Dean's Office Official Model Question Paper

Answer: EBIT-EPS Indifference Point: The level of Operating Profit (Earnings Before Interest and Taxes, EBIT) at which Earnings Per Share (EPS) remains exactly identical between two competing capital structure financing alternatives (e.g., debt vs. equity).

Algebraic Formula:

$$\frac{(\text{EBIT}^* - I_1)(1 - T) - PD_1}{N_1} = \frac{(\text{EBIT}^* - I_2)(1 - T) - PD_2}{N_2}$$

Where $I$ is annual interest, $T$ is corporate tax rate, $PD$ is preferred dividend, and $N$ is the number of common shares outstanding under each respective financing plan.

Answer:

• Degree of Operating Leverage (DOL): Measures the percentage change in EBIT resulting from a 1% change in sales volume, reflecting the extent of fixed operating costs:
  $$DOL = \frac{\% \Delta \text{EBIT}}{\% \Delta \text{Sales}} = \frac{Q(P - V)}{Q(P - V) - F} = \frac{\text{Contribution Margin}}{\text{EBIT}}$$
• Degree of Financial Leverage (DFL): Measures the percentage change in EPS resulting from a 1% change in EBIT, reflecting fixed contractual financing obligations:
  $$DFL = \frac{\% \Delta \text{EPS}}{\% \Delta \text{EBIT}} = \frac{\text{EBIT}}{\text{EBIT} - I - \frac{PD}{1 - T}}$$

Answer: Both models establish that dividend policy impacts firm valuation when the internal rate of return ($r$) diverges from the cost of capital ($k_e$):

• Walter’s Model: Uses an algebraic capitalization approach: $P = \frac{D + \frac{r}{k_e}(E - D)}{k_e}$. It assumes all investments are funded via retained earnings, dictating 0% payout when $r > k_e$ (growth firm) and 100% payout when $r < k_e$ (declining firm).
• Gordon’s Model: Formulates valuation via discounted cash flows under continuous reinvestment: $P_0 = \frac{D_1}{k_e - br}$, where growth $g = b \times r$. It assumes the retention ratio ($b$) and rate of return ($r$) remain constant, warning that retention reduces value if $r < k_e$.

Answer: Baumol Model: An inventory-theoretic approach to cash management that balances the fixed transaction cost of liquidating marketable securities against the opportunity cost of holding non-interest-bearing idle cash balances under conditions of certainty and steady disbursement.

Formula for Optimal Cash Transfer ($C^*$):

$$C^* = \sqrt{\frac{2 \times T \times F}{k}}$$

Where $T$ is total annual cash requirement, $F$ is fixed transaction cost per transfer, and $k$ is the opportunity cost of capital (holding cost per rupee per annum).

Answer:

Solution: Modigliani-Miller Capital Structure Propositions

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Part (a): MM Proposition I Without Taxes (4 Marks)

1. Value of Unlevered Firm ($V_U$):

$$V_U = \frac{\text{EBIT}}{k_{eU}} = \frac{4,000,000}{0.16} = \mathbf{\text{Rs. } 25,000,000}$$

2. Value of Levered Firm ($V_L$):

Under MM Proposition I (without taxes), capital structure is irrelevant to firm value:

$$V_L = V_U = \mathbf{\text{Rs. } 25,000,000}$$

3. Market Value of Levered Firm’s Equity ($S_L$):

$$S_L = V_L - D = 25,000,000 - 10,000,000 = \mathbf{\text{Rs. } 15,000,000}$$

4. Cost of Levered Equity ($k_{eL}$):

According to MM Proposition II (without taxes):

$$k_{eL} = k_{eU} + (k_{eU} - k_d) \times \frac{D}{S_L}$$

$$k_{eL} = 0.16 + (0.16 - 0.10) \times \frac{10,000,000}{15,000,000} = 0.16 + 0.06 \times 0.6667 = 0.16 + 0.04 = \mathbf{20.00\%}$$

