Chapter 13: Business Valuation

Comparison Matrix: Economic Value Added (EVA) vs Market Value Added (MVA)

Elaboration on Relative Valuation (Valuation by Multiples)

While Discounted Cash Flow (DCF) models estimate the intrinsic value of an asset based on its fundamental cash flows and risk profile, Relative Valuation estimates value by benchmarking an enterprise against how similar, comparable assets are priced in the open market.

1. Underlying Economic Premise: Similar assets should sell at similar prices (Law of One Price). By comparing standardized financial ratios across peer group companies in the same industry, analysts identify whether a target company is undervalued, fairly priced, or overvalued relative to the sector.
2. Standardized Multiples Classification:

   Multiple Family	Popular Ratios	Analytical Strengths & Context
   Equity Multiples	• Price-to-Earnings ($P/E$) • Price-to-Book Value ($P/BV$) • Price-to-Sales ($P/S$)	Relates market equity capitalization directly to equity metrics (PAT, Net Worth). Sensitive to differing financial leverage and capital structures.
   Enterprise Value Multiples	• Enterprise Value to EBITDA ($EV/\text{EBITDA}$) • Enterprise Value to Sales ($EV/\text{Sales}$) • Enterprise Value to Invested Capital	Capital-structure neutral; widely preferred in cross-border acquisitions because EBITDA eliminates distortions from differing depreciation policies, tax rates, and debt gearing.
   Sector-Specific Multiples	• EV / Monthly Active Users (Digital) • EV / Bed (Hospitals) • EV / Room (Hotels)	Captures physical operating capacity and network scale where accounting profits are not yet mature.

3. Practical Steps in Execution:
   • Select a true "peer group" with similar operating risk, size, growth prospects, and business models.
   • Normalize historical earnings by removing non-recurring, extraordinary, and non-operating gains/losses.
   • Apply peer median or average multiples to the target company's metrics to derive indicated equity value.
4. Key Limitations:
   • Prone to market bubbles and collective mispricing: if the entire industry is overvalued, relative valuation will simply confirm the bubble.
   • True "pure-play" clones rarely exist; adjustments for scale, debt differences, and competitive moats are necessary.

1. Valuation Based on Current Market Price (Lower Band)

$$\text{Market Price per Share} = ₹ 400$$

$$\text{Total Business Market Value} = 1.5 \text{ Cr shares} \times ₹ 400 = \mathbf{₹ 600 \text{ Crores}}$$

This represents the minimum price that XYZ Ltd.'s shareholders would expect to receive in any takeover transaction.

2. Valuation Based on Discounted Cash Flow (DCF) (Upper Band)

$$\text{DCF Value per Share} = \frac{₹ 747.15 \text{ Crores}}{1.5 \text{ Crores shares}} = \mathbf{₹ 498.10 \text{ per share}}$$

3. Recommended Range of Valuation for Negotiation

Part (i): Computation of Business Value via Capitalization Rate (14%)

Step 1: Normalize Existing Operating Profits Before Tax:

$$\text{Reported Profit Before Tax} = \frac{\text{PAT}}{1 - T} = \frac{₹ 77 \text{ Lakhs}}{1 - 0.30} = ₹ 110.00 \text{ Lakhs}$$

Step 2: Capitalization of Maintainable Earnings:

$$\mathbf{\text{Value of the Business}} = \frac{\text{Maintainable PAT}}{\text{Capitalization Rate}} = \frac{₹ 98.00 \text{ Lakhs}}{0.14} = \mathbf{₹ 700.00 \text{ Lakhs}}$$

Part (ii): Determination of Market Price Per Equity Share (P/E = 8x)

Step 1: Sales and Operating Projections for 4 Years (Growth = 30% p.a.)

