Dean's Office Official Model Question Paper

Answer:

Shareholder Wealth Maximization (maximizing common stock price) is superior because:

1. Considers Timing of Cash Flows: It accounts for the time value of money, whereas profit maximization ignores when cash is received.
2. Incorporates Risk and Uncertainty: Stock price explicitly reflects the riskiness of cash flow streams and corporate leverage.
3. Focuses on Free Cash Flows: It evaluates actual realizable cash generation rather than easily manipulated accounting net income.

Answer:

Agency Problem: The inherent conflict of interest arising between corporate managers (agents) and shareholders (principals) when self-interested managers pursue personal perquisites, empire-building, or risk avoidance at the expense of shareholder value.

Mitigation Mechanisms:

1. Performance-Tied Compensation: Aligning executive incentives via stock options (ESOPs) and restricted equity grants tied to long-term stock performance.
2. Independent Board Oversight & Threat of Takeover: Vigilant independent audit committees and the market threat of hostile corporate takeovers for underperforming boards.

Solution:

Perpetuity: A perpetual annuity that delivers an identical periodic cash flow ($PMT$) indefinitely without a maturity date.

$$\text{PV of Perpetuity} = \frac{PMT}{r}$$

Given $PMT = \text{Rs. } 60{,}000$ and $r = 0.08$:

$$\text{PV} = \frac{60{,}000}{0.08} = \mathbf{750{,}000 \text{ Rs.}}$$

The present value of the perpetual cash flow is Rs. 750,000.

Solution:

Formula for the Effective Annual Rate:

$$\text{EAR} = \left(1 + \frac{r_{\text{nom}}}{m}\right)^m - 1$$

Where nominal rate $r_{\text{nom}} = 0.12$ and compounding frequency $m = 4$:

$$\text{EAR} = \left(1 + \frac{0.12}{4}\right)^4 - 1 = (1 + 0.03)^4 - 1 = (1.03)^4 - 1 = 1.12551 - 1 = \mathbf{0.1255} \quad (\text{or } \mathbf{12.55\%})$$

The effective annual rate is 12.55%.

Answer:

• Diversifiable Risk (Unsystematic Risk): Risk unique to a single company or industry (e.g., product recall, lawsuit, management strikes). It can be completely eliminated at zero cost by holding a well-diversified portfolio of 25–30 uncorrelated securities.
• Non-Diversifiable Risk (Systematic / Market Risk): Macroeconomic risk affecting all corporate issuers simultaneously (e.g., GDP recessions, interest rate hikes, war, inflation). It cannot be eliminated through diversification and is measured by Beta ($\beta$).

Solution:

The CAPM equation is:

$$E(R_i) = R_f + \beta_i \left[E(R_m) - R_f\right]$$

Given:

• $R_f = 6\%$
• $E(R_m) = 14\%$
• $\beta_i = 1.25$
• Market Risk Premium $[E(R_m) - R_f] = 14\% - 6\% = 8\%$$E(R_i) = 6\% + 1.25 \times (8\%) = 6\% + 10\% = \mathbf{16.00\%}$$

The investor’s required rate of return for the stock is 16.00%.

Answer:

Yield to Maturity (YTM): The internal rate of return earned by an investor who purchases a bond at its current market price and holds it until maturity, assuming all scheduled coupon payments and par redemption values are received and reinvested at the same YTM rate.

Answer:

NPV is theoretically superior because:

1. Realistic Reinvestment Rate Assumption: NPV assumes intermediate project cash flows are reinvested at the firm’s realistic cost of capital ($WACC$), whereas IRR assumes reinvestment at the project’s own internal rate of return (which may be unrealistically high).
2. Avoids Multiple Rates & Scale Distortions: NPV always provides a unique dollar measure of absolute wealth added, avoiding the multiple-IRR problem of non-conventional cash flows and scale bias.

Answer:

Because interest payments on debt obligations are tax-deductible expenses under corporate tax laws. The government effectively subsidizes a fraction equal to the corporate tax rate ($t$), lowering the net cash cost of debt to the firm:

$$\text{After-Tax Cost of Debt} = r_d \times (1 - t)$$

Answer:

Cash Conversion Cycle (CCC): The length of time in days that elapses between the firm’s actual cash disbursement for raw materials and the final cash realization from the collection of receivables.