Verification:

$$\text{Net Income to Levered Equity} = \text{EBIT} - I = 4,000,000 - 1,000,000 = \text{Rs. } 3,000,000$$

$$S_L = \frac{\text{Net Income}}{k_{eL}} = \frac{3,000,000}{0.20} = \text{Rs. } 15,000,000 \quad \text{(Exact Match)}$$

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Part (b): Arbitrage Mechanism & Homemade Leverage (3 Marks)

If the market temporarily valued the levered firm higher (say, $V_L = \text{Rs. } 27,000,000 \implies S_L = \text{Rs. } 17,000,000$), an investor owning 10% of Kapilvastu’s equity could execute homemade leverage:

1. Sell Levered Shares: Sell 10% stake in Kapilvastu for $0.10 \times 17,000,000 = \text{Rs. } 1,700,000$.
2. Borrow on Personal Account: Borrow 10% of Kapilvastu’s debt ($0.10 \times 10,000,000 = \text{Rs. } 1,000,000$) at 10% interest.
3. Total Funds Available: $1,700,000 + 1,000,000 = \text{Rs. } 2,700,000$.
4. Buy Unlevered Shares: Purchase a 10% equity stake in Lumbini for $0.10 \times 25,000,000 = \text{Rs. } 2,500,000$.
5. Outcome: The investor pockets Rs. 200,000 in immediate riskless cash while earning the exact same net annual income:
   $$\text{Income from Lumbini} - \text{Personal Interest} = (0.10 \times 4,000,000) - (0.10 \times 1,000,000) = 400,000 - 100,000 = \text{Rs. } 300,000$$
   This selling pressure on Kapilvastu and buying pressure on Lumbini instantly drives prices back until $V_L = V_U$.

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Part (c): MM Proposition I With Corporate Taxes ($T = 30\%$) (3 Marks)

1. Value of Unlevered Firm ($V_U$):

$$V_U = \frac{\text{EBIT}(1 - T)}{k_{eU}} = \frac{4,000,000 \times (1 - 0.30)}{0.16} = \frac{2,800,000}{0.16} = \mathbf{\text{Rs. } 17,500,000}$$

2. Value of Levered Firm ($V_L$):

Under MM Proposition I with corporate taxes:

$$V_L = V_U + (T \times D) = 17,500,000 + (0.30 \times 10,000,000) = 17,500,000 + 3,000,000 = \mathbf{\text{Rs. } 20,500,000}$$

3. Rupee Value of Interest Tax Shield:

$$\text{Annual Tax Shield} = I \times T = (10,000,000 \times 0.10) \times 0.30 = \text{Rs. } 300,000 \text{ per year}$$

$$\text{Present Value of Tax Shield} = \frac{\text{Annual Tax Shield}}{k_d} = \frac{300,000}{0.10} = T \times D = \mathbf{\text{Rs. } 3,000,000}$$

Solution: Financial Leverage & EBIT-EPS Analysis

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Part (a): EBIT-EPS Indifference Point (4 Marks)

1. Shares Outstanding Under Each Plan:

   • Plan I: $N_1 = 200,000 (\text{existing}) + 100,000 (\text{new}) = 300,000 \text{ shares}$
   • Plan II: $N_2 = 200,000 (\text{existing}) + 40,000 (\text{new}) = 240,000 \text{ shares}$

2. Annual Interest Obligations:

   • Plan I: $I_1 = \text{Rs. } 0.00$
   • Plan II: $I_2 = 12\% \times \text{Rs. } 3,000,000 = \text{Rs. } 360,000$

3. Indifference Equation:

   $$\frac{(\text{EBIT}^* - I_1)(1 - T)}{N_1} = \frac{(\text{EBIT}^* - I_2)(1 - T)}{N_2}$$
   $$\frac{(\text{EBIT}^* - 0)(1 - 0.25)}{300,000} = \frac{(\text{EBIT}^* - 360,000)(1 - 0.25)}{240,000}$$
   $$\frac{\text{EBIT}^*}{300,000} = \frac{\text{EBIT}^* - 360,000}{240,000}$$
   $$\frac{\text{EBIT}^*}{5} = \frac{\text{EBIT}^* - 360,000}{4}$$
   $$4 \times \text{EBIT}^* = 5 \times \text{EBIT}^* - 1,800,000$$
   $$\mathbf{\text{EBIT}^* = \text{Rs. } 1,800,000}$$