Step 2: Computation of WACC

Total Equity = $100 + 100 = 200$. Debt = 40. Total Capital = 240.

$$k_e = 18\%, \quad k_d(\text{post-tax}) = 12\% \times (1 - 0.30) = 8.40\%$$

$$\text{WACC} = 18\% \times \left(\frac{200}{240}\right) + 8.40\% \times \left(\frac{40}{240}\right) = 15.00\% + 1.40\% = \mathbf{16.40\%}$$

Step 3: Present Value of Explicit FCFF (Years 1 to 4)

Step 4: Terminal Value at Year 4 & Overall Value

$$\text{Terminal Value at Year 4} = \frac{\text{FCFF}_4 \times (1 + g)}{\text{WACC} - g} = \frac{40.532 \times 1.04}{0.164 - 0.04} = \frac{42.153}{0.124} = ₹ 339.94 \text{ thousand}$$

$$\text{PV of Terminal Value} = 339.94 \times 0.5448 = \mathbf{₹ 185.20 \text{ thousand}}$$

$$\text{Total Enterprise Value} = 75.40 + 185.20 = \mathbf{₹ 260.60 \text{ thousand}}$$

$$\text{Value of Equity} = \text{Enterprise Value} - \text{Debt} = 260.60 - 40.00 = \mathbf{₹ 220.60 \text{ thousand}}$$

$$\text{Shareholder Value Added (SVA)} = \text{Equity Value} - \text{Book Equity} = 220.60 - 200.00 = \mathbf{₹ 20.60 \text{ thousand}}$$

Part (i): Net Asset Value (NAV) Method

Total number of equity shares = ₹ 1.00 Crore ÷ ₹ 10 = 10,00,000 shares (0.10 Crore shares).

As per ICAI Study Material, Net Assets = ₹ 3.50 Crores.

$$\mathbf{\text{NAV per Share}} = \frac{₹ 3.50 \text{ Crores}}{0.10 \text{ Crore shares}} = \mathbf{₹ 35.00 \text{ per share}}$$

Part (ii): Profit Earning Capacity Value (PECV) Method

$$\text{Capitalized Value of Profits} = \frac{\text{Maintainable PAT}}{\text{Normal Rate of Return}} = \frac{₹ 0.40 \text{ Crores}}{0.10} = \mathbf{₹ 4.00 \text{ Crores}}$$

$$\mathbf{\text{PECV per Share}} = \frac{₹ 4.00 \text{ Crores}}{0.10 \text{ Crore shares}} = \mathbf{₹ 40.00 \text{ per share}}$$

Part (iii): Market Value Method

Given directly in the problem: $\mathbf{\text{Market Value per Share} = ₹ 45.00}$.

Part (iv): Fair Value Method (Average of NAV and PECV)

$$\mathbf{\text{Fair Value per Share}} = \frac{\text{NAV per share} + \text{PECV per share}}{2} = \frac{₹ 35.00 + ₹ 40.00}{2} = \mathbf{₹ 37.50 \text{ per share}}$$

(Or average including Market Price: $\frac{35 + 40 + 45}{3} = ₹ 40.00$ per share).

1. Net Asset Value (NAV) Method

• AB Ltd.: Net Assets = $₹ 20.00\text{L} + ₹ 64.00\text{L} = ₹ 84.00 \text{ Lakhs}$.

Number of shares = 2,00,000 shares $\implies \text{NAV per share} = \frac{₹ 84,00,000}{2,00,000} = \mathbf{₹ 42.00}$.

• XY Ltd.: Net Assets = $₹ 10.00\text{L} + ₹ 14.50\text{L} = ₹ 24.50 \text{ Lakhs}$.

Number of shares = 1,00,000 shares $\implies \text{NAV per share} = \frac{₹ 24,50,000}{1,00,000} = \mathbf{₹ 24.50}$.

$$\mathbf{\text{Swap Ratio (NAV Basis)}} = \frac{\text{NAV of Target (XY)}}{\text{NAV of Acquirer (AB)}} = \frac{₹ 24.50}{₹ 42.00} = \mathbf{0.5833} \quad (\text{or } 7 \text{ shares of AB for } 12 \text{ shares of XY})$$

2. Price-Earnings (P/E) Multiple Method

• AB Ltd.: $\text{EPS} = \frac{₹ 12,00,000}{2,00,000} = ₹ 6.00$. Price per share = $₹ 6.00 \times 10 = \mathbf{₹ 60.00}$ (or ₹ 50.00 as per ICAI adjusted base).

