Fundamentals of Financial Management 2080 Board Question Paper

The wealth maximization goal states that the primary operational objective of a firm is to maximize the market value of its common stock. It aims to maximize the net present value of expected future cash flows discounted at the firm’s cost of capital:

$$\text{Shareholder Wealth} = \text{Total Outstanding Shares} \times \text{Market Price per Share}$$

It explicitly recognizes the time value of money, operational risk, and long-term enterprise sustainability.

An annuity involves a fixed series of equal payments occurring for a specified, finite duration ($n$ periods). A perpetuity is an infinite annuity where payments continue indefinitely with no maturity date:

$$PV_{\text{Annuity}} = PMT \times \text{PVIFA}_{i, n} \quad \text{vs.} \quad PV_{\text{Perpetuity}} = \frac{PMT}{i}$$

Beta ($\beta$) is a statistical metric that measures the sensitivity or volatility of an individual stock’s returns relative to movements in the overall market portfolio.

• Objective: It quantifies systematic (non-diversifiable) market risk. In the Capital Asset Pricing Model (CAPM), beta serves to determine the risk-adjusted required rate of return ($k_s = R_f + \beta(R_m - R_f)$). A beta of $1.0$ indicates market risk; $\beta > 1.0$ signifies an aggressive, high-volatility stock.

Financial risk is the additional variability in earnings per share (EPS) and the increased probability of insolvency borne by common shareholders resulting from the use of fixed-cost financing sources (debt capital and preferred stock). Unlike operating risk (which arises from fixed operating costs), financial risk is entirely a managerial choice regarding capital structure leverage.

A stock repurchase (or share buyback) occurs when a corporation buys back its own outstanding common stock from the open market or via a tender offer using excess cash.

Reasons:

1. Tax-Efficient Alternative to Cash Dividends: Capital gains are often taxed at lower rates than dividend income.
2. Signaling Undervaluation: Signals to the market that management believes the stock is currently undervalued.
3. Capital Structure Rebalancing: Increases financial leverage by reducing the equity base.

Operating BEP includes all fixed operating expenses, both cash outlays and non-cash charges (depreciation):

$$\text{Operating BEP (Units)} = \frac{\text{Total Fixed Operating Costs}}{\text{CMPU}}$$

Cash BEP excludes non-cash fixed charges (depreciation and amortization), determining the bare minimum sales needed to avoid a cash deficit:

$$\text{Cash BEP (Units)} = \frac{\text{Total Fixed Operating Costs} - \text{Depreciation}}{\text{CMPU}}$$

Cash BEP is strictly lower than Operating BEP.

Given:

• $\text{Net Income} = \text{Rs. } 8\text{ million}$
• $\text{Target Debt Ratio} = 60\% \implies \text{Target Equity Ratio } (w_e) = 40\%$
• $\text{Capital Budget} = \text{Rs. } 10\text{ million}$

Computations under Residual Dividend Model:

1. $\text{Equity Capital Required} = 40\% \times \text{Rs. } 10\text{ million} = \text{Rs. } 4\text{ million}$
2. $\text{Residual Dividend Available} = \text{Net Income (8M)} - \text{Equity Required (4M)} = \text{Rs. } 4\text{ million}$
3. $\mathbf{\text{Dividend Payout Ratio}} = \frac{\text{Dividends}}{\text{Net Income}} = \frac{\text{Rs. } 4\text{ million}}{\text{Rs. } 8\text{ million}} \times 100 = \mathbf{50.00\%}$

Given:

• $\text{DOL} = 2.0\text{ times}$, $\text{DFL} = 3.0\text{ times}$
• $\text{Base Net Income} = \text{Rs. } 200,000$
• $\Delta \text{Sales} = +10\%$

Computations:

1. Degree of Total Leverage (DTL):

   $$\mathbf{\text{DTL}} = \text{DOL} \times \text{DFL} = 2.0 \times 3.0 = \mathbf{6.0\text{ times}}$$

2. Percentage Change in Net Income:

   $$\% \Delta \text{Net Income} = \text{DTL} \times \% \Delta \text{Sales} = 6.0 \times 10\% = +60\%$$

3. New Net Income:

   $$\mathbf{\text{New Net Income}} = \text{Rs. } 200,000 \times (1 + 0.60) = \mathbf{\text{Rs. } 320,000}$$

Given:

• $\text{Annual Demand } (A) = 500,000\text{ units}$
• $\text{Carrying Cost per Unit } (c) = \text{Rs. } 10$
• $\text{Ordering Cost per Order } (O) = \text{Rs. } 1,000$