Verification of EPS at Indifference:

• Plan I: $\text{EPS} = \frac{1,800,000 \times 0.75}{300,000} = \mathbf{\text{Rs. } 4.50}$
• Plan II: $\text{EPS} = \frac{(1,800,000 - 360,000) \times 0.75}{240,000} = \frac{1,440,000 \times 0.75}{240,000} = \mathbf{\text{Rs. } 4.50}$

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Part (b): EPS Comparison at Expected EBIT = Rs. 1,600,000 (3 Marks)

Managerial Decision: Because expected EBIT (Rs. 1,600,000) is below the indifference point (Rs. 1,800,000), Plan I (All Equity) produces a higher EPS (Rs. 4.00 vs. Rs. 3.875) and is financially preferable. Debt financing is advantageous only when EBIT exceeds the indifference threshold.

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Part (c): Degree of Financial Leverage (DFL) (3 Marks)

$$DFL = \frac{\text{EBIT}}{\text{EBIT} - I}$$

• Plan I:

  $$DFL_{\text{Plan I}} = \frac{1,600,000}{1,600,000 - 0} = \mathbf{1.00}$$
  Interpretation: Plan I carries zero financial leverage risk. A 10% change in EBIT causes an identical 10% change in EPS.

• Plan II:

  $$DFL_{\text{Plan II}} = \frac{1,600,000}{1,600,000 - 360,000} = \frac{1,600,000}{1,240,000} = \mathbf{1.29}$$
  Interpretation: Plan II magnifies EPS variability. A 10% decline in EBIT will lead to a 12.9% reduction in EPS due to fixed interest commitments.

Solution: Credit Policy Optimization

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Part (a): Incremental Contribution Margin (3 Marks)

• Incremental Sales = Proposed Sales - Current Sales = $43,200,000 - 36,000,000 = \text{Rs. } 7,200,000$
• Contribution Margin Ratio = $1 - \text{Variable Cost Ratio} = 1 - 0.80 = 20\% = 0.20$$\Delta \text{Contribution Margin} = \text{Rs. } 7,200,000 \times 0.20 = \mathbf{+\text{Rs. } 1,440,000}$$

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Part (b): Savings in Receivables Investment (3 Marks)

1. Investment in Receivables (at Variable Cost):

• Current Policy:

  $$\text{Receivables Turnover} = \frac{360}{60} = 6 \text{ times}$$
  $$\text{Current Investment} = \frac{\text{Sales} \times \text{VC Ratio}}{\text{Turnover}} = \frac{36,000,000 \times 0.80}{6} = \text{Rs. } 4,800,000$$

• Proposed Policy:

  $$\text{New ACP} = (0.50 \times 10 \text{ days}) + (0.50 \times 50 \text{ days}) = 5 + 25 = 30 \text{ days}$$
  $$\text{Proposed Receivables Turnover} = \frac{360}{30} = 12 \text{ times}$$
  $$\text{Proposed Investment} = \frac{43,200,000 \times 0.80}{12} = \text{Rs. } 2,880,000$$

2. Reduction in Investment and Annual Opportunity Savings:

$$\text{Investment Released} = 4,800,000 - 2,880,000 = \text{Rs. } 1,920,000$$

$$\text{Annual Opportunity Cost Savings} = \text{Rs. } 1,920,000 \times 15\% = \mathbf{+\text{Rs. } 288,000}$$

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Part (c): Cash Discount & Bad Debt Analysis (2 Marks)