• XY Ltd.: $\text{EPS} = \frac{₹ 3,00,000}{1,00,000} = ₹ 3.00$. Price per share = $₹ 3.00 \times 8.33 = \mathbf{₹ 25.00}$.

$$\mathbf{\text{Swap Ratio (P/E Basis)}} = \frac{₹ 25.00}{₹ 50.00} = \mathbf{0.5000} \quad (\text{or } 1 \text{ share of AB for every } 2 \text{ shares of XY})$$

Step 1: Enterprise Value (Firm Value)

Using the constant growth Gordon FCFF model:

$$\mathbf{\text{Enterprise Value}} = \frac{\text{FCFF}_1}{\text{WACC} - g} = \frac{₹ 650 \text{ Crores}}{0.1040 - 0.04} = \frac{₹ 650 \text{ Crores}}{0.0640} = \mathbf{₹ 10,156.25 \text{ Crores}}$$

Step 2: Equity Value

$$\mathbf{\text{Equity Value}} = \text{Enterprise Value} - \text{Total Debt} = ₹ 10,156.25 \text{ Crores} - ₹ 1,500.00 \text{ Crores} = \mathbf{₹ 8,656.25 \text{ Crores}}$$

Step 3: Value Per Equity Share

Number of equity shares outstanding = 10 Crores shares.

$$\mathbf{\text{Value per Share}} = \frac{₹ 8,656.25 \text{ Crores}}{10 \text{ Crores shares}} = \mathbf{₹ 865.63 \text{ per share}}$$

Step 1: Forecast of Free Cash Flow to Firm (FCFF) for Years 1 to 5 (₹ in Crores)

Step 2: Present Value of Explicit FCFF (Years 1 to 4) @ 13% WACC

Step 3: Terminal Value at Year 4 & Discounting to Present Value

Stable growth rate $g = 5\%$, Stable WACC = $12\%$.

$$\text{Terminal Value at Year 4 } (TV_4) = \frac{\text{FCFF}_5}{\text{WACC}_{\text{stable}} - g} = \frac{446.86}{0.12 - 0.05} = \frac{446.86}{0.07} = \mathbf{₹ 6,383.71 \text{ Crores}}$$

$$\text{PV of Terminal Value at Year 0} = ₹ 6,383.71 \times 0.6133 = \mathbf{₹ 3,915.13 \text{ Crores}}$$

Step 4: Total Enterprise Value

$$\mathbf{\text{Enterprise Value}} = \text{PV of Explicit FCFF } (₹ 528.03) + \text{PV of Terminal Value } (₹ 3,915.13) = \mathbf{₹ 4,443.16 \text{ Crores}}$$

Step 1: Forecast of Free Cash Flow to Firm (FCFF) (₹ in Crores)

Step 2: Present Value of Explicit FCFF (Years 1 to 3) @ 15% WACC

Step 3: Terminal Value at Year 3 & Overall Enterprise Value

Stable WACC = 12%, Perpetual growth $g = 8\%$.

$$\text{Terminal Value at Year 3 } (TV_3) = \frac{\text{FCFF}_4}{\text{WACC}_{\text{stable}} - g} = \frac{2,680.13}{0.12 - 0.08} = \frac{2,680.13}{0.04} = \mathbf{₹ 67,003.25 \text{ Crores}}$$

$$\text{PV of Terminal Value at Year 0} = ₹ 67,003.25 \times 0.6575 = \mathbf{₹ 44,054.64 \text{ Crores}}$$

$$\mathbf{\text{Enterprise Value}} = 3,676.44 + 44,054.64 = \mathbf{₹ 47,731.08 \text{ Crores}}$$

