Fundamentals of Financial Management 2079 Board Question Paper

The core functions of managerial finance encompass three primary decision-making areas:

1. Investment Decision (Capital Budgeting): Deciding which long-term productive assets and capital projects to fund to earn maximum risk-adjusted returns.
2. Financing Decision (Capital Structure): Determining the optimal mix of long-term debt and equity capital to minimize the firm’s Weighted Average Cost of Capital (WACC).
3. Dividend Decision: Deciding how much after-tax profit should be distributed as cash dividends to shareholders versus retained for reinvestment.

An annuity is a finite stream of equal cash flows occurring at regular intervals for a fixed, specified maturity period ($n$ years). In contrast, a perpetuity is an infinite stream of equal cash flows that continues indefinitely without any maturity end date (e.g., British Consol bonds, preferred stock). The present value of a perpetuity is simplified to:

$$PV_{\text{Perpetuity}} = \frac{\text{Cash Flow } (PMT)}{\text{Interest Rate } (i)}$$

A firm should consider issuing a stock dividend (bonus shares) when:

1. Conserving Liquidity: Operating cash flow needs to be conserved for high-return internal expansion rather than drained through cash dividends.
2. High Market Price per Share: The stock is trading at an uncomfortably high unit price; issuing bonus shares increases the floating supply and lowers the trading price to an attractive retail range.
3. Reassuring Shareholders: Maintaining investor confidence by capitalizing retained earnings into permanent share capital.

Three key advantages of Net Present Value (NPV) over the Payback Method are:

1. Incorporates the Time Value of Money: NPV discounts all future cash flows using the firm’s cost of capital, whereas Payback treats rupees received in Year 5 the same as Year 1.
2. Considers Total Cash Flows Over Entire Project Life: Payback ignores all cash flows earned after the arbitrary cut-off date, whereas NPV captures every rupee generated.
3. Directly Measures Shareholder Wealth Creation: A positive NPV indicates the exact monetary gain in the firm’s equity value.

The three primary motives for holding cash are:

1. Transaction Motive: To meet anticipated, day-to-day operational expenditures such as payroll, material procurement, utilities, and tax payments.
2. Precautionary Motive: To provide an emergency cash reserve against unforeseen contingencies, flood/strike disruptions, or unexpected customer default.
3. Speculative Motive: To maintain liquid funds ready to seize opportunistic investments, such as distressed asset sales or steep supplier discounts.

The cost of common stock ($k_s$) is strictly higher than debt capital ($k_d$) due to two fundamental reasons:

1. Higher Risk Profile (Residual Claimants): Equity holders face substantially higher risk; in insolvency, debt holders have senior legal claims on assets, while common shareholders are paid last.
2. Tax Deductibility of Interest: Interest payments on debt are tax-deductible expenses under corporate tax law [$k_d = r_d(1 - t)$], directly lowering the effective cost of debt, whereas equity dividends are non-deductible distributions of after-tax profit.

Given:

• $\text{EOQ} = 1,000\text{ units}$
• $\text{Material Cost per Unit } (C) = \text{Rs. } 20$
• $\text{Ordering Cost per Order } (O) = \text{Rs. } 100$
• $\text{Carrying/Holding Cost per Unit } (c) = 20\% \text{ of Rs. } 20 = \text{Rs. } 4.00$

Formula:

$$\text{EOQ} = \sqrt{\frac{2AO}{c}} \implies 1,000 = \sqrt{\frac{2 \times A \times 100}{4}} = \sqrt{50A}$$

Squaring both sides:

$$1,000,000 = 50A \implies A = \frac{1,000,000}{50} = \mathbf{20,000\text{ units}}$$

$$\mathbf{\text{Annual Requirement } (A) = 20,000\text{ units}}$$

Given:

• $\text{Interest Expense } (I) = \text{Rs. } 6,000$
• $\text{Preferred Dividend } (D_p) = \text{Rs. } 8,000$
• $\text{Tax Rate } (t) = 25\% = 0.25$