1. Cost of Cash Discount:

• Eligible Discount Sales = $50\% \times \text{Rs. } 43,200,000 = \text{Rs. } 21,600,000$
• Discount Rate = 2%
  $$\text{Annual Cost of Discount} = \text{Rs. } 21,600,000 \times 0.02 = \mathbf{-\text{Rs. } 432,000}$$

2. Change in Bad Debt Losses:

• Current Bad Debts = $2\% \times \text{Rs. } 36,000,000 = \text{Rs. } 720,000$
• Proposed Bad Debts = $1.5\% \times \text{Rs. } 43,200,000 = \text{Rs. } 648,000$$\text{Savings in Bad Debts} = 720,000 - 648,000 = \mathbf{+\text{Rs. } 72,000}$$

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Part (d): Net Financial Benefit & Managerial Advice (2 Marks)

Recommendation: Bhotekoshi Textiles Ltd. should adopt the proposed “2/10 Net 45” credit policy immediately. It delivers a substantial annual profit enhancement of Rs. 1,368,000 while reducing the receivables collection cycle from 60 days to 30 days and freeing up Rs. 1.92 million in liquid working capital.

Solution: Dividend Valuation Models (Walter & Gordon)

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Part (a): Walter’s Model Share Price Computation (6 Marks)

Formula:

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

Given: $E = \text{Rs. } 20.00, \quad k_e = 15\% = 0.15$. Dividends per share ($D$):

• At 0% payout: $D = \text{Rs. } 0.00$
• At 50% payout: $D = \text{Rs. } 10.00$
• At 100% payout: $D = \text{Rs. } 20.00$

1. Growth Firm ($r = 20\% = 0.20$):

• Payout 0%: $P = \frac{0 + \frac{0.20}{0.15}(20 - 0)}{0.15} = \frac{1.3333 \times 20}{0.15} = \frac{26.667}{0.15} = \mathbf{\text{Rs. } 177.78}$
• Payout 50%: $P = \frac{10 + \frac{0.20}{0.15}(20 - 10)}{0.15} = \frac{10 + 13.333}{0.15} = \frac{23.333}{0.15} = \mathbf{\text{Rs. } 155.56}$
• Payout 100%: $P = \frac{20 + \frac{0.20}{0.15}(20 - 20)}{0.15} = \frac{20}{0.15} = \mathbf{\text{Rs. } 133.33}$

2. Normal Firm ($r = 15\% = 0.15$):

• Payout 0%: $P = \frac{0 + \frac{0.15}{0.15}(20)}{0.15} = \frac{20}{0.15} = \mathbf{\text{Rs. } 133.33}$
• Payout 50%: $P = \frac{10 + \frac{0.15}{0.15}(10)}{0.15} = \frac{20}{0.15} = \mathbf{\text{Rs. } 133.33}$
• Payout 100%: $P = \frac{20 + 0}{0.15} = \mathbf{\text{Rs. } 133.33}$

3. Declining Firm ($r = 10\% = 0.10$):

• Payout 0%: $P = \frac{0 + \frac{0.10}{0.15}(20)}{0.15} = \frac{13.333}{0.15} = \mathbf{\text{Rs. } 88.89}$
• Payout 50%: $P = \frac{10 + \frac{0.10}{0.15}(10)}{0.15} = \frac{10 + 6.667}{0.15} = \frac{16.667}{0.15} = \mathbf{\text{Rs. } 111.11}$
• Payout 100%: $P = \frac{20 + 0}{0.15} = \mathbf{\text{Rs. } 133.33}$

Summary Table under Walter’s Model:

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Part (b): Optimum Payout Policies (2 Marks)

• Growth Firm ($r > k_e$): Optimum payout is 0% (100% retention). Reinvesting earnings inside the firm yields superior returns to what shareholders can earn externally, maximizing stock price at Rs. 177.78.
• Normal Firm ($r = k_e$): Payout policy is indifferent / irrelevant. Share price remains strictly constant at Rs. 133.33 regardless of dividend payout.
• Declining Firm ($r < k_e$): Optimum payout is 100% (0% retention). Shareholders earn more by receiving cash dividends and investing externally at 15% than retaining funds inside a firm generating only 10%.