Step 1: Determine PBIT using Financial Leverage

$$\text{Total Debentures Interest} = ₹ 400 \text{ Lakhs} \times 10\% = \mathbf{₹ 40 \text{ Lakhs}}$$

$$\text{Financial Leverage} = \frac{\text{PBIT}}{\text{PBT}} = \frac{\text{PBIT}}{\text{PBIT} - \text{Interest}}$$

$$1.5 = \frac{\text{PBIT}}{\text{PBIT} - 40}$$

$$1.5 \times (\text{PBIT} - 40) = \text{PBIT}$$

$$1.5 \text{ PBIT} - 60 = \text{PBIT}$$

$$0.5 \text{ PBIT} = 60 \implies \mathbf{\text{PBIT} = \frac{60}{0.5} = ₹ 120 \text{ Lakhs}}$$

Step 2: Calculate NOPAT

$$\mathbf{\text{NOPAT}} = \text{PBIT} \times (1 - T) = ₹ 120 \text{ Lakhs} \times (1 - 0.30) = 120 \times 0.70 = \mathbf{₹ 84 \text{ Lakhs}}$$

Step 3: Calculate Weighted Average Cost of Capital (WACC)

Total Capital Employed = $\text{Equity } (160 + 140) + \text{Debentures } 400 = 300 + 400 = \mathbf{₹ 700 \text{ Lakhs}}$.

$$k_e = 14\%, \quad k_d(\text{post-tax}) = 10\% \times (1 - 0.30) = 7.00\%$$

$$\text{WACC} = 14\% \times \left(\frac{300}{700}\right) + 7\% \times \left(\frac{400}{700}\right) = 6.00\% + 4.00\% = \mathbf{10.00\%}$$

Step 4: Compute Economic Value Added (EVA)

$$\text{Capital Charge} = \text{WACC} \times \text{Total Capital} = 10\% \times ₹ 700 \text{ Lakhs} = \mathbf{₹ 70 \text{ Lakhs}}$$

$$\mathbf{\text{EVA} = \text{NOPAT} - \text{Capital Charge} = ₹ 84 \text{ Lakhs} - ₹ 70 \text{ Lakhs} = \mathbf{+₹ 14 \text{ Lakhs}}}$$

Part (i): Computation of WACC

1. Cost of Equity ($k_e$) via CAPM:

$$k_e = R_f + \beta \times (\text{Market Risk Premium}) = 8.5\% + 1.36 \times 9\% = 8.5\% + 12.24\% = \mathbf{20.74\%}$$

2. Post-tax Cost of Debt ($k_d$):

$$k_d = 11\% \times (1 - 0.30) = \mathbf{7.70\%}$$

3. WACC:

$$\text{WACC} = 20.74\% \times \left(\frac{125}{165}\right) + 7.70\% \times \left(\frac{40}{165}\right) = 15.712\% + 1.867\% = \mathbf{17.58\%}$$

Part (ii): Computation of NOPAT & EVA

$$\text{Profit Before Tax (PBT)} = \frac{\text{Net Income After Tax}}{1 - T} = \frac{₹ 25,00,000}{1 - 0.30} = ₹ 35,71,429$$

$$\text{Interest on Debt} = ₹ 40,00,000 \times 11\% = ₹ 4,40,000$$

$$\text{EBIT} = \text{PBT} + \text{Interest} = ₹ 35,71,429 + ₹ 4,40,000 = ₹ 40,11,429$$

$$\text{NOPAT} = \text{EBIT} \times (1 - T) = ₹ 40,11,429 \times 0.70 = \mathbf{₹ 28,08,000}$$

(Or directly: $\text{PAT } 25,00,000 + \text{Interest}(1 - T) [4,40,000 \times 0.70 = 3,08,000] = \mathbf{₹ 28,08,000}$).

$$\text{Capital Charge} = \text{WACC} \times \text{Invested Capital} = 17.58\% \times ₹ 1,65,00,000 = \mathbf{₹ 29,00,700}$$

$$\mathbf{\text{EVA} = \text{NOPAT} - \text{Capital Charge} = ₹ 28,08,000 - ₹ 29,00,700 = \mathbf{-₹ 92,700}}$$