Mathematical Formula:

$$CCC = \text{Inventory Conversion Period (ICP)} + \text{Receivables Collection Period (RCP)} - \text{Payables Deferral Period (PDP)}$$

Solution:

Given:

• Principal ($PV$) = Rs. 1,000,000
• Annual Interest Rate ($r$) = 12% ($0.12$)
• Number of Payments ($n$) = 4 years

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Part (a): Equal Annual Payment ($PMT$)

The formula for the present value of an ordinary annuity is:

$$PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right] = PMT \times PVIFA_{r, n}$$

$$PVIFA_{12\%, 4} = \frac{1 - (1.12)^{-4}}{0.12} = \frac{1 - 0.635518}{0.12} = \frac{0.364482}{0.12} \approx 3.03735$$

$$PMT = \frac{1{,}000{,}000}{3.03735} \approx \mathbf{329{,}234.45 \text{ Rs.}}$$

The equal annual installment is Rs. 329,234.45.

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Part (b): Loan Amortization Schedule

*Adjusted by Rs. 0.06 for rounding precision.

The total interest paid over 4 years is Rs. 316,937.74 on the principal of Rs. 1,000,000.

Solution:

Given:

• $w_A = 0.60, \quad E(R_A) = 12\%, \quad \sigma_A = 15\%$
• $w_B = 0.40, \quad E(R_B) = 18\%, \quad \sigma_B = 25\%$
• Correlation coefficient $r_{AB} = 0.20$

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Part (a): Expected Return of the Portfolio ($E(R_p)$)

$$E(R_p) = w_A E(R_A) + w_B E(R_B) = (0.60 \times 12\%) + (0.40 \times 18\%)$$

$$E(R_p) = 7.2\% + 7.2\% = \mathbf{14.40\%}$$

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Part (b): Standard Deviation of the Portfolio ($\sigma_p$)

$$\sigma_p = \sqrt{w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \sigma_A \sigma_B r_{AB}}$$

Compute individual terms:

• $w_A^2 \sigma_A^2 = (0.60)^2 \times (15)^2 = 0.36 \times 225 = 81.00$
• $w_B^2 \sigma_B^2 = (0.40)^2 \times (25)^2 = 0.16 \times 625 = 100.00$
• $2 w_A w_B \sigma_A \sigma_B r_{AB} = 2(0.60)(0.40)(15)(25)(0.20) = 0.48 \times 375 \times 0.20 = 36.00$$\text{Portfolio Variance } (\sigma_p^2) = 81.00 + 100.00 + 36.00 = 217.00$$
  $$\sigma_p = \sqrt{217.00} \approx \mathbf{14.73\%}$$

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Part (c): Diversification Effect Analysis

Weighted average risk without diversification benefit:

$$\bar{\sigma} = w_A \sigma_A + w_B \sigma_B = (0.60 \times 15\%) + (0.40 \times 25\%) = 9\% + 10\% = \mathbf{19.00\%}$$

$$\text{Risk Reduction (Diversification Benefit)} = 19.00\% - 14.73\% = \mathbf{4.27\%}$$

Interpretation: Because the correlation coefficient is less than 1 ($r_{AB} = 0.20 < 1.0$), portfolio risk ($\sigma_p = 14.73\%$) is significantly lower than the weighted average risk ($19.00\%$) and is even lower than the risk of Stock A alone ($15\%$). This confirms Markowitz’s principle of portfolio diversification: combining imperfectly correlated assets eliminates firm-specific variance without sacrificing proportionate expected return.

Solution:

Given:

• Par Value ($M$) = Rs. 1,000
• Annual Coupon ($I$) = $10\% \times 1{,}000 = \text{Rs. } 100$
• Maturity ($n$) = 8 years

Bond valuation formula:

$$V_d = I \times PVIFA_{k_d, n} + M \times PVIF_{k_d, n}$$

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Part (a): Intrinsic Values

Case (i): Required Yield $k_d = 8\%$$PVIFA_{8\%, 8} = \frac{1 - (1.08)^{-8}}{0.08} = \frac{1 - 0.540269}{0.08} = 5.7466$$

$$PVIF_{8\%, 8} = (1.08)^{-8} = 0.5403$$

$$V_d = (100 \times 5.7466) + (1{,}000 \times 0.5403) = 574.66 + 540.30 = \mathbf{1{,}114.96 \text{ Rs.}}$$

(The bond trades at a Premium of Rs. 114.96).