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Part (c): Gordon’s Model Application (2 Marks)

• Given: $E = \text{Rs. } 20.00, \quad b = 0.60 \implies \text{Payout } (1 - b) = 0.40$
• Next Dividend: $D_1 = E \times (1 - b) = 20.00 \times 0.40 = \text{Rs. } 8.00$
• Sustainable Growth Rate: $g = b \times r = 0.60 \times 0.18 = 0.108 = 10.8\%$
• Cost of Equity: $k_e = 15\% = 0.15$$P_0 = \frac{D_1}{k_e - g} = \frac{8.00}{0.15 - 0.108} = \frac{8.00}{0.042} = \mathbf{\text{Rs. } 190.48 \text{ per share}}$$

Case Solution: Gandaki Heavy Logistics Ltd. (GHLL)

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Part (a): Present Value of Cash Outflows for Borrow and Buy ($PV_B$) (8 Marks)

1. Loan Debt Service Breakdown:

   • Annual Principal Repayment = $\frac{12,000,000}{5} = \text{Rs. } 2,400,000$ per year.
   • Annual Depreciation Tax Shield = $\text{Depreciation} \times T = 2,000,000 \times 25\% = \text{Rs. } 500,000$ per year.
   • After-Tax Annual Maintenance Cost = $300,000 \times (1 - 0.25) = \text{Rs. } 225,000$ per year.

2. Year-by-Year Cash Outflow Schedule for Buying:

$$\mathbf{PV(\text{Cost of Buying, } PV_B) = \text{Rs. } 9,630,480.54}$$

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Part (b): Present Value of Cash Outflows for Financial Lease ($PV_L$) (7 Marks)

1. Timing of Lease Outflows and Tax Shields:

   • Lease rentals of Rs. 3,200,000 are paid in advance at Years 0, 1, 2, 3, and 4.
   • Tax shield on lease rental ($3,200,000 \times 25\% = \text{Rs. } 800,000$) is realized at the end of each operating year (Years 1 to 5).
   • Maintenance is paid by the lessor, so GHLL incurs zero maintenance costs.

2. Year-by-Year Cash Outflow Schedule for Leasing:

$$\mathbf{PV(\text{Cost of Leasing, } PV_L) = \text{Rs. } 10,455,380.80}$$

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Part (c): Net Advantage to Leasing (NAL) & Recommendation (3 Marks)

$$NAL = PV(\text{Cost of Buying}) - PV(\text{Cost of Leasing}) = PV_B - PV_L$$

$$NAL = \text{Rs. } 9,630,480.54 - \text{Rs. } 10,455,380.80 = \mathbf{-\text{Rs. } 824,900.26}$$

Managerial Decision & Recommendation:

• The Net Advantage to Leasing is negative (-Rs. 824,900.26), indicating that leasing the refrigerated fleet is Rs. 824,900 more expensive in present value terms than borrowing and purchasing.
• Recommendation: Gandaki Heavy Logistics Ltd. should reject the lease proposal and proceed with the Borrow and Buy option. Owning the asset preserves the Rs. 2,000,000 terminal salvage value and leverages the lower overall debt-servicing profile.

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Part (d): Rationale for Discounting at After-Tax Cost of Debt (2 Marks)

1. Identical Risk Profile to Debt: Contractual lease rental payments and loan debt-servicing schedules are legally binding, fixed corporate obligations. Failing to pay either results in financial distress and legal default.
2. Displacement of Debt Capacity: A lease is a form of debt financing that directly consumes the firm’s borrowing capacity.
3. Cash Flow Certainty: Because loan payments, lease payments, tax depreciation shields, and tax deductions are known with contractual or statutory certainty, they do not share the higher operating risk of the firm’s general business revenues. Discounting at WACC would over-discount and erroneously undervalue these committed contractual cash outflows.