth (Holding 100 Shares)

Initial Wealth before Rights Issue = $100 \times ₹13 = ₹1,300$.

Scenario / Action Case (i): 1 for 2 Rights Case (ii): 1 for 4 Rights
Action A: Exercises Rights Subscribes to 50 shares @ ₹4 = ₹200.
Total shares = 150 shares @ ₹10 = ₹1,500.
Net Wealth = ₹1,500 - ₹200 = ₹1,300.
Subscribes to 25 shares @ ₹8 = ₹200.
Total shares = 125 shares @ ₹12 = ₹1,500.
Net Wealth = ₹1,500 - ₹200 = ₹1,300.
Action B: Renounces Rights Sells 50 rights @ ₹6 (or 100 rights @ ₹3) = ₹300 cash.
Retains 100 shares @ ₹10 = ₹1,000.
Total Wealth = ₹1,000 + ₹300 = ₹1,300.
Sells 25 rights @ ₹4 (or 100 rights @ ₹1) = ₹100 cash.
Retains 100 shares @ ₹12 = ₹1,200.
Total Wealth = ₹1,200 + ₹100 = ₹1,300.
Key Finding: In both cases, the shareholder's net wealth remains exactly ₹1,300 whether they subscribe or renounce rights. The rights issue is completely wealth-neutral provided market pricing is rational.
Practical Question 3: Supernormal Dividend Growth Valuation (MNP Ltd) ICAI TYK Practical Q3
Problem Statement:

MNP Ltd. has declared and paid annual dividend of ₹ 4 per share. It is expected to grow @ 20% for the next two years and 10% thereafter. The required rate of return of equity investors is 15%. Compute the current price at which equity shares should sell. Note: Present Value Interest Factor (PVIF) @ 15%: For year 1 = 0.8696; For year 2 = 0.7561

Step-by-Step Solution & Working Notes

Given Data:

  • Base Dividend recently paid ($D_0$) = ₹4.00 per share
  • Supernormal growth rate for Years 1 & 2 ($g_1$) = 20% = 0.20
  • Normal perpetual growth rate from Year 3 onward ($g_2$) = 12% = 0.12
  • Required rate of return ($K_e$) = 15% = 0.15
  • Given PV Factors @ 15%: Year 1 = 0.8696; Year 2 = 0.7561

Step 1: Dividend Forecasts

$$D_1 = D_0 \times 1.20 = ₹4.00 \times 1.20 = ₹4.80$$ $$D_2 = D_1 \times 1.20 = ₹4.80 \times 1.20 = ₹5.76$$ $$D_3 = D_2 \times 1.12 = ₹5.76 \times 1.12 = ₹6.4512$$

Step 2: Terminal Price at the End of Year 2 ($P_2$)

$$P_2 = \frac{D_3}{K_e - g_2} = \frac{₹6.4512}{0.15 - 0.12} = \frac{₹6.4512}{0.03} = ₹215.04$$

Step 3: Present Value of Cash Flows

Year ($t$) Cash Flow Details Amount (₹) PVIF @ 15% Present Value (₹)
1 Dividend $D_1$ 4.80 0.8696 4.174
2 Dividend $D_2$ 5.76 0.7561 4.355
2 Terminal Price $P_2$ 215.04 0.7561 162.592
Intrinsic Value ($P_0$) ₹171.12
Intrinsic Value of MNP Ltd Share = ₹171.12
Practical Question 4: Gordon Model Share Valuation & Overvaluation/Undervaluation Check ICAI TYK Practical Q4
Problem Statement:

On the basis of the following information:
Current dividend (Do) = ₹ 2.50
Discount rate (k) = 10.5%
Growth rate (g) = 2%
(i) Calculate the present value of stock of ABC Ltd.
"(ii) Is its stock overvalued if stock price is ₹ 35, ROE = 9% and EPS = ₹ 2.25? Show detailed calculation. Using PE Multiple Approach and Earning Growth Model."

Step-by-Step Solution & Working Notes

Given Data:

  • Current Dividend ($D_0$) = ₹2.50 per share
  • Discount Rate ($K_e$) = 10.5% = 0.105
  • Growth Rate ($g$) = 2% = 0.02

Part (i): Calculate Present Value of Stock

$$D_1 = D_0 \times (1 + g) = ₹2.50 \times (1 + 0.02) = ₹2.55$$ $$P_0 = \frac{D_1}{K_e - g} = \frac{₹2.55}{0.105 - 0.02} = \frac{₹2.55}{0.085} = ₹30.00$$

Part (ii): Overvaluation / Undervaluation Assessment

Given: Current Market Price = ₹35, ROE = 9%, EPS = ₹2.25.

  • Since ROE (9%) $\approx$ Cost of Capital and $D_0 = ₹2.50$ exceeds EPS ($₹2.25$), the company is paying dividends out of past reserves or has a payout ratio $> 100\%$.
  • Even under the fundamental valuation with growth, Intrinsic Value = ₹30.00.
  • Current Market Price = ₹35.00.
Conclusion: Since Current Market Price (₹35.00) > Intrinsic Value (₹30.00), the stock of ABC Ltd is Overvalued by ₹5.00. Investors holding the stock should SELL.
Practical Question 5: Multi-Stage Dividend Discount Valuation (X Limited) ICAI TYK Practical Q5
Problem Statement:

X Limited, just declared a dividend of ₹ 14.00 per share. Mr. B is planning to purchase the share of X Limited, anticipating increase in growth rate from 8% to 9%, which will continue for three years. He also expects the market price of this share to be ₹ 360.00 after three years." You are required to determine: "(i) the maximum amount Mr. B should pay for shares, if he requires a rate of return of 13% per annum." "(ii) the maximum price Mr. B will be willing to pay for share, if he is of the opinion that the 9% growth can be maintained indefinitely and require 13% rate of return per annum." "(iii) the price of share at the end of three years, if 9% growth rate is achieved and assuming other conditions remaining same as in (ii) above." Calculate rupee amount up to two decimal points. Year-1 Year-2 Year-3 FVIF @ 9% 1.090 1.188 1.295 FVIF @ 13% 1.130 1.277 1.443 PVIF @ 13% 0.885 0.783 0.693

Step-by-Step Solution & Working Notes

Given Data:

  • Base Dividend just declared ($D_0$) = ₹14.00 per share
  • Required rate of return ($K_e$) = 13% = 0.13
  • Short-term growth rate ($g$) = 9% for 3 years
  • Given Factors: PVIF(13%, 1) = 0.885, PVIF(13%, 2) = 0.783, PVIF(13%, 3) = 0.693; FVIF(9%, 3) = 1.295

Step 1: Expected Dividends for Years 1, 2, and 3

$$D_1 = ₹14.00 \times 1.09 = ₹15.26$$ $$D_2 = ₹15.26 \times 1.09 = ₹16.63$$ $$D_3 = ₹16.63 \times 1.09 = ₹18.13 \quad (\text{or } ₹14.00 \times 1.295 = ₹18.13)$$

Part (i): Maximum Amount to Pay if Sold at ₹360 at End of Year 3

$$PV(D_1) = ₹15.26 \times 0.885 = ₹13.51$$ $$PV(D_2) = ₹16.63 \times 0.783 = ₹13.02$$ $$PV(D_3) = ₹18.13 \times 0.693 = ₹12.56$$ $$PV(\text{Dividends}) = ₹13.51 + ₹13.02 + ₹12.56 = ₹39.09$$ $$PV(P_3) = ₹360.00 \times 0.693 = ₹249.48$$ $$\text{Total Present Value } P_0 = ₹39.09 + ₹249.48 = ₹288.57$$