Case (ii): Required Yield $k_d = 10\%$$PVIFA_{10\%, 8} = \frac{1 - (1.10)^{-8}}{0.10} = 5.3349$$

$$PVIF_{10\%, 8} = (1.10)^{-8} = 0.4665$$

$$V_d = (100 \times 5.3349) + (1{,}000 \times 0.4665) = 533.49 + 466.50 = \mathbf{1{,}000.00 \text{ Rs.}}$$

(The bond trades At Par).

Case (iii): Required Yield $k_d = 12\%$$PVIFA_{12\%, 8} = \frac{1 - (1.12)^{-8}}{0.12} = 4.9676$$

$$PVIF_{12\%, 8} = (1.12)^{-8} = 0.4039$$

$$V_d = (100 \times 4.9676) + (1{,}000 \times 0.4039) = 496.76 + 403.90 = \mathbf{900.66 \text{ Rs.}}$$

(The bond trades at a Discount of Rs. 99.34).

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Part (b): The Fundamental Bond Pricing Theorems

1. When $k_d < \text{Coupon Rate}$ ($8\% < 10\%$): Bond Price $>$ Par Value (Premium Bond).
2. When $k_d = \text{Coupon Rate}$ ($10\% = 10\%$): Bond Price = Par Value (Par Bond).
3. When $k_d > \text{Coupon Rate}$ ($12\% > 10\%$): Bond Price $<$ Par Value (Discount Bond).
4. Inverse Price-Yield Relationship: Bond prices are inversely related to market interest rates (YTM). As market yield rises, bond market price falls.

Solution:

Given:

• Recent dividend paid ($D_0$) = Rs. 20
• Constant growth rate ($g$) = 7% ($0.07$)
• Stock Beta ($\beta$) = 1.20
• Risk-free rate ($R_f$) = 5% ($0.05$)
• Market return ($E(R_m)$) = 15% ($0.15$)
• Current Market Price ($P_0$) = Rs. 350

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Part (a): Investor’s Required Rate of Return ($r_s$) via CAPM

$$r_s = R_f + \beta \left[E(R_m) - R_f\right] = 5\% + 1.20 \times (15\% - 5\%)$$

$$r_s = 5\% + 1.20(10\%) = 5\% + 12\% = \mathbf{17.00\%} \quad (\text{or } 0.17)$$

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Part (b): Intrinsic Value of Common Stock ($\hat{P}_0$)

Expected dividend for next year ($D_1$):

$$D_1 = D_0(1 + g) = 20(1 + 0.07) = \text{Rs. } 21.40$$

Using the Gordon Constant Growth Dividend Discount Model:

$$\hat{P}_0 = \frac{D_1}{r_s - g} = \frac{21.40}{0.17 - 0.07} = \frac{21.40}{0.10} = \mathbf{214.00 \text{ Rs.}}$$

The estimated intrinsic value of the stock is Rs. 214.00 per share.

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Part (c): Market Valuation and Investment Recommendation

• Current Market Price ($P_0$) = Rs. 350.00
• Intrinsic Value ($\hat{P}_0$) = Rs. 214.00

$$\text{Valuation Status: } P_0 (\text{Rs. } 350) > \hat{P}_0 (\text{Rs. } 214)$$

Interpretation & Advice: The stock is substantially overvalued in the secondary market (trading at a 63.5% premium above its intrinsic fundamental value). Recommendation: An investor should NOT buy the stock at current market prices. Current shareholders should consider selling (or short-selling) the stock before market prices correct downward toward fundamental value.

Solution:

Given:

• Annual Sales = Rs. 36,000,000
• Cost of Goods Sold ($COGS$) = Rs. 27,000,000
• Annual Credit Purchases = Rs. 18,000,000
• Average Inventory = Rs. 3,000,000
• Average Receivables = Rs. 4,500,000
• Average Payables = Rs. 2,500,000
• Operating Days per year = 360 days

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Part (a): Inventory Conversion Period ($ICP$)

$$ICP = \frac{\text{Average Inventory}}{COGS / 360} = \frac{3{,}000{,}000}{27{,}000{,}000 / 360} = \frac{3{,}000{,}000}{75{,}000} = \mathbf{40.00 \text{ days}}$$

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Part (b): Receivables Collection Period ($RCP$)

$$RCP = \frac{\text{Average Receivables}}{\text{Annual Credit Sales} / 360} = \frac{4{,}500{,}000}{36{,}000{,}000 / 360} = \frac{4{,}500{,}000}{100{,}000} = \mathbf{45.00 \text{ days}}$$

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Part (c): Payables Deferral Period ($PDP$)

$$PDP = \frac{\text{Average Payables}}{\text{Annual Purchases} / 360} = \frac{2{,}500{,}000}{18{,}000{,}000 / 360} = \frac{2{,}500{,}000}{50{,}000} = \mathbf{50.00 \text{ days}}$$

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Part (d): Cash Conversion Cycle ($CCC$)

$$CCC = ICP + RCP - PDP = 40 + 45 - 50 = \mathbf{35.00 \text{ days}}$$

Interpretation: The firm requires 35 days to convert its cash outflows for raw materials back into realized cash collections from customer sales. During this 35-day financing gap, the company must fund its operating cycle via bank overdrafts or short-term working capital lines.