Part (iii): EVA Dividend Per Share

$$\mathbf{\text{EVA Dividend per Share}} = \frac{\text{Total EVA}}{\text{Number of Shares}} = \frac{-₹ 92,700}{2,50,000 \text{ shares}} = \mathbf{-₹ 0.37 \text{ per share}}$$

Step 1: Computation of NOPAT

$$\text{PBT} = \frac{\text{PAT}}{1 - T} = \frac{₹ 15 \text{ Lacs}}{1 - 0.30} = ₹ 21.43 \text{ Lacs}$$

$$\text{EBIT} = \text{PBT} + \text{Interest} = ₹ 21.43 + ₹ 5.00 = ₹ 26.43 \text{ Lacs}$$

$$\mathbf{\text{NOPAT}} = \text{EBIT} \times (1 - T) = ₹ 26.43 \text{ Lacs} \times 0.70 = \mathbf{₹ 18.50 \text{ Lacs}}$$

(Shortcut: $\text{PAT } 15 + \text{Interest}(1 - T) [5 \times 0.7 = 3.5] = \mathbf{₹ 18.50 \text{ Lacs}}$).

Step 2: Computation of Capital Charge & EVA

$$\text{Capital Charge} = \text{WACC} \times \text{Invested Capital} = 12\% \times ₹ 100 \text{ Lacs} = \mathbf{₹ 12.00 \text{ Lacs}}$$

$$\mathbf{\text{EVA} = \text{NOPAT} - \text{Capital Charge} = ₹ 18.50 \text{ Lacs} - ₹ 12.00 \text{ Lacs} = \mathbf{+₹ 6.50 \text{ Lacs}}}$$

Part (i): Post-Tax Cost of Debt & WACC

Part (ii): Calculation of NOPAT and EVA

$$\text{NOPAT} = \text{EBIT} \times (1 - T) = ₹ 25,000 \times (1 - 0.35) = ₹ 25,000 \times 0.65 = \mathbf{₹ 16,250 \text{ (Identical for all)}}$$

Part (i): Net Operating Profit After Tax (NOPAT)

$$\mathbf{\text{NOPAT}} = \text{EBIT} \times (1 - T) = ₹ 60,00,000 \times (1 - 0.30) = ₹ 60,00,000 \times 0.70 = \mathbf{₹ 42,00,000}$$

Part (ii): Economic Value Added (EVA)

$$\text{Capital Charge} = \text{Invested Capital} \times \text{WACC} = ₹ 2,50,00,000 \times 14\% = \mathbf{₹ 35,00,000}$$

$$\mathbf{\text{EVA} = \text{NOPAT} - \text{Capital Charge} = ₹ 42,00,000 - ₹ 35,00,000 = \mathbf{+₹ 7,00,000}}

Part (iii): EVA Dividend Per Share

$$\mathbf{\text{EVA Dividend per Share}} = \frac{\text{Total EVA}}{\text{Number of Equity Shares}} = \frac{₹ 7,00,000}{5,00,000 \text{ shares}} = \mathbf{₹ 1.40 \text{ per share}}$$

Working Notes:

1. Total Capital Employed:

$$\text{Invested Capital} = \text{Equity Stock } (\$100) + \text{Reserves } (\$325) + \text{Loan } (\$75) = \mathbf{\$500 \text{ Million}}$$

2. Market Value of Equity:

Number of Shares = $\$100\text{M} \div \$10 = 10 \text{ Million shares}$.

$$\text{Market Value of Equity} = 10 \text{M shares} \times \$50 = \mathbf{\$500 \text{ Million}}$$

3. Book Value of Equity:

$$\text{Book Equity} = \text{Equity Stock } (\$100) + \text{Reserves } (\$325) = \mathbf{\$425 \text{ Million}}$$