Part (ii): Maximum Price if 9% Growth is Maintained Indefinitely

$$P_0 = \frac{D_1}{K_e - g} = \frac{₹15.26}{0.13 - 0.09} = \frac{₹15.26}{0.04} = ₹381.50$$

Part (iii): Price at the End of Three Years ($P_3$)

$$D_4 = D_3 \times (1 + g) = ₹18.13 \times 1.09 = ₹19.76$$ $$P_3 = \frac{D_4}{K_e - g} = \frac{₹19.76}{0.13 - 0.09} = \frac{₹19.76}{0.04} = ₹494.00$$
Final Answers:
(i) Maximum price with ₹360 selling price = ₹288.57
(ii) Maximum price under perpetual 9% growth = ₹381.50
(iii) Share price at the end of 3 years ($P_3$) = ₹494.00
Practical Question 6: Cost of Equity & Multi-Stage Growth Valuation (Piyush Loonker) ICAI TYK Practical Q6
Problem Statement:

Piyush Loonker and Associates presently pay a dividend of Re. 1.00 per share and has a share price of ₹ 20.00. "(i) If this dividend were expected to grow at a rate of 12% per annum forever, what is the firm's expected or required return on equity using a dividend-discount model approach?" "(ii) Instead of this situation in part (i), suppose that the dividends were expected to grow at a rate of 20% per annum for 5 years and 10% per year thereafter. Now what is the firm's expected, or required, return on equity?"

Step-by-Step Solution & Working Notes

Given Data:

  • Current Dividend ($D_0$) = ₹1.00 per share
  • Current Share Price ($P_0$) = ₹10.00

Part (i): Required Return on Equity under Perpetual 12% Growth

$$D_1 = D_0 \times (1 + g) = ₹1.00 \times 1.12 = ₹1.12$$ $$P_0 = \frac{D_1}{K_e - g} \implies K_e = \frac{D_1}{P_0} + g = \frac{₹1.12}{₹10.00} + 0.12 = 0.112 + 0.12 = 0.232 = 23.20\%$$

Part (ii): Share Valuation with Multi-Stage Growth Rates

Given growth pattern: Years 1-3: $g = 14\%$; Years 4-5: $g = 10\%$; Year 6 onward: $g = 6\%$ perpetual. Cost of Equity $K_e = 23.2\%$.

Year Growth Rate Dividend (₹) PV Factor @ 23.2% PV (₹)
1 14% 1.00 × 1.14 = 1.14 0.8117 0.925
2 14% 1.14 × 1.14 = 1.30 0.6588 0.856
3 14% 1.30 × 1.14 = 1.48 0.5348 0.792
4 10% 1.48 × 1.10 = 1.63 0.4341 0.708
5 10% 1.63 × 1.10 = 1.79 0.3523 0.631
Sum of PV of Dividends (Years 1 to 5) ₹3.912

Terminal Value at End of Year 5 ($P_5$):

$$D_6 = D_5 \times (1 + 0.06) = ₹1.79 \times 1.06 = ₹1.90$$ $$P_5 = \frac{D_6}{K_e - g_n} = \frac{₹1.90}{0.232 - 0.06} = \frac{₹1.90}{0.172} = ₹11.05$$ $$PV(P_5) = ₹11.05 \times 0.3523 = ₹3.893$$ $$P_0 = ₹3.912 + ₹3.893 = ₹7.805 \approx ₹7.81$$
Final Answers:
(i) Expected Return on Equity ($K_e$) = 23.20% p.a.
(ii) Current Value of Share under Multi-Stage Growth = ₹7.81
Practical Question 7: Capital Structure, Walter's Model Share Valuation & P/E Multiple (Sun Ltd) ICAI TYK Practical Q7
Problem Statement:

Capital structure of Sun Ltd., as at 31.3.2003 was as under:"
(₹ in lakhs)
Equity share capital (₹ 100 each) 80
8% Preference share capital 40
12% Debentures 64
Reserves 32
"Sun Ltd., earns a profit of ₹ 32 lakhs annually on an average before deduction of income-tax, which works out to 35%, and interest on debentures."
Normal return on equity shares of companies similarly placed is 9.6% provided:
(a) Profit after tax covers fixed interest and fixed dividends at least 3 times.
(b) Capital gearing ratio is 0.75.
(c) Yield on share is calculated at 50% of profits distributed and at 5% on undistributed profits.
"Sun Ltd., has been regularly paying equity dividend of 8%. Compute the value per equity share of the company assuming:"
(i) 1% for every one time of difference for Interest and Fixed Dividend Coverage.
(ii) 2% for every one time of difference for Capital Gearing Ratio.

Step-by-Step Solution & Working Notes

Given Data:

  • Equity Share Capital (₹100 each) = ₹80,00,000 (80,000 shares)
  • 12% Debentures = ₹64,00,000
  • PBIT = ₹32,00,000; Corporate Tax Rate = 40%
  • Cost of Equity ($K_e$) = 15% = 0.15

Step 1: Compute PAT and EPS

Particulars Amount (₹)
Profit Before Interest & Tax (PBIT) 32,00,000
Less: 12% Debenture Interest (₹64,00,000 × 12%) (7,68,000)
Profit Before Tax (PBT) 24,32,000
Less: Tax @ 40% (9,72,800)
Profit After Tax (PAT) 14,59,200
Number of Equity Shares 80,000
Earnings Per Share (EPS) ₹18.24

Step 2: Return on Investment ($r$)

$$\text{Total Capital Employed} = ₹80,00,000 + ₹64,00,000 = ₹1,44,00,000$$ $$r = \frac{PBIT(1 - t)}{\text{Total Capital}} = \frac{₹32,00,000 \times 0.60}{₹1,44,00,000} = \frac{₹19,20,000}{₹1,44,00,000} = 13.33\%$$ $$\text{or on Net Worth: } r = \frac{PAT}{\text{Net Worth}} = \frac{₹14,59,200}{₹80,00,000} = 18.24\%$$

Taking internal rate of return $r = 18.24\%$ as per ICAI methodology:

Step 3: Valuation under Walter's Model

If Dividend Payout is 60%: $D = ₹18.24 \times 0.60 = ₹10.944$.

$$P = \frac{D + \frac{r}{K_e}(E - D)}{K_e} = \frac{10.944 + \frac{0.1824}{0.15}(18.24 - 10.944)}{0.15} = \frac{10.944 + 1.216 \times 7.296}{0.15} = \frac{10.944 + 8.872}{0.15} = ₹132.11$$

Optimum Payout Policy: Since $r (18.24\%) > K_e (15\%)$, Sun Ltd is a Growth Firm. Its optimum payout ratio is 0% ($D = 0$):

$$P_{optimum} = \frac{0 + \frac{0.1824}{0.15}(18.24)}{0.15} = \frac{22.18}{0.15} = ₹147.87$$
Key Conclusions:
• EPS = ₹18.24
• Walter's Price at current payout = ₹132.11
• Walter's Price at optimum 0% payout = ₹147.87 (Maximizes shareholder wealth)
Practical Question 8: CAPM Expected Return & Gordon Model Intrinsic Value (ABC Ltd) ICAI TYK Practical Q8
Problem Statement:

ABC Ltd. has been maintaining a growth rate of 10 percent in dividends. The company has paid dividend @ ₹ 3 per share. The rate of return on market portfolio is 12 percent and the risk free rate of return in the market has been observed as 8 percent. The Beta co-efficient of company's share is 1.5. You are required to calculate the expected rate of return on company's shares as per CAPM model and equilibrium price per share by dividend growth model.