Solution:

Given:

• Weight of Debt ($w_d$) = 0.40, Pre-tax cost $r_d = 10\%$, Tax rate $t = 25\%$ ($0.25$)
• Weight of Preferred Stock ($w_p$) = 0.10, Cost $r_p = 9\%$
• Weight of Common Equity ($w_e$) = 0.50, $P_0 = \text{Rs. } 400, D_1 = \text{Rs. } 24, g = 6\%$

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Part (a): After-Tax Cost of Debt ($r_d^*$)

$$r_d^* = r_d \times (1 - t) = 10\% \times (1 - 0.25) = 10\% \times 0.75 = \mathbf{7.50\%}$$

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Part (b): Component Costs of Equity

1. Cost of Preferred Stock ($r_p$):
   $$r_p = \mathbf{9.00\%}$$
2. Cost of Common Equity ($r_s$) via Gordon Model:
   $$r_s = \frac{D_1}{P_0} + g = \frac{24}{400} + 0.06 = 0.06 + 0.06 = 0.12 = \mathbf{12.00\%}$$

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Part (c): Weighted Average Cost of Capital ($WACC$)

$$WACC = (w_d \times r_d^*) + (w_p \times r_p) + (w_e \times r_s)$$

$$WACC = (0.40 \times 7.50\%) + (0.10 \times 9.00\%) + (0.50 \times 12.00\%)$$

$$WACC = 3.00\% + 0.90\% + 6.00\% = \mathbf{9.90\%}$$

The firm’s overall Weighted Average Cost of Capital is 9.90%.

Solution:

Initial Outlay: $I_0 = \text{Rs. } 3{,}000{,}000$ for both projects. Discount rate $k = 10\%$.

Part (a): Payback Period

1. Project Alpha Cumulative Cash Flows:

   • Year 1: Rs. 1,200,000
   • Year 2: $1{,}200{,}000 + 1{,}100{,}000 = \text{Rs. } 2{,}300{,}000$
   • Year 3: $2{,}300{,}000 + 900{,}000 = \text{Rs. } 3{,}200{,}000$$\text{Payback}_{\text{Alpha}} = 2 + \frac{3{,}000{,}000 - 2{,}300{,}000}{900{,}000} = 2 + \frac{700{,}000}{900{,}000} \approx \mathbf{2.78 \text{ years}}$$

2. Project Beta Cumulative Cash Flows:

   • Year 1: Rs. 400,000
   • Year 2: $400{,}000 + 800{,}000 = \text{Rs. } 1{,}200{,}000$
   • Year 3: $1{,}200{,}000 + 1{,}200{,}000 = \text{Rs. } 2{,}400{,}000$
   • Year 4: $2{,}400{,}000 + 1{,}500{,}000 = \text{Rs. } 3{,}900{,}000$$\text{Payback}_{\text{Beta}} = 3 + \frac{3{,}000{,}000 - 2{,}400{,}000}{1{,}500{,}000} = 3 + \frac{600{,}000}{1{,}500{,}000} = \mathbf{3.40 \text{ years}}$$

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Part (b) & (c): NPV and Profitability Index (PI @ 10%)

Profitability Index ($PI = \frac{\text{Total PV}}{\text{Initial Outlay}}$):

• Project Alpha: $PI = \frac{3{,}402{,}590}{3{,}000{,}000} = \mathbf{1.134}$
• Project Beta: $PI = \frac{3{,}944{,}260}{3{,}000{,}000} = \mathbf{1.315}$

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Part (d): Internal Rate of Return (IRR)