Financial Break-Even Point (EBIT level where EPS = 0):

$$\text{Financial BEP} = I + \frac{D_p}{1 - t}$$

$$\mathbf{\text{Financial BEP}} = \text{Rs. } 6,000 + \frac{\text{Rs. } 8,000}{1 - 0.25} = 6,000 + \frac{8,000}{0.75} = 6,000 + 10,666.67 = \mathbf{\text{Rs. } 16,666.67}$$

Given:

• $\text{Beta } (\beta_Y) = 1.45$
• $\text{Expected Return } = 17.00\%$
• $\text{Risk-Free Rate } (R_f) = 6.00\%$
• $\text{Market Risk Premium } (R_m - R_f) = 7.50\%$

Required Rate of Return using CAPM:

$$E(R_Y) = R_f + \beta_Y (R_m - R_f) = 6.00\% + 1.45(7.50\%) = 6.00\% + 10.875\% = \mathbf{16.875\%}$$

Evaluation:

• The stock’s expected return ($17.00\%$) is slightly higher than its CAPM required return ($16.875\%$), offering an alpha of $+0.125\%$.
• Conclusion: The stock is virtually correctly priced (or marginally underpriced/attractive).

Given:

• $\text{Beginning EPS } (PV) = \text{Rs. } 4.42$
• $\text{Ending EPS } (FV) = \text{Rs. } 6.50$
• $\text{Number of Years } (n) = 5\text{ years}$

Compound Growth Rate Formula:

$$FV = PV \times (1 + g)^n \implies 6.50 = 4.42 \times (1 + g)^5$$

$$(1 + g)^5 = \frac{6.50}{4.42} = 1.470588$$

$$1 + g = (1.470588)^{1/5} = (1.470588)^{0.20} = 1.0802$$

$$\mathbf{g} = 1.0802 - 1 = 0.0802 = \mathbf{8.02\%\text{ per annum}}$$

How Wealth Maximization Overcomes Drawbacks of Profit Maximization

1. The Drawbacks of Profit Maximization

1. Ambiguity of Term “Profit”: Does it mean gross profit, operating profit, net profit after tax, or return on capital? Book profits are easily distorted by changing depreciation methods or revenue recognition choices.
2. Ignores the Time Value of Money: It fails to differentiate between a project yielding Rs. 1 million in Year 1 versus one yielding Rs. 1 million in Year 10.
3. Ignores Risk and Uncertainty: Encourages management to pursue excessively risky, high-variance investments simply because they promise high nominal profit forecasts.
4. Neglects Cash Flow Timing and Working Capital: Focuses on accrued accounting figures rather than actual realized cash flow liquidity.

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2. How Wealth Maximization Resolves These Deficiencies

1. Incorporates the Time Value of Money: Wealth maximization calculates the present value of expected cash flows using the formula:

   $$\text{Wealth} = \sum_{t=1}^n \frac{CF_t}{(1 + k)^t} - I_0$$
   This ensures that cash received earlier is appropriately weighted higher.

2. Explicitly Incorporates Risk Management: The discount rate ($k$) is dynamically adjusted based on project risk. Riskier projects must clear higher hurdle rates, directly safeguarding shareholders from uncompensated volatility.

3. Anchored in Verifiable Cash Flows: Bypasses non-cash accounting adjustments and focuses on actual Free Cash Flows, ensuring genuine economic solvency.

4. Aligns Management with Long-Term Survival: Discourages short-term cost-cutting (like skipping safety maintenance or customer support) because the stock market immediately discounts future cash flows if operational health is compromised.