Step-by-Step Solution & Working Notes

Given Data:

  • Dividend growth rate ($g$) = 10% = 0.10
  • Latest dividend paid ($D_0$) = ₹1.50 per share
  • Risk-free rate ($R_f$) = 9% = 0.09
  • Market return ($R_m$) = 13% = 0.13
  • Beta of stock ($\beta$) = 1.2

Step 1: Compute Required Return on Equity ($K_e$) using CAPM

$$K_e = R_f + \beta \times (R_m - R_f) = 9\% + 1.2 \times (13\% - 9\%) = 9\% + 1.2 \times 4\% = 9\% + 4.8\% = 13.80\%$$

Step 2: Expected Dividend for Next Year ($D_1$)

$$D_1 = D_0 \times (1 + g) = ₹1.50 \times 1.10 = ₹1.65$$

Step 3: Intrinsic Value per Gordon Model

$$P_0 = \frac{D_1}{K_e - g} = \frac{₹1.65}{0.138 - 0.10} = \frac{₹1.65}{0.038} = ₹43.42$$
Intrinsic Value of ABC Ltd Share = ₹43.42
Practical Question 9: Three-Stage Dividend Discount Valuation ICAI TYK Practical Q9
Problem Statement:

A Company pays a dividend of ₹ 2.00 per share with a growth rate of 7%. The risk free rate is 9% and the market rate of return is 13%. The Company has a beta factor of 1.50. However, due to a decision of the Finance Manager, beta is likely to increase to 1.75. Find out the present as well as the likely value of the share after the decision."

Step-by-Step Solution & Working Notes

Given Data:

  • Base Dividend ($D_0$) = ₹2.00 per share
  • Stage 1: Years 1 & 2: Growth rate $g_1 = 10\%$
  • Stage 2: Years 3 & 4: Growth rate $g_2 = 5\%$
  • Stage 3: Year 5 onward: Perpetual growth $g_3 = 3\%$
  • Required rate of return ($K_e$) = 15% = 0.15

Step 1: Forecast Dividends and Present Values

Year Growth Rate Dividend (₹) PVIF @ 15% PV (₹)
1 10% 2.00 × 1.10 = 2.200 0.8696 1.913
2 10% 2.20 × 1.10 = 2.420 0.7561 1.830
3 5% 2.42 × 1.05 = 2.541 0.6575 1.671
4 5% 2.541 × 1.05 = 2.668 0.5718 1.525
PV of Dividends for Years 1 to 4 ₹6.939

Step 2: Terminal Value at End of Year 4 ($P_4$)

$$D_5 = D_4 \times (1 + g_3) = ₹2.668 \times 1.03 = ₹2.748$$ $$P_4 = \frac{D_5}{K_e - g_3} = \frac{₹2.748}{0.15 - 0.03} = \frac{₹2.748}{0.12} = ₹22.90$$ $$PV(P_4) = ₹22.90 \times 0.5718 = ₹13.094$$

Step 3: Total Intrinsic Value

$$P_0 = ₹6.939 + ₹13.094 = ₹20.033 \approx ₹20.03$$
Intrinsic Value of Share = ₹20.03
Practical Question 10: Valuation of Equity Shares from Balance Sheet & Earnings Data ICAI TYK Practical Q10
Problem Statement:

Calculate the value of share from the following financial data:

Parameter Value
Profit after Tax (PAT)₹ 290 Crores
Equity Share Capital₹ 1,300 Crores (Face Value ₹ 40 each)
Debt Ratio ($\frac{\text{Debt}}{\text{Debt} + \text{Equity}}$)27%
Long-run Growth Rate ($g$)8%
Beta ($\beta$)0.10
Risk-Free Interest Rate ($R_f$)8.7%
Market Return ($R_m$)10.3%
Capital Expenditure per share₹ 47.00
Depreciation per share₹ 39.00
Change in Working Capital per share₹ 3.45
Step-by-Step Solution & Working Notes

Given Data:

  • Total Capital Employed = ₹400 Lakhs
  • Debt-to-Equity Ratio = 3 : 1
  • Reserves & Surplus = 1/3rd of Equity Share Capital
  • Return on Equity (ROE) = 20% = 0.20
  • Industry P/E Multiple = 10 times; Face Value = ₹10 per share

Step 1: Compute Capital Structure Components

$$\text{Total Equity Funds (Net Worth)} = \frac{₹400 \text{ Lakhs}}{3 + 1} = ₹100 \text{ Lakhs}$$ $$\text{Debt Funds} = ₹300 \text{ Lakhs}$$

Since Reserves are 1/3 of Equity Share Capital, let Equity Capital be $C$:

$$C + \frac{1}{3}C = ₹100 \text{ Lakhs} \implies \frac{4}{3}C = 100 \implies C = ₹75 \text{ Lakhs}$$ $$\text{Reserves & Surplus} = ₹25 \text{ Lakhs}$$ $$\text{Number of Equity Shares} = \frac{₹75,00,000}{₹10} = 7,50,000 \text{ shares}$$

Step 2: Earnings & Valuation

$$\text{PAT} = \text{Net Worth} \times ROE = ₹100 \text{ Lakhs} \times 20\% = ₹20 \text{ Lakhs}$$ $$EPS = \frac{₹20,00,000}{7,50,000} = ₹2.667$$ $$P_0 = EPS \times P/E = ₹2.667 \times 10 = ₹26.67$$ $$\text{Book Value per share} = \frac{₹100 \text{ Lakhs}}{7,50,000} = ₹13.33$$
Final Answers:
• Value of Share using P/E Multiple = ₹26.67
• Book Value of Share = ₹13.33
Practical Question 11: Cost of Capital & Valuation of Voyage Ltd ICAI TYK Practical Q11
Problem Statement:

Shares of Voyage Ltd. are being quoted at a price-earning ratio of 8 times. The company retains ₹ 5 per share which is 45% of its Earning Per Share.
You are required to compute
(i) The cost of equity to the company if the market expects a growth rate of 15% p.a.
"(ii) If the anticipated growth rate is 16% per annum, calculate the indicative market price with the same cost of capital."
"(iii) If the company's cost of capital is 20% p.a. & the anticipated growth rate is 19% p.a., calculate the market price per share."

Step-by-Step Solution & Working Notes

Given Data:

  • P/E Ratio = 8 times $\implies$ Earnings Yield = $1/8 = 12.5\%$
  • Share Capital = ₹20 Lakhs (Face value ₹10 $\implies$ 2,00,000 shares)
  • Net Profit = ₹5 Lakhs $\implies EPS = \frac{₹5,00,000}{2,00,000} = ₹2.50$
  • Market Price per share = $EPS \times P/E = ₹2.50 \times 8 = ₹20.00$
  • Dividend per share ($D_0$) = ₹1.50; Growth rate ($g$) = 10%

Part (i): Cost of Capital ($K_e$)

$$D_1 = D_0 \times (1 + g) = ₹1.50 \times 1.10 = ₹1.65$$ $$K_e = \frac{D_1}{P_0} + g = \frac{₹1.65}{₹20.00} + 0.10 = 0.0825 + 0.10 = 18.25\%$$

Part (ii): Value of Share if Growth increases to 12%

$$D_1 = ₹1.50 \times 1.12 = ₹1.68$$ $$P_0 = \frac{D_1}{K_e - g} = \frac{₹1.68}{0.1825 - 0.12} = \frac{₹1.68}{0.0625} = ₹26.88$$
Final Answers:
(i) Cost of Capital ($K_e$) = 18.25% p.a.
(ii) Value of Share at 12% growth = ₹26.88
Practical Question 12: Free Cash Flow Valuation (FCFF & FCFE) - PQR Ltd ICAI TYK Practical Q12
Problem Statement:

Following Financial data are available for PQR Ltd. for the financial year 2008:
(₹ in lakh)
8% debentures 125
10% bonds (2007) 50
Equity shares (₹ 10 each) 100
Reserves and Surplus 300
Total Assets 600
Assets Turnovers ratio 1.1
Effective interest rate 8%
Effective tax rate 40%
Operating margin 10%
Dividend payout ratio 16.67%
Current market Price of Share ₹ 14
Required rate of return of investors 15%
You are required to:
(i) Draw income statement for the year
(ii) Calculate its sustainable growth rate of earnings
"(iii) Calculate the fair price of the Company's share using dividend discount model, and"
(iv) What is your opinion on investment in the company's share at current price?

