Dean's Office Official Model Question Paper

Wealth Maximization vs. Profit Maximization

Wealth Maximization focuses on maximizing the market value of the firm’s equity shares. It is superior to profit maximization because:

1. It explicitly accounts for the Time Value of Money (present value of expected future cash flows).
2. It explicitly incorporates Risk and Uncertainty, whereas profit maximization ignores risk and encourages myopic short-term accounting manipulation.

Operating vs. Financial Leverage

• Operating Leverage: Measures the extent to which fixed operating costs are used in a firm’s operations. $\text{DOL} = \frac{\text{Contribution}}{\text{EBIT}}$.
• Financial Leverage: Measures the extent to which fixed financing costs (debt interest, preference dividends) are used in the firm’s capital structure. $\text{DFL} = \frac{\text{EBIT}}{\text{EBT}}$.

NPV Decision Rule

$$\text{NPV} = \sum_{t=1}^{n} \frac{CF_t}{(1 + k)^t} - CF_0$$

• Accept Project: If $\text{NPV} > 0$ (adds net economic value to the firm).
• Reject Project: If $\text{NPV} < 0$ (destroys shareholder wealth).
• Indifferent: If $\text{NPV} = 0$.

Gross vs. Net Working Capital

• Gross Working Capital: The total investment in all current assets (Cash + Receivables + Inventories + Prepayments).
• Net Working Capital: The excess of current assets over current liabilities ($\text{NWC} = \text{Current Assets} - \text{Current Liabilities}$).

Liquidity Ratio Formulas

$$\text{Current Ratio} = \frac{\text{Current Assets}}{\text{Current Liabilities}} \quad (\text{Standard Benchmark: } 2:1)$$

$$\text{Quick Ratio} = \frac{\text{Current Assets} - \text{Inventory} - \text{Prepaid Expenses}}{\text{Current Liabilities}} \quad (\text{Standard Benchmark: } 1:1)$$

Capital Budgeting Analysis

a. Payback Period:

• Project A: Cumulative inflows: Yr 1 = 800,000; Yr 2 = 1,500,000; Balance needed = 500,000. $\text{Payback} = 2 + \frac{500{,}000}{600{,}000} = 2.83 \text{ years}$.
• Project B: Cumulative inflows: Yr 1 = 400,000; Yr 2 = 1,000,000; Yr 3 = 1,800,000; Balance needed = 200,000. $\text{Payback} = 3 + \frac{200{,}000}{1{,}000{,}000} = 3.20 \text{ years}$.

b. Net Present Value (NPV):

• Project A:

  • Yr 1: $800{,}000 \times 0.909 = 727{,}200$
  • Yr 2: $700{,}000 \times 0.826 = 578{,}200$
  • Yr 3: $600{,}000 \times 0.751 = 450{,}600$
  • Yr 4: $500{,}000 \times 0.683 = 341{,}500$
  • Total PV = Rs 2,097,500
  • $\text{NPV}_A = 2{,}097{,}500 - 2{,}000{,}000 = \textbf{Rs 97,500}$

• Project B:

  • Yr 1: $400{,}000 \times 0.909 = 363{,}600$
  • Yr 2: $600{,}000 \times 0.826 = 495{,}600$
  • Yr 3: $800{,}000 \times 0.751 = 600{,}800$
  • Yr 4: $1{,}000{,}000 \times 0.683 = 683{,}000$
  • Total PV = Rs 2,143,000
  • $\text{NPV}_B = 2{,}143{,}000 - 2{,}000{,}000 = \textbf{Rs 143,000}$

c. Profitability Index (PI):

$$\text{PI}_A = \frac{2{,}097{,}500}{2{,}000{,}000} = 1.049$$

$$\text{PI}_B = \frac{2{,}143{,}000}{2{,}000{,}000} = 1.072$$

d. Recommendation:

Project B should be accepted because it generates a higher Net Present Value (Rs 143,000 vs. Rs 97,500) and higher Profitability Index (1.072 vs. 1.049), adding greater net wealth to shareholders, despite Project A having a shorter payback period.

The Cash Conversion Cycle (CCC)

The Cash Conversion Cycle measures the time span (in days) required for a firm to convert its investments in inventory and operational resources into cash inflows from sales.

$$\text{CCC} = \text{Days Sales of Inventory (DSI)} + \text{Days Sales Outstanding (DSO)} - \text{Days Payables Outstanding (DPO)}$$

1. Components:

• DSI (Inventory Days): Average days food and beverage provisions remain in storage before consumption: $\text{DSI} = \frac{\text{Average Inventory}}{\text{COGS}} \times 365$.
• DSO (Receivables Days): Average collection period for guest ledger and city ledger credit accounts: $\text{DSO} = \frac{\text{Accounts Receivable}}{\text{Total Credit Revenue}} \times 365$.
• DPO (Payables Days): Average days taken to settle dues to suppliers: $\text{DPO} = \frac{\text{Accounts Payable}}{\text{Total Purchases}} \times 365$.

2. Strategies to Shorten CCC in Hotels:

1. Just-in-Time Procurement: Shorten DSI by maintaining minimum par stocks and ordering daily perishables from local vendors.
2. Accelerated Receivable Collections: Shorten DSO by enforcing upfront credit card pre-authorizations and offering 2% prompt settlement discounts to corporate clients.
3. Optimizing Vendor Credit: Maximize DPO by negotiating extended 45-day credit terms with established wholesale food suppliers without forfeiting cash discounts.