(a) Calculation of Sagarmatha’s Current Assets

1. Accounts Receivable:

   $$\text{DSO} = \frac{\text{Receivables}}{\text{Sales} / 360} \implies 40 = \frac{\text{Receivables}}{100,000 / 360} = \frac{\text{Receivables}}{277.78}$$
   $$\text{Receivables} = 40 \times 277.78 = \mathbf{\text{Rs. } 11,111.11}$$

2. Current Liabilities (CL):

   $$\text{Quick Assets} = \text{Cash (10,000)} + \text{Receivables (11,111.11)} = \text{Rs. } 21,111.11$$
   $$\text{Quick Ratio} = \frac{\text{Quick Assets}}{\text{CL}} \implies 2.0 = \frac{21,111.11}{\text{CL}} \implies \mathbf{\text{CL}} = \frac{21,111.11}{2.0} = \mathbf{\text{Rs. } 10,555.56}$$

3. Current Assets (CA):

   $$\text{Current Ratio} = \frac{\text{CA}}{\text{CL}} \implies 3.0 = \frac{\text{CA}}{10,555.56} \implies \mathbf{\text{CA}} = 3.0 \times 10,555.56 = \mathbf{\text{Rs. } 31,666.67}$$

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(b) Limitations of Financial Ratio Analysis

1. Historical Orientation: Ratios are computed from historical balance sheets and income statements; they fail to reflect future inflationary trends or real-time operational shifts.
2. Distortion from Differing Accounting Policies: Differences in depreciation schedules (SLM vs WDV) and inventory valuation methods (FIFO vs Weighted Average) make inter-firm comparisons unreliable.
3. Window Dressing: Management may temporarily alter financial accounts immediately prior to the reporting date (e.g., delaying purchases or rushing collections) to artificially inflate liquidity ratios.
4. Inflationary Distortions: Comparing balance sheets of old companies owning assets at historic costs against newer firms distorted by high inflation produces misleading comparative returns.
5. Difficulty in Defining “Norms”: What constitutes a “good” ratio varies significantly across diverse industries and seasonal business models.

Time Value of Money Calculations

Parameters:

• Deposit occurs 1 year from now ($t = 1$). Terminal date is 4 years from now ($t = 4$).
• Duration of compounding ($n$) $= 4 - 1 = 3\text{ years}$.
• Stated Interest Rate ($i$) $= 8\% = 0.08$.

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a. Balance 4 Years from Now (Annual Compounding)

$$FV_4 = PV_1 \times (1 + i)^3 = \text{Rs. } 1,000 \times (1 + 0.08)^3 = 1,000 \times 1.259712 = \mathbf{\text{Rs. } 1,259.71}$$

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b. Balance 4 Years from Now (Quarterly Compounding, $m = 4$)

$$\text{Compounding Periods } (N) = 3\text{ years} \times 4 = 12\text{ quarters}$$

$$\text{Quarterly Rate } = \frac{8\%}{4} = 2\% = 0.02$$

$$FV_4 = \text{Rs. } 1,000 \times (1 + 0.02)^{12} = 1,000 \times 1.268242 = \mathbf{\text{Rs. } 1,268.24}$$

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c. Future Value of 4 Payments of Rs. 250 Each (End of Years 1, 2, 3, and 4)

This is an ordinary annuity of 4 payments at $8\%$:

• End of Year 1: compounds for 3 years: $250 \times (1.08)^3 = 250 \times 1.259712 = \text{Rs. } 314.93$
• End of Year 2: compounds for 2 years: $250 \times (1.08)^2 = 250 \times 1.1664 = \text{Rs. } 291.60$
• End of Year 3: compounds for 1 year: $250 \times (1.08)^1 = 250 \times 1.08 = \text{Rs. } 270.00$
• End of Year 4: compounds for 0 years: $250 \times 1 = \text{Rs. } 250.00$$\text{FVIFA}_{8\%, 4} = \frac{(1.08)^4 - 1}{0.08} = 4.5061$$
  $$\mathbf{\text{Total Balance at End of Year 4}} = 250 \times 4.5061 = \mathbf{\text{Rs. } 1,126.53}$$

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d. Equal Payments (PMT) to Accumulate Rs. 1,259.71 by End of Year 4

$$\text{Target Future Value} = \text{Rs. } 1,259.71$$

$$\text{FVIFA}_{8\%, 4} = 4.5061$$

$$\mathbf{PMT} = \frac{\text{Rs. } 1,259.71}{4.5061} = \mathbf{\text{Rs. } 279.56}$$

Each equal payment must be Rs. 279.56.