Step-by-Step Solution & Working Notes

Given Data:

  • Asset Turnover Ratio = 1.1; Total Assets = ₹600 Lakhs $\implies$ Turnover = $600 \times 1.1 = ₹660 \text{ Lakhs}$
  • EBITDA Margin = 25% of Turnover = ₹165 Lakhs
  • Depreciation = ₹40 Lakhs; Corporate Tax Rate = 30%
  • Capital Expenditure = ₹50 Lakhs; Change in Working Capital = ₹15 Lakhs
  • Total Debt = ₹200 Lakhs @ 8% interest
  • WACC = 12%; Cost of Equity ($K_e$) = 15%; Constant growth ($g$) = 5%

Step 1: Compute FCFF

$$EBIT = EBITDA - \text{Depreciation} = ₹165 - ₹40 = ₹125 \text{ Lakhs}$$ $$EBIT(1 - t) = ₹125 \times (1 - 0.30) = ₹87.50 \text{ Lakhs}$$ $$FCFF = EBIT(1 - t) + \text{Depreciation} - \text{CapEx} - \Delta WC$$ $$FCFF = ₹87.50 + ₹40 - ₹50 - ₹15 = ₹62.50 \text{ Lakhs}$$

Step 2: Value of the Firm (Enterprise Value)

$$V_{Firm} = \frac{FCFF_1}{WACC - g} = \frac{FCFF_0(1 + g)}{WACC - g} = \frac{₹62.50 \times 1.05}{0.12 - 0.05} = \frac{₹65.625}{0.07} = ₹937.50 \text{ Lakhs}$$

Step 3: Value of Equity via Enterprise Value

$$\text{Value of Equity} = V_{Firm} - \text{Total Debt} = ₹937.50 - ₹200.00 = ₹737.50 \text{ Lakhs}$$

Step 4: Verification via FCFE Direct Valuation

$$\text{Interest}(1 - t) = (₹200 \times 8\%) \times (1 - 0.30) = ₹16 \times 0.70 = ₹11.20 \text{ Lakhs}$$ $$FCFE_0 = FCFF_0 - \text{Interest}(1 - t) = ₹62.50 - ₹11.20 = ₹51.30 \text{ Lakhs}$$ $$FCFE_1 = ₹51.30 \times 1.05 = ₹53.865 \text{ Lakhs}$$ $$\text{Value of Equity} = \frac{FCFE_1}{K_e - g} = \frac{₹53.865}{0.15 - 0.05} = \frac{₹53.865}{0.10} = ₹538.65 \text{ Lakhs}$$
Final Answers:
• Value of Firm (FCFF approach) = ₹937.50 Lakhs
• Value of Equity (Firm - Debt) = ₹737.50 Lakhs
• Value of Equity (Direct FCFE approach) = ₹538.65 Lakhs
Practical Question 13: Impact of Reinvestment Rate on Equity Valuation (M/s X Ltd) ICAI TYK Practical Q13
Problem Statement:

M/s X Ltd. has paid a dividend of ₹ 2.50 per share on a face value of ₹ 10 in the financial year ending on 31st March, 2009. The details are as follows:

Parameter Value
Current Market Price ($P_0$)₹ 60.00
Growth Rate of Earnings & Dividends ($g$)10%
Beta of Share ($\beta$)0.75
Average Market Return ($R_m$)15%
Risk-Free Rate of Return ($R_f$)9%

Required: Calculate the intrinsic value of the share and advise the investor whether to buy or sell.

Step-by-Step Solution & Working Notes

Given Data: Latest dividend ($D_0$) = ₹2.50, ROE = 15%, $K_e = 14\%$.

Case A: Retention Ratio = 40% ($b = 0.40$)

$$g = b \times r = 0.40 \times 0.15 = 0.06 = 6.0\%$$ $$D_1 = D_0 \times (1 + g) = ₹2.50 \times 1.06 = ₹2.65$$ $$P_0 = \frac{D_1}{K_e - g} = \frac{₹2.65}{0.14 - 0.06} = \frac{₹2.65}{0.08} = ₹33.13$$

Case B: Retention Ratio = 60% ($b = 0.60$)

$$g = b \times r = 0.60 \times 0.15 = 0.09 = 9.0\%$$ $$D_1 = D_0 \times (1 + g) = ₹2.50 \times 1.09 = ₹2.725$$ $$P_0 = \frac{D_1}{K_e - g} = \frac{₹2.725}{0.14 - 0.09} = \frac{₹2.725}{0.05} = ₹54.50$$
Key Takeaway: Since ROE (15%) > Cost of Capital (14%), increasing the retention ratio from 40% to 60% enhances intrinsic value from ₹33.13 to ₹54.50 per share.
Practical Question 14: Investment Decision with Multi-Year Dividend Stream (Mr. A) ICAI TYK Practical Q14
Problem Statement:

Mr. A is thinking of buying shares at ₹ 500 each having face value of ₹ 100. He is expecting a bonus at the ratio of 1: 5 during the fourth year. Annual expected dividend is 20% and the same rate is expected to be maintained on the expanded capital base. He intends to sell the shares at the end of seventh year at an expected price of ₹ 900 each. Incidental expenses for purchase and sale of shares are estimated to be 5% of the market price. He expects a minimum return of 12% per annum. "Should Mr. A buy the share? If so, what maximum price should he pay for each share? Assume no tax on dividend income and capital gain."

Step-by-Step Solution & Working Notes

Given Data: Current price = ₹500; Face value = ₹100; Annual dividend = ₹10 for 5 years; Expected selling price at Year 5 = ₹550; Required return = 12%.

Present Value Calculation

  • PVIFA(12%, 5) = 3.605
  • PVIF(12%, 5) = 0.567
$$PV(\text{Dividends}) = ₹10 \times 3.605 = ₹36.05$$ $$PV(\text{Sale Proceeds}) = ₹550 \times 0.567 = ₹311.85$$ $$\text{Total Intrinsic Value } P_0 = ₹36.05 + ₹311.85 = ₹347.90$$
Decision: Current asking price is ₹500, but the intrinsic present value is only ₹347.90. The share is substantially Overvalued. Mr. A should NOT buy the share.
Practical Question 15: CAPM Equilibrium Price & Alpha Decision Rule ICAI TYK Practical Q15
Problem Statement:

The risk free rate of return Rf is 9 percent. The expected rate of return on the market portfolio Rm is 13 percent. The expected rate of growth for the dividend of Platinum Ltd. is 7 percent. The last dividend paid on the equity stock of firm A was ₹ 2.00. The beta of Platinum Ltd. equity stock is 1.2.
(i) What is the equilibrium price of the equity stock of Platinum Ltd.?
(ii) How would the equilibrium price change when
 The inflation premium increases by 2 percent?
 The expected growth rate increases by 3 percent?
 The beta of Platinum Ltd. equity rises to 1.3?

Step-by-Step Solution & Working Notes

Given Data: $R_f = 9\%$, $R_m = 15\%$, $\beta = 1.4$, Current Market Price $P_{mkt} = ₹20$, $D_0 = ₹2.00$, $g = 8\%$.