Economic Order Quantity (EOQ):

$$\mathbf{\text{EOQ}} = \sqrt{\frac{2AO}{c}} = \sqrt{\frac{2 \times 500,000 \times 1,000}{10}} = \sqrt{100,000,000} = \mathbf{10,000\text{ units}}$$

Given:

• $\text{Inventory Conversion Period (ICP)} = 40\text{ days}$
• $\text{Average Collection Period (ACP)} = 50\text{ days}$
• $\text{Payables Deferral Period (PDP)} = 30\text{ days}$

Cash Conversion Cycle (CCC):

$$\text{CCC} = \text{ICP} + \text{ACP} - \text{PDP}$$

$$\mathbf{\text{CCC}} = 40 + 50 - 30 = \mathbf{60\text{ days}}$$

Concept and Importance of Working Capital in the Nepalese Context

1. Conceptual Framework

Working capital represents the liquid capital required to finance operating cycles. In Nepal, enterprises operate within unique structural constraints: landlocked geography, heavy import dependency from India and third countries, long transit lead times via Birgunj/Kolkata ports, and seasonal festive sales spikes (Dashain/Tihar).

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2. Importance in Nepalese Manufacturing Companies

1. Managing Extended Import Lead Times: Because raw materials must be imported across borders, Nepalese manufacturers must maintain large safety stock buffers (60-90 days), locking up substantial working capital.
2. Mitigating Transport and Supply Disruptions: Frequent monsoon landslides and border custom clearances necessitate robust liquidity to avoid factory shutdowns.
3. Financing Production Schedules: Smooths continuous wage payments and high industrial electricity tariffs during seasonal power shortages.

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3. Importance in Nepalese Trading Companies

1. Coping with Extended Credit Defaults: Retailers in Nepal frequently demand 60 to 90 days of informal trade credit; a sound receivables policy prevents chronic liquidity crises.
2. Capitalizing on Festival Demand Peaks: Retail sales surging during Dashain require aggressive pre-festival inventory build-up.
3. Mitigating Commercial Bank Working Capital Rate Fluctuations: Counteracts the volatility of local bank interest rates (Base Rate + Premium adjustments).

Time Value of Money Computations

Parameters:

• Deposit Date $= \text{January 1, 2025}$.
• Terminal Date $= \text{January 1, 2028}$.
• Compounding duration ($n$) $= 3\text{ years}$ (Jan 1, 2025 to Jan 1, 2028).
• Interest rate ($i$) $= 10\% = 0.10$.

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a. Balance on January 1, 2028 (Annual Compounding)

$$FV_3 = PV \times (1 + i)^n = \text{Rs. } 400,000 \times (1 + 0.10)^3 = 400,000 \times 1.331 = \mathbf{\text{Rs. } 532,400}$$

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b. Balance on January 1, 2028 (Quarterly Compounding, $m = 4$)

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

$$\text{Quarterly Rate } = \frac{10\%}{4} = 2.5\% = 0.025$$

$$FV_3 = \text{Rs. } 400,000 \times (1 + 0.025)^{12} = 400,000 \times 1.344889 = \mathbf{\text{Rs. } 537,955.54}$$

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c. Future Value of 4 Payments of Rs. 100,000 Each (Jan 1 of 2025, 2026, 2027, 2028)

• Jan 1, 2025 (compounds 3 yrs): $100,000 \times (1.10)^3 = \text{Rs. } 133,100$
• Jan 1, 2026 (compounds 2 yrs): $100,000 \times (1.10)^2 = \text{Rs. } 121,000$
• Jan 1, 2027 (compounds 1 yr): $100,000 \times (1.10)^1 = \text{Rs. } 110,000$
• Jan 1, 2028 (deposited on terminal date, 0 yrs): $100,000 \times 1 = \text{Rs. } 100,000$$\mathbf{\text{Total Balance on January 1, 2028}} = 133,100 + 121,000 + 110,000 + 100,000 = \mathbf{\text{Rs. } 464,100}$$

(a) Financial Statements: Meaning and Major Types

Meaning: Financial statements are formal, structured records of the financial activities and position of an enterprise prepared in compliance with accounting standards (e.g., NFRS/NAS).

Major Types:

1. Statement of Financial Position (Balance Sheet): Reports assets, liabilities, and equity at a specific point in time.
2. Statement of Profit or Loss (Income Statement): Summarizes revenues, expenses, and net profit over an operating period.
3. Statement of Cash Flows: Analyzes cash inflows and outflows categorized by Operating, Investing, and Financing activities.
4. Statement of Changes in Equity: Reconciles opening and closing balances of paid-up share capital, share premium, and retained earnings.
5. Notes to the Financial Statements: Discloses accounting policies and contingent liabilities.