Weighted Average Cost of Capital (WACC)

WACC is the average rate of return a company must earn on its existing asset base to satisfy all providers of capital (debtholders, preferred shareholders, and equity owners), weighted by their respective proportions in the capital structure.

Mathematical Formulation:

$$\text{WACC} = \left( w_d \times k_d \times (1 - t) \right) + \left( w_p \times k_p \right) + \left( w_e \times k_e \right)$$

Where:

• $w_d, w_p, w_e$ = Proportions (weights) of Debt, Preferred Stock, and Common Equity in total capital
• $k_d$ = Pre-tax cost of debt; $(1 - t)$ = Tax shield adjustment factor ($t$ = corporate tax rate)
• $k_p$ = Cost of preferred stock: $k_p = \frac{D_p}{P_0}$
• $k_e$ = Cost of common equity (computed via CAPM: $k_e = R_f + \beta(R_m - R_f)$ or Gordon Dividend Growth Model: $k_e = \frac{D_1}{P_0} + g$)

Significance in Hospitality:

WACC serves as the universal hurdle rate / discount rate for evaluating new hotel developments, room renovations, and resort acquisitions.

Financial Ratio Analysis in Hospitality

1. Debt-to-Equity Ratio (Solvency / Leverage):
   $$\text{D/E Ratio} = \frac{\text{Total Long-Term Debt}}{\text{Shareholders' Equity}}$$
   • Interpretation: Assesses financial leverage and risk. A ratio $> 2:1$ in hotels signals heavy fixed interest obligations that increase vulnerability during off-peak seasons.
2. Interest Coverage Ratio (Debt Service Capacity):
   $$\text{Interest Coverage} = \frac{\text{EBIT}}{\text{Interest Expense}}$$
   • Interpretation: Measures how comfortably operating profits cover debt interest. A ratio below $2.0\times$ triggers loan covenant warnings from commercial banks.
3. Return on Assets (ROA - Operational Efficiency):
   $$\text{ROA} = \frac{\text{Net Profit After Tax}}{\text{Total Assets}} \times 100$$
   • Interpretation: Evaluates how effectively capital-intensive hotel properties generate net returns from their physical plant.
4. Return on Equity (ROE - Shareholder Profitability):
   $$\text{ROE} = \frac{\text{Net Income}}{\text{Shareholders' Equity}} \times 100$$
   • Interpretation: Measures the rate of return earned on shareholders’ common equity investment (DuPont analysis: $\text{ROE} = \text{Net Profit Margin} \times \text{Asset Turnover} \times \text{Equity Multiplier}$).

Comprehensive Capital Structure Case Analysis

a. Earnings Per Share (EPS) Computation at EBIT = Rs 26,000,000

Observation: At the projected EBIT of Rs 26M, Plan B yields an EPS of Rs 15.90, which is higher by Rs 1.97 per share (+14.1%) compared to Plan A due to positive financial leverage.

b. EBIT-EPS Indifference Point

Set $EPS_{\text{Plan A}} = EPS_{\text{Plan B}}$:

$$\frac{(EBIT - 0)(1 - 0.25)}{1{,}400{,}000} = \frac{(EBIT - 4{,}800{,}000)(1 - 0.25)}{1{,}000{,}000}$$

Cancel $(1 - 0.25)$ from both sides and simplify share ratios ($1.4 : 1$):

$$EBIT = 1.4 \times (EBIT - 4{,}800{,}000)$$

$$EBIT = 1.4 \cdot EBIT - 6{,}720{,}000$$

$$0.4 \cdot EBIT = 6{,}720{,}000 \implies \textbf{EBIT} = \frac{6{,}720{,}000}{0.4} = \textbf{Rs 16,800,000}$$

Interpretation: At an EBIT of exactly Rs 16,800,000, both plans produce identical EPS of Rs 9.00. Since projected EBIT (Rs 26M) is well above the indifference point, Debt Financing (Plan B) is financially superior in terms of shareholder returns.

c. Degree of Financial Leverage (DFL)

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

• Plan A: $\text{DFL}_A = \frac{26{,}000{,}000}{26{,}000{,}000} = \textbf{1.00}$ (Zero financial risk).
• Plan B: $\text{DFL}_B = \frac{26{,}000{,}000}{26{,}000{,}000 - 4{,}800{,}000} = \frac{26{,}000{,}000}{21{,}200{,}000} = \textbf{1.226}$. (A 1% change in EBIT will result in a 1.226% change in EPS under Plan B).

d. Strategic Recommendation for the Board

1. Adopt Plan B (Debt Financing): The after-tax cost of debt ($12\% \times (1 - 0.25) = 9\%$) is significantly lower than the cost of equity (estimated at 14–16%), and the interest tax shield creates Rs 1,200,000 annual tax savings.
2. Manageable Financial Risk: A DFL of 1.226 and an Interest Coverage Ratio of $5.42\times$ ($\frac{26M}{4.8M}$) demonstrate that the hotel can comfortably service the debt even during moderate tourist downturns.