Step 1: Required Return via CAPM

$$K_e = R_f + \beta(R_m - R_f) = 9\% + 1.4(15\% - 9\%) = 9\% + 8.4\% = 17.40\%$$

Step 2: Equilibrium Intrinsic Price

$$D_1 = D_0(1 + g) = ₹2.00 \times 1.08 = ₹2.16$$ $$P_0 = \frac{D_1}{K_e - g} = \frac{₹2.16}{0.174 - 0.08} = \frac{₹2.16}{0.094} = ₹22.98$$

Step 3: Jensen's Alpha & Investment Decision

$$\text{Expected Return from Market Price } r = \frac{D_1}{P_{mkt}} + g = \frac{₹2.16}{₹20} + 0.08 = 10.8\% + 8\% = 18.80\%$$ $$\alpha = \text{Expected Return} - \text{Required Return} = 18.80\% - 17.40\% = +1.40\%$$
Conclusion: Intrinsic Value (₹22.98) > Market Price (₹20.00), and Alpha is positive (+1.40%). The stock is Undervalued. The investor should BUY.
Practical Question 16: Supernormal Dividend Growth & H-Model Valuation (SAM Ltd) ICAI TYK Practical Q16
Problem Statement:

SAM Ltd. has just paid a dividend of ₹ 2 per share and it is expected to grow @ 6% p.a. After paying dividend, the Board declared to take up a project by retaining the next three annual dividends. It is expected that this project is of same risk as the existing projects. The results of this project will start coming from the 4th year onward from now. The dividends will then be" ₹ 2.50 per share and will grow @ 7% p.a. "An investor has 1,000 shares in SAM Ltd. and wants a receipt of at least ₹ 2,000 p.a. from this investment." Show that the market value of the share is affected by the decision of the Board. Also show "as to how the investor can maintain his target receipt from the investment for first 3 years and improved income thereafter, given that the cost of capital of the firm is 8%."

Step-by-Step Solution & Working Notes

Given Data: Current dividend ($D_0$) = ₹2.00, Cost of equity ($K_e$) = 16% = 0.16. Growth is 25% for 4 years, declining linearly over 5 years to stable 10%.

Step 1: Supernormal Growth Stage (Years 1 to 4 @ 25%)

Year Dividend Calculation (₹) Amount (₹) PV Factor @ 16% Present Value (₹)
1 2.00 × 1.25 2.50 0.8621 2.155
2 2.50 × 1.25 3.125 0.7432 2.323
3 3.125 × 1.25 3.906 0.6407 2.503
4 3.906 × 1.25 4.883 0.5523 2.697
PV of Stage 1 Dividends (Years 1 to 4) ₹9.678

Step 2: Transition & Stable Growth Valuation using H-Model at Year 4

At $t=4$, $D_4 = ₹4.883$. High initial transition growth $g_a = 25\%$, normal growth $g_n = 10\%$, transition period $= 5$ years $\implies H = 5/2 = 2.5$ years.

$$P_4 = \frac{D_4(1 + g_n)}{K_e - g_n} + \frac{D_4 \times H \times (g_a - g_n)}{K_e - g_n}$$ $$P_4 = \frac{4.883 \times 1.10}{0.16 - 0.10} + \frac{4.883 \times 2.5 \times (0.25 - 0.10)}{0.16 - 0.10} = \frac{5.3713}{0.06} + \frac{1.8311}{0.06} = 89.52 + 30.52 = ₹120.04$$ $$PV(P_4) = ₹120.04 \times 0.5523 = ₹66.30$$

Step 3: Total Intrinsic Value of Share

$$P_0 = ₹9.678 + ₹66.30 = ₹75.98 \approx ₹76.00$$
Intrinsic Value of SAM Ltd Share = ₹76.00
Practical Question 17: Covariance Beta, CAPM Cost of Equity & Gordon Share Value (XYZ Ltd) ICAI TYK Practical Q17
Problem Statement:

XYZ Ltd. paid a dividend of ₹ 2 for the current year. The dividend is expected to grow at 40% for the next 5 years and at 15% per annum thereafter. The return on 182 days T-bills is 11% per annum and the market return is expected to be around 18% with a variance of 24%. The co-variance of XYZ's return with that of the market is 30%. You are required to calculate the required rate of return and intrinsic value of the stock.

Step-by-Step Solution & Working Notes

Given Data: Current dividend ($D_0$) = ₹2.00, Growth rate ($g$) = 5% = 0.05, Covariance of stock with market $\text{Cov}(i,m) = 0.0225$, Variance of market returns $\sigma_m^2 = 0.015$, Risk-free rate ($R_f$) = 7% = 0.07, Market return ($R_m$) = 11% = 0.11.

Step 1: Calculate Beta ($\beta$)

Beta Formula
$$\beta = \frac{\text{Covariance}(R_i, R_m)}{\text{Variance of Market Return } \sigma_m^2} = \frac{0.0225}{0.0150} = 1.50$$

Step 2: Cost of Equity ($K_e$) via CAPM

$$K_e = R_f + \beta \times (R_m - R_f) = 7\% + 1.50 \times (11\% - 7\%) = 7\% + 6.0\% = 13.00\%$$

Step 3: Intrinsic Value per Gordon Model

$$D_1 = D_0 \times (1 + g) = ₹2.00 \times 1.05 = ₹2.10$$ $$P_0 = \frac{D_1}{K_e - g} = \frac{₹2.10}{0.13 - 0.05} = \frac{₹2.10}{0.08} = ₹26.25$$
Final Answers:
• Stock Beta ($\beta$) = 1.50
• Cost of Equity ($K_e$) = 13.00% p.a.
• Intrinsic Value of Share = ₹26.25
Practical Question 18: Share Buyback Valuation, Post-Buyback EPS & Market Price (Rahul Ltd) ICAI TYK Practical Q18
Problem Statement:

Rahul Ltd. has surplus cash of ₹ 100 lakhs and wants to distribute 27% of it to the shareholders. The company decides to buy back shares. The Finance Manager of the company estimates that its share price after re-purchase is likely to be 10% above the buyback price-if the buyback route is taken. The number of shares outstanding at present is 10 lakhs and the current EPS is ₹ 3. You are required to determine: "(i) The price at which the shares can be re-purchased, if the market capitalization of the company should be ₹ 210 lakhs after buyback," "(ii) The number of shares that can be re-purchased, and" "(iii) The impact of share re-purchase on the EPS, assuming that net income is the same."

Step-by-Step Solution & Working Notes

Given Data: Surplus cash available = ₹100 Lakhs, Total existing shares = 10 Lakhs, PAT = ₹30 Lakhs, Current P/E = 10, Current Market Price = ₹30. Rahul Ltd deploys 27% of cash in buyback, and market price post-buyback is expected to be 1.1P.

Step 1: Formulate Post-Buyback Capitalisation Equation

Funds deployed in buyback = $27\% \times ₹100 \text{ Lakhs} = ₹27 \text{ Lakhs}$.

$$\text{Shares bought back} = \frac{₹27,00,000}{P}$$ $$\text{Remaining shares} = 10,00,000 - \frac{27,00,000}{P}$$

Post-buyback market capitalisation is $1.1P \times \text{Remaining Shares}$:

$$1.1P \left( 10,00,000 - \frac{27,00,000}{P} \right) = 11,00,000 P - 29,70,000$$

Equating post-buyback market capitalisation to target valuation:

$$P = ₹36.00$$ $$\text{Shares bought back} = \frac{₹27,00,000}{₹36} = 75,000 \text{ shares}$$ $$\text{Remaining shares} = 10,00,000 - 75,000 = 9,25,000 \text{ shares}$$

Step 2: Post-Buyback Financial Metrics

$$EPS_{post} = \frac{\text{PAT}}{\text{Remaining Shares}} = \frac{₹30,00,000}{9,25,00,000} = ₹3.24$$ $$\text{Post-Buyback Market Price} = 1.1 \times P = 1.1 \times ₹36.00 = ₹39.60$$
Final Answers:
• Buyback Price ($P$) = ₹36.00 per share
• Number of Shares Bought Back = 75,000 shares
• Post-Buyback EPS = ₹3.24
• Post-Buyback Market Price = ₹39.60
Practical Question 19: Bond Valuation at Varying Required Yields (Par, Premium, Discount) ICAI TYK Practical Q19
Problem Statement:

Nominal value of 10% bonds issued by a company is ₹100. The bonds are redeemable at "₹ 110 at the end of year 5. Determine the value of the bond if required yield is (i) 5%, (ii) 5.1%, (iii) 10% and (iv) 10.1%."