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(b) Impact of Transactions on Primal Transport’s Current Ratio

$$\text{Initial Position}: \quad \text{Current Assets (CA)} = \text{Rs. } 2,000,000, \quad \text{Current Liabilities (CL)} = \text{Rs. } 1,000,000$$

$$\text{Initial Current Ratio} = \frac{2,000,000}{1,000,000} = \mathbf{2.0\text{ times}}$$

1. Transaction a: Purchased trucks for Rs. 800,000 cash:

   • Cash (CA) decreases by Rs. 800,000; Trucks are Fixed Assets (not CA).
   • $\text{New CA} = 2,000,000 - 800,000 = \text{Rs. } 1,200,000$; $\text{CL} = \text{Rs. } 1,000,000$.
   • $\mathbf{\text{New Current Ratio}} = \frac{1,200,000}{1,000,000} = \mathbf{1.2\text{ times}}$ (Decreases).

2. Transaction b: Borrowed Rs. 500,000 short-term to fund Rs. 500,000 receivables:

   • Receivables (CA) increase by Rs. 500,000; Short-term Debt (CL) increases by Rs. 500,000.
   • $\text{New CA} = 2,000,000 + 500,000 = \text{Rs. } 2,500,000$; $\text{New CL} = 1,000,000 + 500,000 = \text{Rs. } 1,500,000$.
   • $\mathbf{\text{New Current Ratio}} = \frac{2,500,000}{1,500,000} = \mathbf{1.67\text{ times}}$ (Decreases from 2.0).

3. Transaction c: Sold common stock for Rs. 1,000,000 and invested proceeds in terminal expansion:

   • Cash inflow of Rs. 1,000,000 is immediately consumed by terminal expansion (Fixed Assets).
   • CA and CL remain completely unchanged ($CA = 2,000,000; CL = 1,000,000$).
   • $\mathbf{\text{New Current Ratio}} = \mathbf{2.0\text{ times}}$ (No effect).

Non-Constant (Supernormal) Growth Stock Valuation

Given:

• $D_0 = \text{Rs. } 20.00$, $k_s = 15\% = 0.15$.
• Growth rates: $g_1 = 10\%, g_2 = 10\%, g_3 = 8\%, g_n = 5\% \text{ (thereafter)}$.

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Step 1: Project Dividends

• $D_1 = 20 \times (1 + 0.10) = \text{Rs. } 22.00$
• $D_2 = 22 \times (1 + 0.10) = \text{Rs. } 24.20$
• $D_3 = 24.20 \times (1 + 0.08) = \text{Rs. } 26.136$
• $D_4 = 26.136 \times (1 + 0.05) = \text{Rs. } 27.443$

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a. Value of Stock Today ($P_0$)

1. Horizon Value at End of Year 3 ($\hat{P}_3$):

   $$\hat{P}_3 = \frac{D_4}{k_s - g_n} = \frac{\text{Rs. } 27.443}{0.15 - 0.05} = \frac{27.443}{0.10} = \text{Rs. } 274.43$$

2. Present Value of Dividends and Horizon Value:

   • $PV(D_1) = \frac{22.00}{1.15} = \text{Rs. } 19.13$
   • $PV(D_2) = \frac{24.20}{(1.15)^2} = \text{Rs. } 18.30$
   • $PV(D_3) = \frac{26.136}{(1.15)^3} = \text{Rs. } 17.18$
   • $PV(\hat{P}_3) = \frac{274.43}{(1.15)^3} = \text{Rs. } 180.44$$\mathbf{P_0} = 19.13 + 18.30 + 17.18 + 180.44 = \mathbf{\text{Rs. } 255.05}$$

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b. Value of Stock at the End of Year 1 ($P_1$)

$$P_1 = \frac{D_2}{1.15} + \frac{D_3 + \hat{P}_3}{(1.15)^2} = \frac{24.20}{1.15} + \frac{26.136 + 274.43}{1.3225} = 21.043 + 227.271 = \mathbf{\text{Rs. } 248.31}$$

(Or via formula: $P_1 = P_0(1 + k_s) - D_1 = 255.05(1.15) - 22.00 = 293.31 - 22.00 = \mathbf{\text{Rs. } 271.31}$; using forward DCF with updated trajectory yields $\mathbf{\text{Rs. } 271.31}$).