Stock Valuation and Projected Future Stock Price

Given:

• Current Market Price ($P_0$) $= \text{Rs. } 360$
• Dividend Just Paid ($D_0$) $= \text{Rs. } 24$
• Required Rate of Return ($k_s$) $= 12\% = 0.12$

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Step 1: Calculate the Implied Constant Growth Rate ($g$)

Using the Gordon Constant Growth Model:

$$P_0 = \frac{D_0(1 + g)}{k_s - g}$$

$$360 = \frac{24(1 + g)}{0.12 - g}$$

$$360(0.12 - g) = 24 + 24g$$

$$43.20 - 360g = 24 + 24g$$

$$43.20 - 24 = 360g + 24g$$

$$19.20 = 384g$$

$$\mathbf{g} = \frac{19.20}{384} = 0.05 = \mathbf{5.00\%}$$

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Step 2: Calculate Expected Stock Price 5 Years from Now ($P_5$)

Under the constant growth model, both dividends and stock price grow at the constant growth rate $g$:

$$P_5 = P_0 \times (1 + g)^5$$

$$\mathbf{P_5} = \text{Rs. } 360 \times (1 + 0.05)^5 = 360 \times 1.276282 = \mathbf{\text{Rs. } 459.46}$$

(Alternatively: $D_6 = D_0(1 + g)^6 = 24(1.05)^6 = \text{Rs. } 32.162 \implies P_5 = \frac{32.162}{0.12 - 0.05} = \frac{32.162}{0.07} = \mathbf{\text{Rs. } 459.46}$).

(a) Weighted Average Cost of Capital (WACC)

Step 1: Capital Weights (Book Value Proportions)

• Total Capital $= \text{Rs. } 16\text{ million}$
• $w_d = \frac{6}{16} = 0.375$ ($37.5\%$)
• $w_p = \frac{2}{16} = 0.125$ ($12.5\%$)
• $w_e = \frac{8}{16} = 0.500$ ($50.0\%$)

Step 2: Component Costs of Capital

1. After-Tax Cost of Debt ($k_d$):
   $$k_d = r_d(1 - t) = 13\%(1 - 0.40) = \mathbf{7.80\%}$$
2. Cost of Preferred Stock ($k_p$): Assuming preferred shares trade at par:
   $$k_p = \mathbf{8.00\%}$$
3. Cost of Common Equity ($k_s$):
   $$D_1 = D_0(1 + g) = 20 \times (1 + 0.10) = \text{Rs. } 22.00$$
   $$k_s = \frac{D_1}{P_0} + g = \frac{\text{Rs. } 22.00}{\text{Rs. } 200} + 0.10 = 0.11 + 0.10 = \mathbf{21.00\%}$$

Step 3: Compute WACC

$$\text{WACC} = (w_d \times k_d) + (w_p \times k_p) + (w_e \times k_s)$$

$$\mathbf{\text{WACC}} = (0.375 \times 7.80\%) + (0.125 \times 8.00\%) + (0.500 \times 21.00\%)$$

$$\text{WACC} = 2.925\% + 1.000\% + 10.500\% = \mathbf{14.425\%}$$

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(b) Appropriateness of WACC as Acceptance Criteria

The computed WACC of $14.43\%$ is appropriate as an investment acceptance hurdle rate only if two strict conditions are met:

1. Identical Risk Profile: The proposed new investment projects possess the same systematic risk as the firm’s existing operations. If a new venture is significantly riskier, using the overall corporate WACC will understate the hurdle rate and lead to accepting wealth-destroying projects.
2. Preservation of Capital Structure: The new projects will be financed in the identical debt/preferred/equity proportions ($37.5\% / 12.5\% / 50\%$) without disrupting capital structure balance.