Step-by-Step Solution & Working Notes

Given Data: Face Value ($M$) = ₹100, Coupon Rate = 10% (Annual coupon $C = ₹10$), Term to Maturity ($n$) = 5 years.

Case Required Yield ($y$) Coupon ($C$) PVIFA($y$, 5) PVIF($y$, 5) Bond Price $B_0 = C(PVIFA) + M(PVIF)$ (₹) Relationship
(i) 5.0% ₹10 4.329 0.784 10(4.329) + 100(0.784) = ₹121.69 Yield < Coupon $\implies$ Premium
(ii) 5.1% ₹10 4.318 0.780 10(4.318) + 100(0.780) = ₹121.18 Yield < Coupon $\implies$ Premium
(iii) 10.0% ₹10 3.791 0.621 10(3.791) + 100(0.621) = ₹100.00 Yield = Coupon $\implies$ Par
(iv) 10.1% ₹10 3.781 0.618 10(3.781) + 100(0.618) = ₹99.61 Yield > Coupon $\implies$ Discount
Key Principle Demonstrated: When required yield < coupon rate, bond sells at a premium (> ₹100). When yield = coupon rate, bond sells at par (= ₹100). When yield > coupon rate, bond sells at a discount (< ₹100).
Practical Question 20: Maximum Purchase Price & Semi-Annual Bond Yield (11% Bond) ICAI TYK Practical Q20
Problem Statement:

An investor is considering the purchase of the following Bond: "Face value ₹ 100 Coupon rate 11% Maturity 3 years" "(i) If he wants a yield of 13% what is the maximum price, he should be ready to pay for?" "(ii) If the Bond is selling for ₹ 97.60, what would be his yield?"

Step-by-Step Solution & Working Notes

Given Data: Face Value = ₹100, Coupon Rate = 11% (Annual coupon = ₹11), Maturity = 3 years, Required Yield = 13%.

Part (i): Maximum Price an Investor Should Pay at 13% Yield

  • PVIFA(13%, 3) = 2.361
  • PVIF(13%, 3) = 0.693
$$B_0 = C \times PVIFA(13\%, 3) + M \times PVIF(13\%, 3)$$ $$B_0 = ₹11 \times 2.361 + ₹100 \times 0.693 = ₹25.97 + ₹69.30 = ₹95.27$$

Part (ii): Semi-Annual Compounding Yield

If coupons are semi-annual (₹5.50 each half-year for 6 periods) and market price is ₹95.27:

$$YTM_{semi-annual} = 6.45\% \implies \text{Annualized Yield} = 6.45\% \times 2 = 12.90\%$$
Final Answers:
(i) Maximum Purchase Price = ₹95.27
(ii) Approximate Yield to Maturity = 13.00% (Annual) / 12.90% (Semi-Annual)
Practical Question 21: Market Price of Bond: Current Yield vs. YTM ICAI TYK Practical Q21
Problem Statement:

Calculate Market Price of: "(i) 10% Government of India security currently quoted at ₹ 110 (Face Value ₹ 100), but yield is expected to go up by 1%." "(ii) A bond with 7.5% coupon interest, Face Value ₹ 10,000 & term to maturity of 2 years, presently yielding 6%. Interest payable half yearly."

Step-by-Step Solution & Working Notes

Given Data: 10-year 12% Bond with Face Value = ₹100, Annual Coupon $C = ₹12$.

Case (i): When Current Yield is 13%

Current Yield Formula
$$CY = \frac{\text{Annual Coupon}}{B_0} \implies 0.13 = \frac{₹12}{B_0} \implies B_0 = \frac{₹12}{0.13} = ₹92.31$$

Case (ii): When Yield to Maturity (YTM) is 13%

  • PVIFA(13%, 10) = 5.426
  • PVIF(13%, 10) = 0.295
$$B_0 = ₹12 \times 5.426 + ₹100 \times 0.295 = ₹65.11 + ₹29.50 = ₹94.61$$
Final Answers:
(i) Market Price when Current Yield is 13% = ₹92.31
(ii) Market Price when YTM is 13% = ₹94.61
Practical Question 22: Convertible Bond Valuation & Premium Analysis ICAI TYK Practical Q22
Problem Statement:

A convertible bond with a face value of ₹ 1,000 is issued at ₹ 1,350 with a coupon rate of 10.5%. The conversion rate is 14 shares per bond. The current market price of bond and share is ₹ 1,475 and ₹ 80 respectively. What is the premium over conversion value?"

Step-by-Step Solution & Working Notes

Given Data: Face value = ₹1,000, Market price of bond = ₹950, Conversion ratio = 14 shares, Current market price per equity share = ₹60.

Step 1: Conversion Value of Bond

$$CV = \text{Conversion Ratio} \times \text{Stock Price} = 14 \times ₹60 = ₹840$$

Step 2: Market Conversion Price per Share

$$\text{Market Conversion Price} = \frac{\text{Market Price of Bond}}{\text{Conversion Ratio}} = \frac{₹950}{14} = ₹67.86$$

Step 3: Conversion Premium

$$\text{Conversion Premium (\%)} = \frac{₹950 - ₹840}{₹840} \times 100 = \frac{₹110}{₹840} \times 100 = 13.10\%$$
Final Answers:
• Conversion Value = ₹840.00
• Market Conversion Price = ₹67.86 per share
• Conversion Premium = 13.10%
Practical Question 23: Straight Bond Value vs. Conversion Value (Saranam Ltd) ICAI TYK Practical Q23
Problem Statement:

Saranam Ltd. has issued convertible debentures with coupon rate 12%. Each debenture has an option to convert to 20 equity shares at any time until the date of maturity. Debentures will be redeemed at ₹ 100 on maturity of 5 years. An investor generally requires a rate of return of 8% p.a. on a 5-year security. As an investor when will you exercise conversion for given market prices of the equity share of (i) ₹ 4, (ii) ₹ 5 and (iii) ₹ 6." Cumulative PV factor for 8% for 5 years : 3.993 PV factor for 8% for year 5 : 0.681

Step-by-Step Solution & Working Notes

Given Data: Coupon = 10%, Face value = ₹100, Maturity = 3 years. Converts into 2 shares of ₹50 each at maturity. Straight debentures yield 12%.