1. For Project Alpha:

   • At 10%: NPV = +Rs. 402,590
   • At 18%:
     $$\text{PV} = 1{,}200{,}000(0.8475) + 1{,}100{,}000(0.7182) + 900{,}000(0.6086) + 700{,}000(0.5158) + 400{,}000(0.4371)$$
     $$\text{PV} = 1{,}017{,}000 + 790{,}020 + 547{,}740 + 361{,}060 + 174{,}840 = 2{,}890{,}660 \implies \text{NPV}_{18\%} = -109{,}340$$
     $$\text{IRR}_{\text{Alpha}} = 10\% + \frac{402{,}590}{402{,}590 - (-109{,}340)} \times (18\% - 10\%) = 10\% + \left(\frac{402{,}590}{511{,}930}\right) \times 8\% \approx \mathbf{16.29\%}$$

2. For Project Beta:

   • At 10%: NPV = +Rs. 944,260
   • At 20%:
     $$\text{PV} = 400{,}000(0.8333) + 800{,}000(0.6944) + 1{,}200{,}000(0.5787) + 1{,}500{,}000(0.4823) + 1{,}600{,}000(0.4019)$$
     $$\text{PV} = 333{,}320 + 555{,}520 + 694{,}440 + 723{,}450 + 643{,}040 = 2{,}949{,}770 \implies \text{NPV}_{20\%} = -50{,}230$$
     $$\text{IRR}_{\text{Beta}} = 10\% + \frac{944{,}260}{944{,}260 - (-50{,}230)} \times (20\% - 10\%) = 10\% + \left(\frac{944{,}260}{994{,}490}\right) \times 10\% \approx \mathbf{19.49\%}$$

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Part (e): Final Evaluation and Recommendation

Recommendation: Although Project Alpha features a shorter payback period, for mutually exclusive decisions, Project Beta should be selected. Project Beta yields a dramatically higher Net Present Value (Rs. 944,260 vs Rs. 402,590), a superior Profitability Index (1.315), and a higher IRR (19.49%). Accepting Project Beta maximizes absolute shareholder wealth.

Solution:

Given:

• Output ($Q$) = 100,000 units
• Selling Price ($P$) = Rs. 50
• Variable Cost ($V$) = Rs. 30
• Unit Contribution Margin ($P - V$) = Rs. 20
• Fixed Operating Costs ($FC$) = Rs. 1,000,000
• 10% Debt = Rs. 1,500,000 $\implies$ Annual Interest ($I$) = $1{,}500{,}000 \times 10\% = \text{Rs. } 150{,}000$
• Tax rate ($t$) = 25% ($0.25$)
• Common shares ($N$) = 50,000 shares

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Step 1: Base Income Calculation

• Total Sales ($TR$) = $100{,}000 \times 50 = \text{Rs. } 5{,}000{,}000$
• Variable Costs ($TVC$) = $100{,}000 \times 30 = \text{Rs. } 3{,}000{,}000$
• Total Contribution ($S - V$) = $5{,}000{,}000 - 3{,}000{,}000 = \text{Rs. } 2{,}000{,}000$
• $EBIT = \text{Contribution} - FC = 2{,}000{,}000 - 1{,}000{,}000 = \mathbf{1{,}000{,}000 \text{ Rs.}}$
• Less Interest: $1{,}000{,}000 - 150{,}000 = EBT = \text{Rs. } 850{,}000$
• Less Taxes (25%): $850{,}000 \times 0.25 = \text{Rs. } 212{,}500 \implies EAT = \mathbf{637{,}500 \text{ Rs.}}$
• Base $EPS = \frac{637{,}500}{50{,}000} = \mathbf{12.75 \text{ Rs./share}}$

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Step 2: Leverage Calculations

1. Degree of Operating Leverage ($DOL$):

   $$DOL = \frac{\text{Contribution}}{EBIT} = \frac{2{,}000{,}000}{1{,}000{,}000} = \mathbf{2.00}$$

2. Degree of Financial Leverage ($DFL$):

   $$DFL = \frac{EBIT}{EBIT - I} = \frac{1{,}000{,}000}{1{,}000{,}000 - 150{,}000} = \frac{1{,}000{,}000}{850{,}000} \approx \mathbf{1.1765}$$

3. Degree of Total Leverage ($DTL$):

   $$DTL = \frac{\text{Contribution}}{EBIT - I} = \frac{2{,}000{,}000}{850{,}000} \approx \mathbf{2.353}$$

Verification:

$$DOL \times DFL = 2.00 \times 1.1765 = \mathbf{2.353}$$

The mathematical equality is confirmed.