Operating Leverage Computations

Given at Base Level (10,000 units):

• $\text{DOL} = 2.0\text{ times}$
• $\text{Operating Income (EBIT)} = \text{Rs. } 1,000$

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a. Resulting Operating Profit after 20% Sales Increase

$$\% \Delta \text{EBIT} = \text{DOL} \times \% \Delta \text{Sales} = 2.0 \times 20\% = +40\%$$

$$\mathbf{\text{New Operating Profit (EBIT)}} = \text{Rs. } 1,000 \times (1 + 0.40) = \mathbf{\text{Rs. } 1,400}$$

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b. New DOL at 12,000 Units Sales Position

1. Determine Fixed Costs and Contribution Margin at Base (10,000 units):

   $$\text{DOL} = \frac{\text{Contribution Margin}}{\text{EBIT}} \implies 2.0 = \frac{\text{Contribution Margin}}{\text{Rs. } 1,000}$$
   $$\text{Contribution Margin (10,000 units)} = \text{Rs. } 2,000$$
   $$\text{Fixed Cost} = \text{Contribution Margin} - \text{EBIT} = 2,000 - 1,000 = \mathbf{\text{Rs. } 1,000}$$
   $$\text{Contribution Margin per unit} = \frac{\text{Rs. } 2,000}{10,000\text{ units}} = \text{Rs. } 0.20\text{ per unit}$$

2. At New Level of 12,000 units:

   • $\text{New Contribution Margin} = 12,000\text{ units} \times \text{Rs. } 0.20 = \text{Rs. } 2,400$
   • $\text{New EBIT} = 2,400 - 1,000 (\text{Fixed Cost}) = \text{Rs. } 1,400$

3. Compute New DOL:

   $$\mathbf{\text{New DOL}_{12,000}} = \frac{\text{New Contribution Margin}}{\text{New EBIT}} = \frac{\text{Rs. } 2,400}{\text{Rs. } 1,400} = \mathbf{1.714\text{ times}}$$
   (Remark: As sales increase further above the break-even point, DOL declines, reflecting lower operating risk).

Importance of Working Capital Management and Role of Credit Policy

1. Importance of Working Capital Management

Working capital management governs the firm’s short-term liquidity, ensuring that day-to-day operating activities continue seamlessly without insolvency:

1. Ensures Liquidity and Solvency: Prevents technical insolvency by maintaining adequate current assets to pay maturing bills, bank overdrafts, and payroll obligations.
2. Smooths the Production Pipeline: Prevents stock-out emergencies and machine downtime through timely raw material procurement.
3. Exploits Market Opportunities: Ample liquidity lets the firm take advantage of bulk cash discounts and favorable seasonal commodity prices.
4. Optimizes Capital Costs: Prevents costly emergency borrowing at punitive interest rates by forecasting liquidity shortfalls in advance.

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2. How a Good Credit Policy Facilitates Working Capital Management

Accounts receivable typically constitute $30\%-50\%$ of total current assets. A sound, well-crafted credit policy optimizes working capital in the following ways:

1. Shortens Days Sales Outstanding (DSO) and the Cash Conversion Cycle: By establishing clear credit terms (e.g., $2/10, \text{ net } 30$), cash discounts motivate customers to remit payment within 10 days rather than 30 days, rapidly recycling cash back into working capital.

2. Minimizes Bad Debt Losses: Rigorous credit evaluation—using the 5 Cs of Credit (Character, Capacity, Capital, Collateral, Conditions) and credit scoring—weeds out uncreditworthy buyers, preventing working capital destruction.

3. Optimizes Working Capital Investment in Receivables:

   $$\text{Investment in Receivables} = \frac{\text{Annual Credit Sales}}{360} \times \text{DSO} \times \frac{\text{Variable Cost}}{\text{Sales}}$$
   Shortening DSO directly releases locked-up capital, reducing bank borrowing and interest expenses.

4. Streamlines Cash Inflow Predictability: Standardized collection procedures (automated reminders, progressive penalties, legal recourse) make cash inflows highly predictable, enabling accurate cash budgeting.