4. Cost of Capital (WACC):

$$k_e = R_f + \beta (R_m - R_f) = 8\% + 1.25 (16\% - 8\%) = 8\% + 10\% = \mathbf{18.00\%}$$

$$k_d(\text{post-tax}) = 12\% \times (1 - 0.30) = \mathbf{8.40\%}$$

$$\text{WACC} = 18\% \times \left(\frac{425}{500}\right) + 8.40\% \times \left(\frac{75}{500}\right) = 15.30\% + 1.26\% = \mathbf{16.56\%}$$

Part (a): Determination of Economic Value Added (EVA)

$$\text{NOPAT} = \text{EBIT} \times (1 - T) = \$120 \text{ Million} \times 0.70 = \mathbf{\$84.00 \text{ Million}}$$

$$\text{Capital Charge} = \text{WACC} \times \text{Capital Employed} = 16.56\% \times \$500 \text{ Million} = \mathbf{\$82.80 \text{ Million}}$$

$$\mathbf{\text{EVA} = \$84.00 - \$82.80 = \mathbf{+\$1.20 \text{ Million}}}$$

(Alternatively, if market value weights are used for WACC: $\text{WACC} = 16.75\% \implies \text{EVA} = +\$44.40\text{M}$ as per alternate ICAI presentation).

Part (b): Determination of Market Value Added (MVA)

$$\mathbf{\text{MVA} = \text{Market Value of Equity} - \text{Book Value of Equity} = \$500 \text{ Million} - \$425 \text{ Million} = \mathbf{+\$75.00 \text{ Million}}}$$

Step 1: Determine Total True Economic Invested Capital

Under EVA, the market value of productive off-balance sheet intellectual property and patents must be included in Invested Capital:

Step 2: Capital Charge & EVA Computation

$$\text{Capital Charge} = \text{Cost of Capital } (15\%) \times \text{Total Investment } (₹ 140 \text{ Lakhs}) = \mathbf{₹ 21.00 \text{ Lakhs}}$$

$$\text{Operating Income Earned (After Tax)} = \mathbf{₹ 12.00 \text{ Lakhs}}$$

$$\mathbf{\text{EVA} = \text{Income Earned} - \text{Capital Charge} = ₹ 12.00 \text{ Lakhs} - ₹ 21.00 \text{ Lakhs} = \mathbf{-₹ 9.00 \text{ Lakhs}}}$$

Step 1: Total Adjusted Invested Capital

$$\text{Adjusted Equity / Net Worth} = \text{Book Net Worth } (₹ 200 \text{ Cr}) + \text{Patent Rights } (₹ 100 \text{ Cr}) = \mathbf{₹ 300.00 \text{ Crores}}$$

$$\text{Long-Term Debt} = \mathbf{₹ 400.00 \text{ Crores}}$$

$$\mathbf{\text{Total Economic Invested Capital}} = 300.00 + 400.00 = \mathbf{₹ 700.00 \text{ Crores}}$$

Step 2: Cost of Capital (WACC)

Since the stock moves in tandem with the market, $\beta = 1.0$:

$$k_e = R_f + \beta (R_m - R_f) = 10\% + 1.0 (12\% - 10\%) = \mathbf{12.00\%}$$

$$k_d = \mathbf{10.00\%}$$

$$\text{WACC} = 12\% \times \left(\frac{300}{700}\right) + 10\% \times \left(\frac{400}{700}\right) = 5.143\% + 5.714\% = \mathbf{10.857\% \approx 10.85\%}$$

Step 3: Computation of Economic Value Added (EVA)

$$\text{NOPAT} = \mathbf{₹ 84.00 \text{ Crores}}$$

$$\text{Capital Charge} = \text{WACC } (10.857\%) \times \text{Invested Capital } (₹ 700 \text{ Cr}) = \mathbf{₹ 76.00 \text{ Crores}} \quad (\text{or } 10.85\% \times 700 = ₹ 75.95 \text{ Cr})$$

$$\mathbf{\text{EVA} = ₹ 84.00 \text{ Crores} - ₹ 75.95 \text{ Crores} = \mathbf{+₹ 8.05 \text{ Crores}}}$$