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Step 3: Impact of 20% Increase in Sales ($\Delta \text{Sales} = +20\%$)

1. Percentage Change in EBIT:

   $$\%\Delta EBIT = DOL \times \%\Delta \text{Sales} = 2.00 \times 20\% = \mathbf{+40.00\%}$$
   $$\text{New } EBIT = 1{,}000{,}000 \times (1 + 0.40) = \mathbf{1{,}400{,}000 \text{ Rs.}}$$

2. Percentage Change in EPS:

   $$\%\Delta EPS = DTL \times \%\Delta \text{Sales} = 2.353 \times 20\% = \mathbf{+47.06\%}$$
   $$\text{New } EPS = 12.75 \times (1 + 0.4706) = \mathbf{18.75 \text{ Rs./share}}$$

Direct Verification:

• New Contribution ($120{,}000 \times 20$): Rs. 2,400,000
• Less $FC$: Rs. 1,000,000 $\implies$ New $EBIT$ = Rs. 1,400,000 (+40%)
• Less Interest: Rs. 150,000 $\implies$ New $EBT$ = Rs. 1,250,000
• Less Taxes (25%): Rs. 312,500 $\implies$ New $EAT$ = Rs. 937,500
• New $EPS = \frac{937{,}500}{50{,}000} = \mathbf{18.75 \text{ Rs./share}}$ (+47.06%)

Answer:

1. The Dividend Policy Controversy

The central debate in corporate finance is whether dividend payout policy influences the market value of common stock ($P_0$).

A. Dividend Relevance School (Walter and Gordon)

• Prof. James E. Walter and Myron Gordon argue that dividend policy directly affects share price because investors prefer current certain dividends over uncertain future capital gains ("Bird-in-the-Hand Theory").
• The relationship between the firm’s Internal Rate of Return ($r$) and Cost of Capital ($k$) dictates optimal payout:
  1. Growth Firm ($r > k$): Retaining earnings yields higher returns than investors can earn elsewhere. Optimal Payout = 0% (Full retention maximizes share price).
  2. Declining Firm ($r < k$): The firm earns less than the market opportunity cost. Optimal Payout = 100% (Full dividend distribution maximizes share price).
  3. Normal Firm ($r = k$): Dividend payout has zero impact on share price.

B. Dividend Irrelevance Hypothesis (Modigliani and Miller - MM)

• Franco Modigliani and Merton Miller (1961) demonstrated that in a perfect capital market (zero taxes, zero transaction costs, symmetric information), dividend policy is completely irrelevant to corporate valuation.
• Firm value is driven solely by its real investment policy and operating earning power, not by how earnings are divided between dividends and retained earnings. Any cash dividend payout is exactly offset by an equal decline in stock price due to dilution from new share issues.

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2. Numerical Application under Walter’s Model

Walter’s Formula:

$$P = \frac{D + \frac{r}{k}(E - D)}{k}$$

Where:

• Earnings Per Share ($E$) = Rs. 15
• Internal Return ($r$) = 14% ($0.14$)
• Cost of Capital ($k$) = 10% ($0.10$)
• Ratio $\frac{r}{k} = \frac{0.14}{0.10} = \mathbf{1.40}$

Since $r (14\%) > k (10\%)$, the enterprise is a Growth Firm. The optimal dividend payout ratio is 0%.

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Computation of Share Price at Different Payout Ratios:

1. Payout Ratio = 0% ($D = 0$):

$$P_0 = \frac{0 + 1.40(15 - 0)}{0.10} = \frac{1.40 \times 15}{0.10} = \frac{21.00}{0.10} = \mathbf{210.00 \text{ Rs.}}$$

2. Payout Ratio = 40% ($D = 40\% \times 15 = \text{Rs. } 6$):

$$P_{40} = \frac{6 + 1.40(15 - 6)}{0.10} = \frac{6 + 1.40(9)}{0.10} = \frac{6 + 12.60}{0.10} = \frac{18.60}{0.10} = \mathbf{186.00 \text{ Rs.}}$$

3. Payout Ratio = 100% ($D = \text{Rs. } 15$):

$$P_{100} = \frac{15 + 1.40(15 - 15)}{0.10} = \frac{15 + 0}{0.10} = \mathbf{150.00 \text{ Rs.}}$$

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Summary and Conclusion:

Because $r > k$, retaining earnings reinvests capital at a superior 14% rate inside the firm compared to the 10% rate shareholders can obtain externally. Consequently, every increase in dividend payout destroys corporate share value, proving Walter’s theorem that 0% is the optimal dividend payout for growth enterprises.