Step 1: Value of Debentures if NOT Converted (Straight Debt Value)

$$B_{straight} = ₹10 \times PVIFA(12\%, 3) + ₹100 \times PVIF(12\%, 3)$$ $$B_{straight} = ₹10 \times 2.402 + ₹100 \times 0.712 = ₹24.02 + ₹71.20 = ₹95.22$$

Step 2: Value if Converted into Equity

If stock price is ₹50: Conversion value $= 2 \times ₹50 = ₹100$.

$$PV = ₹10 \times PVIFA(12\%, 3) + ₹100 \times PVIF(12\%, 3) = ₹95.22$$

If stock price rises to ₹65: Conversion value $= 2 \times ₹65 = ₹130$.

$$PV = ₹10 \times 2.402 + ₹130 \times 0.712 = ₹24.02 + ₹92.56 = ₹116.58$$
Final Answers:
• Straight Debt Floor Value = ₹95.22
• Debenture Value if share price is ₹65 = ₹116.58
Practical Question 24: Comprehensive Convertible Bond Indicators ICAI TYK Practical Q24
Problem Statement:

The data given below relates to a convertible bond:
Face value ₹ 250
Coupon rate 12%
No. of shares per bond 20
Market price of share ₹ 12
Straight value of bond ₹ 235
Market price of convertible bond ₹ 265
Calculate:
(i) Stock value of bond.
(ii) The percentage of downside risk.
(iii) The conversion premium
(iv) The conversion parity price of the stock.

Step-by-Step Solution & Working Notes

Given Data: Face Value = ₹250, Coupon = 10% (Annual coupon = ₹25), Maturity = 5 years, Market Price of Bond = ₹265, Conversion Ratio = 20 shares, Current Share Price = ₹12, Required yield on straight debt = 12%.

(i) Stock Value / Conversion Value

$$CV = 20 \times ₹12 = ₹240.00$$

(ii) Percentage of Downside Risk

Straight Debt Floor Value:

$$B_{straight} = ₹25 \times PVIFA(12\%, 5) + ₹250 \times PVIF(12\%, 5)$$ $$B_{straight} = ₹25 \times 3.605 + ₹250 \times 0.567 = ₹90.13 + ₹141.75 = ₹231.88 \approx ₹235.00$$ $$\text{Downside Risk} = \frac{₹265 - ₹235}{₹235} \times 100 = 12.77\%$$

(iii) Market Conversion Price

$$\frac{₹265}{20} = ₹13.25 \text{ per share}$$

(iv) Conversion Premium

$$\frac{₹265 - ₹240}{₹240} \times 100 = \frac{₹25}{₹240} \times 100 = 10.42\%$$
Final Answers:
• Conversion Value = ₹240.00
• Downside Risk = 12.77%
• Market Conversion Price = ₹13.25 per share
• Conversion Premium = 10.42%
Practical Question 25: Bond Refunding Decision & NPV (ABC Ltd) ICAI TYK Practical Q25
Problem Statement:

ABC Ltd. has ₹ 300 million, 12 per cent bonds outstanding with six years remaining to maturity. Since interest rates are falling, ABC Ltd. is contemplating of refunding these bonds with a ₹ 300 million issue of 6 year bonds carrying a coupon rate of 10 per cent. Issue cost of the new bond will be ₹ 6 million and the call premium is 4 per cent. ₹ 9 million being the unamortized portion of issue cost of old bonds can be written off no sooner the old bonds are called off. Marginal tax rate of ABC Ltd. is 30 per cent. You are required to analyse the bond" refunding decision.

Step-by-Step Solution & Working Notes

Given Data: ₹300 Million 12% bonds outstanding with 6 years left to maturity. Call premium = 4%. Can be refunded with ₹300 Million 10% bonds having 6 years maturity. Flotation costs on new issue = ₹6 Million. Unamortized flotation cost of old bonds = ₹3 Million. Tax rate = 30%.

Step 1: Initial Cash Outlay for Refunding

Particulars Amount (₹ Millions)
Call Premium on Old Bonds (4% of ₹300M) 12.00
Flotation Cost on New Issue 6.00
Less: Tax Savings on Call Premium (₹12M × 30%) (3.60)
Less: Tax Savings on Unamortized Old Flotation Costs (₹3M × 30%) (0.90)
Net Initial Cash Outflow ₹13.50 Million

Step 2: Annual Net Cash Savings

Particulars Amount (₹ Millions)
Annual Interest on Old Bonds (12% of ₹300M) 36.00
Less: Annual Interest on New Bonds (10% of ₹300M) (30.00)
Gross Annual Interest Savings 6.00
Less: Tax @ 30% on Interest Savings (1.80)
Add: Tax shield on New Flotation Amortization [(₹6M / 6) × 30%] 0.30
Less: Lost Tax shield on Old Flotation Amortization [(₹3M / 6) × 30%] (0.15)
Net Annual After-Tax Cash Inflow ₹4.35 Million

Step 3: NPV of Refunding Decision

Discount rate = After-tax cost of new debt $= 10\% \times (1 - 0.30) = 7.00\%$.

$$PVIFA(7\%, 6) = 4.766$$ $$PV(\text{Annual Savings}) = ₹4.35 \text{ Million} \times 4.766 = ₹20.732 \text{ Million}$$ $$NPV = ₹20.732 \text{ Million} - ₹13.50 \text{ Million} = +₹7.232 \text{ Million}$$
Decision: Since NPV of refunding is positive (+₹7.23 Million), ABC Ltd should PROCEED WITH REFUNDING the old bonds.
Practical Question 26: Macaulay Duration, Volatility & Convexity Price Estimation ICAI TYK Practical Q26
Problem Statement:

The following data are available for a bond "Face value ₹ 1,000 Coupon Rate 16% Years to Maturity 6 Redemption value ₹ 1,000 Yield to maturity 17%" "What is the current market price, duration and volatility of this bond? Calculate the expected market price, if increase in required yield is by 75 basis points."

Step-by-Step Solution & Working Notes

Given Data: Coupon = 16% (Annual coupon = ₹160), Face Value = ₹1,000, Maturity = 6 years, Yield ($y$) = 17%.

Step 1: Market Price of Bond ($P_0$)

  • PVIFA(17%, 6) = 3.589
  • PVIF(17%, 6) = 0.390
$$P_0 = ₹160 \times 3.589 + ₹1,000 \times 0.390 = ₹574.24 + ₹390.00 = ₹964.24$$

Step 2: Macaulay Duration Calculation Table

Year ($t$) Cash Flow (₹) PVIF @ 17% Present Value (₹) Weight ($w_t = PV / P_0$) Weighted Time ($t \times w_t$)
1 160 0.8547 136.75 0.1418 0.1418
2 160 0.7305 116.88 0.1212 0.2424
3 160 0.6244 99.90 0.1036 0.3108
4 160 0.5337 85.39 0.0886 0.3544
5 160 0.4561 72.98 0.0757 0.3785
6 1,160 0.3898 452.17 0.4689 2.8134
Total ₹964.07 1.0000 4.2413 Years
$$\text{Macaulay Duration } D = 4.2413 \text{ Years} \approx 4.24 \text{ Years}$$

Step 3: Modified Duration (Volatility) & Price Change

$$D^* = \frac{D}{1 + y} = \frac{4.2413}{1.17} = 3.625 \text{ Years}$$

If yield increases by 100 bps (+1.0% = 0.01):

$$\Delta P = - D^* \times \Delta y \times P_0 = - 3.625 \times 0.01 \times ₹964.24 = - ₹34.95$$ $$\text{Estimated New Price} = ₹964.24 - ₹34.95 = ₹929.29$$
Final Answers:
• Market Price = ₹964.24
• Macaulay Duration = 4.24 Years
• Volatility (Modified Duration) = 3.625 Years
• Expected Price on +1% Yield Shift = ₹929.29
Practical Question 27: Bond Portfolio Immunization (Mr. A) ICAI TYK Practical Q27
Problem Statement:

Mr. A will need ₹ 1,00,000 after two years for which he wants to make one time necessary investment now. He has a choice of two types of bonds. Their details are as below:" Bond X Bond Y Face value "₹ 1,000" "₹ 1,000" Coupon 7% payable annually 8% payable annually Years to maturity 1 4 Current price ₹ 972.73 ₹ 936.52 Current yield 10% 10% "Advice Mr. A whether he should invest all his money in one type of bond or he should buy both the bonds and, if so, in which quantity? Assume that there will not be any call risk or default risk."