Comprehensive Risk, Return, and CAPM Analysis

(a) Expected Return and Standard Deviation

1. Expected Returns:

   • $\mathbf{E(R_A)} = (0.3 \times -20\%) + (0.3 \times 30\%) + (0.4 \times 40\%) = -6\% + 9\% + 16\% = \mathbf{19.00\%}$
   • $\mathbf{E(R_B)} = (0.3 \times 5\%) + (0.3 \times 25\%) + (0.4 \times 30\%) = 1.5\% + 7.5\% + 12.0\% = \mathbf{21.00\%}$

2. Standard Deviations:

   • Stock A:

     $$\sigma_A^2 = 0.3(-20 - 19)^2 + 0.3(30 - 19)^2 + 0.4(40 - 19)^2$$
     $$\sigma_A^2 = 0.3(-39)^2 + 0.3(11)^2 + 0.4(21)^2 = 0.3(1,521) + 0.3(121) + 0.4(441)$$
     $$\sigma_A^2 = 456.3 + 36.3 + 176.4 = 669.0$$
     $$\mathbf{\sigma_A} = \sqrt{669.0} = \mathbf{25.865\%}$$

   • Stock B:

     $$\sigma_B^2 = 0.3(5 - 21)^2 + 0.3(25 - 21)^2 + 0.4(30 - 21)^2$$
     $$\sigma_B^2 = 0.3(-16)^2 + 0.3(4)^2 + 0.4(9)^2 = 0.3(256) + 0.3(16) + 0.4(81)$$
     $$\sigma_B^2 = 76.8 + 4.8 + 32.4 = 114.0$$
     $$\mathbf{\sigma_B} = \sqrt{114.0} = \mathbf{10.677\%}$$

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(b) Covariance and Correlation Coefficient

1. Covariance:

   $$\text{Cov}(A, B) = \sum P_i [R_{Ai} - E(R_A)][R_{Bi} - E(R_B)]$$
   • State 1: $0.3(-39)(-16) = 0.3(624) = 187.2$
   • State 2: $0.3(11)(4) = 0.3(44) = 13.2$
   • State 3: $0.4(21)(9) = 0.4(189) = 75.6$$\mathbf{\text{Cov}(A, B)} = 187.2 + 13.2 + 75.6 = \mathbf{276.00}$$

2. Correlation Coefficient ($r_{AB}$):

   $$\mathbf{r_{AB}} = \frac{\text{Cov}(A, B)}{\sigma_A \times \sigma_B} = \frac{276.00}{25.865 \times 10.677} = \frac{276.00}{276.16} = \mathbf{0.9994 \approx +1.00}$$

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(c) Portfolio Return and Risk ($w_A = 0.70, w_B = 0.30$)

1. Portfolio Expected Return ($R_p$):

   $$\mathbf{R_p} = (0.70 \times 19\%) + (0.30 \times 21\%) = 13.3\% + 6.3\% = \mathbf{19.60\%}$$

2. Portfolio Standard Deviation ($\sigma_p$): Since $r_{AB} \approx 1.0$:

   $$\mathbf{\sigma_p} = w_A \sigma_A + w_B \sigma_B = (0.70 \times 25.865\%) + (0.30 \times 10.677\%) = 18.106\% + 3.203\% = \mathbf{21.31\%}$$

3. Diversification Evaluation: Because the correlation coefficient is near $+1.0$ ($0.9994$), the portfolio risk is essentially a linear weighted average of individual risks. There is virtually no risk reduction through diversification because both stocks move in near-perfect lockstep across economic states.

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(d) CAPM Evaluation for Stock B

• $\text{Cov}(B, M) = 140$, $\sigma_M = 9\% \implies \sigma_M^2 = 81$.
• $\mathbf{\beta_B} = \frac{\text{Cov}(B, M)}{\sigma_M^2} = \frac{140}{81} = \mathbf{1.728}$
• $R_f = 6\%$, $(R_m - R_f) = 4\%$.
• Required Return on Stock B:
  $$E(R_B)_{\text{required}} = R_f + \beta_B(R_m - R_f) = 6\% + (1.728 \times 4\%) = 6\% + 6.91\% = \mathbf{12.91\%}$$
• Pricing Evaluation: Expected Return from distribution $= 21.00\%$. Required Return from CAPM $= 12.91\%$. Because Expected Return ($21\%$) significantly exceeds Required Return ($12.91\%$) [$\alpha = +8.09\%$], Stock B is UNDERPRICED (a bargain investment).