Step-by-Step Solution & Working Notes

Given Data: Mr. A requires ₹1,00,000 after 2 years. Target investment horizon $H = 2.0$ years. Two bonds available: Bond X (Maturity 1 year) and Bond Y (Maturity 4 years, Duration = 3.50 years).

Step 1: Duration of Individual Bonds

  • Since Bond X matures in 1 year, its duration $D_X = 1.00$ year.
  • Duration of Bond Y ($D_Y$) = 3.50 years.
  • Target Portfolio Duration ($D_p$) = 2.00 years.

Step 2: Solve for Portfolio Weights ($w_X$ and $w_Y$)

$$w_X + w_Y = 1.0 \implies w_Y = 1 - w_X$$ $$D_p = w_X D_X + w_Y D_Y$$ $$2.0 = w_X(1.0) + (1 - w_X)(3.50)$$ $$2.0 = 1.0 w_X + 3.50 - 3.50 w_X \implies 2.50 w_X = 1.50 \implies w_X = \frac{1.50}{2.50} = 0.60 = 60\%$$ $$w_Y = 1 - 0.60 = 0.40 = 40\%$$
Final Allocation for Immunization:
• Invest 60% of funds in Bond X.
• Invest 40% of funds in Bond Y.
This immunizes the portfolio against interest rate fluctuations over the 2-year horizon.
Practical Question 28: 91-Day Treasury Bill Issue Price & Yield (RBI) ICAI TYK Practical Q28
Problem Statement:

RBI sold a 91-day T-bill of face value of ₹ 100 at an yield of 6%. What was the issue price?

Step-by-Step Solution & Working Notes

Given Data: Maturity ($M$) = 91 days, Face Value ($F$) = ₹100, Yield ($Y$) = 6% p.a., Year = 365 days.

T-Bill Yield Formula
$$Y = \left[ \frac{F - P}{P} \right] \times \frac{365}{M} \times 100$$
$$6 = \left[ \frac{100 - P}{P} \right] \times \frac{365}{91} \times 100$$ $$6 = \frac{100 - P}{P} \times 401.0989$$ $$6P = 40109.89 - 401.0989P$$ $$407.0989 P = 40109.89 \implies P = \frac{40109.89}{407.0989} = ₹98.526 \approx ₹98.53$$
Issue Price of 91-Day Treasury Bill = ₹98.53
Practical Question 29: Money Market Investment Decision: T-Bills vs. Commercial Paper ICAI TYK Practical Q29
Problem Statement:

Wonderland Limited has excess cash of ₹ 20 lakhs, which it wants to invest in short term marketable securities. Expenses relating to investment will be ₹ 50,000."
The securities invested will have an annual yield of 9%.
The company seeks your advice
(i) as to the period of investment so as to earn a pre-tax income of 5%. (discuss)
(ii) the minimum period for the company to breakeven its investment expenditure overtime value of money.

Step-by-Step Solution & Working Notes

Given Data: Surplus funds = ₹20 Lakhs for 3 months. Option 1: 91-day T-Bill at ₹98.20 per ₹100 face value. Option 2: 90-day Commercial Paper at 10.5% discount.

Option 1: Effective Annual Yield on 91-Day T-Bills

$$Y_{T-Bill} = \left[ \frac{100 - 98.20}{98.20} \right] \times \frac{365}{91} \times 100 = \frac{1.80}{98.20} \times 4.011 \times 100 = 7.35\% \text{ p.a.}$$

Option 2: Effective Annual Yield on Commercial Paper

$$\text{Issue Price} = 100 - (10.5\% \times 90/365) = ₹97.41$$ $$Y_{CP} = \left[ \frac{100 - 97.41}{97.41} \right] \times \frac{365}{90} \times 100 = 10.78\% \text{ p.a.}$$
Recommendation: Commercial Paper offers a higher yield of 10.78% compared to 7.35% on T-Bills. Wonderland Ltd should invest in Commercial Paper subject to acceptable credit risk.
Practical Question 30: Effective Cost of Funds for Commercial Paper (Z Co. Ltd) ICAI TYK Practical Q30
Problem Statement:

Z Co. Ltd. issued commercial paper worth ₹10 crores as per following details: Date of issue : 16th January, 2019" "Date of maturity: 17th April, 2019" No. of days: 91 Interest rate: 12.04% p.a. What was the net amount received by the company on issue of CP? (Charges of intermediary may be ignored)

Step-by-Step Solution & Working Notes

Given Data: Issue size = ₹10 Crores, Maturity = 90 days, Discount rate = 12% p.a., Credit rating charges = 0.50%, Issue expenses = 0.25%, Year = 365 days.

Step 1: Compute Upfront Costs per ₹100 Face Value

  • Discount amount = $₹100 \times 12\% \times \frac{90}{365} = ₹2.9589$
  • Rating charges = $₹100 \times 0.50\% = ₹0.50$
  • Issue expenses = $₹100 \times 0.25\% = ₹0.25$
  • Total Costs = $₹2.9589 + ₹0.50 + ₹0.25 = ₹3.7089$

Step 2: Net Proceeds Received

$$\text{Net Proceeds} = ₹100 - ₹3.7089 = ₹96.2911$$

Step 3: Effective Cost of Funds

$$\text{Effective Cost} = \left[ \frac{₹3.7089}{₹96.2911} \right] \times \frac{365}{90} \times 100 = 0.038517 \times 4.0555 \times 100 = 15.62\% \text{ p.a.}$$
Effective Cost of Commercial Paper = 15.62% p.a.
Practical Question 31: Repo Transaction: Clean Price, Dirty Price & Repurchase Settlement ICAI TYK Practical Q31
Problem Statement:

Bank A enter into a Repo for 14 days with Bank B in 10% Government of India Bonds 2028 @ 5.65% for ₹ 8 crore. Assuming that clean price (the price that does not have accrued interest) be ₹ 99.42 and initial Margin be 2% and days of accrued interest be 262 days. You are required to determine
(i) Dirty Price
(ii) Repayment at maturity. (Consider 360 days in a year)

Step-by-Step Solution & Working Notes

Given Data: 14-day Repo in 10% GOI Bond. Face Value = ₹100, Clean Price = ₹99.42, Accrued interest days = 262 days (360-day year convention), Repo Rate = 6.00% p.a.

Part (i): Dirty Price for 1st Leg Settlement

$$\text{Accrued Interest} = \text{Face Value} \times \text{Coupon} \times \frac{\text{Days}}{360} = ₹100 \times 10\% \times \frac{262}{360} = ₹7.2778$$ $$\text{Dirty Price} = \text{Clean Price} + \text{Accrued Interest} = ₹99.42 + ₹7.2778 = ₹106.6978 \approx ₹106.70$$

Part (ii): Repurchase Price for 2nd Leg (Settlement after 14 days)

$$\text{Repayment Amount} = \text{Dirty Price} \times \left[ 1 + \left( \text{Repo Rate} \times \frac{14}{360} \right) \right]$$ $$\text{Repayment Amount} = ₹106.6978 \times \left[ 1 + \left( 0.06 \times \frac{14}{360} \right) \right] = ₹106.6978 \times [1 + 0.002333] = ₹106.9467 \approx ₹106.95$$
Final Answers:
• Accrued Interest = ₹7.28
• Dirty Price (1st Leg Outflow) = ₹106.70
• Repayment Price after 14 days (2nd Leg Inflow) = ₹106.95