Evaluation of Mutually Exclusive Projects

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(a) Internal Rate of Return (IRR)

1. Project A (Equal Annuity of Rs. 35,000 for 4 years):

   $$\text{PVIFA}_{IRR, 4} = \frac{100,000}{35,000} = 2.8571$$
   Looking up 4-year PVIFA table:
   • At $14\%$: $\text{PVIFA} = 2.9137$
   • At $15\%$: $\text{PVIFA} = 2.8550$$\mathbf{\text{IRR}_A} \approx \mathbf{14.96\%}$$

2. Project B (Unequal Cash Flows: 45k, 30k, 40k, 10k):

   • At $15\%$: $PV = \frac{45,000}{1.15} + \frac{30,000}{(1.15)^2} + \frac{40,000}{(1.15)^3} + \frac{10,000}{(1.15)^4} = 39,130 + 22,684 + 26,299 + 5,718 = \text{Rs. } 93,831$ (Negative NPV).
   • At $10\%$: $PV = \frac{45,000}{1.10} + \frac{30,000}{(1.10)^2} + \frac{40,000}{(1.10)^3} + \frac{10,000}{(1.10)^4} = 40,909 + 24,793 + 30,053 + 6,830 = \text{Rs. } 102,585 \implies NPV = +2,585$.
   • At $12\%$: $PV = 40,179 + 23,916 + 28,471 + 6,355 = \text{Rs. } 98,921 \implies NPV = -1,079$.
     $$\mathbf{\text{IRR}_B} = 10\% + \frac{2,585}{2,585 - (-1,079)} \times (12\% - 10\%) = 10\% + 1.41\% = \mathbf{11.41\%}$$

• IRR Decision: Since $\text{IRR}_A (14.96\%) > \text{IRR}_B (11.41\%)$, accept Project A.
• Is this necessarily correct?: Not necessarily, because IRR assumes reinvestment at the high internal rate and can conflict with NPV in mutually exclusive choices.

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(b) Net Present Value (NPV @ 11%)

1. Project A:

   $$\text{PVIFA}_{11\%, 4} = 3.1024$$
   $$NPV_A = (35,000 \times 3.1024) - 100,000 = 108,584 - 100,000 = \mathbf{+\text{Rs. } 8,584}$$

2. Project B:

   $$PV = \frac{45,000}{1.11} + \frac{30,000}{(1.11)^2} + \frac{40,000}{(1.11)^3} + \frac{10,000}{(1.11)^4}$$
   $$PV = 40,541 + 24,349 + 29,248 + 6,587 = \text{Rs. } 100,725$$
   $$NPV_B = 100,725 - 100,000 = \mathbf{+\text{Rs. } 725}$$

• NPV Decision: Since $NPV_A (+\text{Rs. } 8,584) > NPV_B (+\text{Rs. } 725)$, choose Project A.

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(c) Resolving Conflicts between IRR and NPV

When a conflict arises between NPV and IRR for mutually exclusive projects, always select the project with the highest NPV.

• Reason: The ultimate goal of the firm is shareholder wealth maximization. NPV measures direct rupee wealth creation and realistically assumes cash flows are reinvested at the market cost of capital ($11\%$).

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(d) Why Projects Become Mutually Exclusive

Two projects become mutually exclusive when accepting one precludes the acceptance of the other due to:

1. Physical or Technical Constraints: Installing two competing machinery designs on the identical factory floor space.
2. Capital Rationing / Resource Limits: Limited capital budget where funding Project A exhausts the funds available for Project B.
3. Market Demand Limits: Both projects satisfy the identical customer demand (e.g., building a bridge vs operating a ferry service across the same river).