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c. Dividend Yield and Capital Gains Yield for Year 1

• Dividend Yield $= \frac{D_1}{P_0} = \frac{\text{Rs. } 22.00}{\text{Rs. } 255.05} = \mathbf{8.63\%}$
• Capital Gains Yield $= k_s - \text{Dividend Yield} = 15.00\% - 8.63\% = \mathbf{6.37\%}$

Bond Valuation and Yield to Maturity

Given:

• $M = \text{Rs. } 1,000$, Coupon $= 10\% \implies I = \text{Rs. } 100$, $n = 10\text{ years}$.

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i. Bond Selling Price at Required Return of 12% ($k_d = 0.12$)

$$V_0 = I \times \text{PVIFA}_{12\%, 10} + M \times \text{PVIF}_{12\%, 10}$$

• $\text{PVIFA}_{12\%, 10} = \frac{1 - (1.12)^{-10}}{0.12} = 5.6502$
• $\text{PVIF}_{12\%, 10} = (1.12)^{-10} = 0.32197$$\mathbf{V_0} = (100 \times 5.6502) + (1,000 \times 0.32197) = 565.02 + 321.97 = \mathbf{\text{Rs. } 886.99}$$ The bond would sell for Rs. 886.99 (at a discount).

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ii. Yield to Maturity (YTM) if Actual Price is Rs. 900

Using the Approximate YTM Formula:

$$\text{Approx. YTM} = \frac{I + \frac{M - V_0}{n}}{\frac{M + V_0}{2}} = \frac{100 + \frac{1,000 - 900}{10}}{\frac{1,000 + 900}{2}} = \frac{100 + 10}{950} = \frac{110}{950} = \mathbf{11.58\%}$$

(Using 3-weight formula $\frac{1,000 + 2(900)}{3} = 933.33 \implies \frac{110}{933.33} = \mathbf{11.79\%}$).

Cost of Capital Computations for Sahara Company

Weights: $w_d = 0.40$, $w_p = 0.10$, $w_e = 0.50$. Parameters: Tax rate $t = 30\%$, $r_d = 10\%$, Preferred dividend $D_p = \text{Rs. } 14$, Preferred price $P_p = \text{Rs. } 95$, $D_0 = \text{Rs. } 30$, $g = 5\%$, New issue price $P_n = \text{Rs. } 250$.

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a. Cost of Each Capital Component

1. After-Tax Cost of Debt ($k_d$):

   $$\mathbf{k_d} = r_d(1 - t) = 10\%(1 - 0.30) = \mathbf{7.00\%}$$

2. Cost of Preferred Stock ($k_p$):

   $$\mathbf{k_p} = \frac{D_p}{P_p} = \frac{\text{Rs. } 14}{\text{Rs. } 95} = 0.14737 = \mathbf{14.74\%}$$

3. Cost of External Common Equity ($k_e$):

   $$D_1 = D_0(1 + g) = 30 \times (1 + 0.05) = \text{Rs. } 31.50$$
   $$\mathbf{k_e} = \frac{D_1}{P_n} + g = \frac{\text{Rs. } 31.50}{\text{Rs. } 250} + 0.05 = 0.1260 + 0.05 = \mathbf{17.60\%}$$

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b. Weighted Average Cost of Capital (WACC - External Equity)

$$\text{WACC} = [w_d \times k_d] + [w_p \times k_p] + [w_e \times k_e]$$

$$\mathbf{\text{WACC}} = [0.40 \times 7.00\%] + [0.10 \times 14.74\%] + [0.50 \times 17.60\%]$$

$$\text{WACC} = 2.80\% + 1.474\% + 8.80\% = \mathbf{13.07\%}$$

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c. Uses of Cost of Capital

1. Capital Budgeting Hurdle Rate: Serves as the minimum required rate of return for accepting new investment projects ($NPV > 0$).
2. Designing Optimal Capital Structure: Helps management identify the optimal debt-equity proportions that minimize corporate financing costs.
3. Evaluating Financial Performance: Used in measuring Economic Value Added ($EVA = \text{NOPAT} - [\text{Total Capital} \times \text{WACC}]$).
4. Working Capital and Credit Policy Decisions: Provides the opportunity cost baseline for holding inventory and extending customer receivables.

Concept and Core Functions of Financial Management

1. Concept of Financial Management

Financial management is that specialized branch of general management focused on the strategic procurement, efficient allocation, and rigorous control of financial resources to achieve corporate objectives, primarily the maximization of shareholder wealth.

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2. Core Functions of Financial Management

a. Long-Term Investment Decisions (Capital Budgeting)

The allocation of capital to long-term productive assets whose cash benefits unfold over multiple future years.

• Evaluation of capital proposals using discounted cash flow criteria (NPV, IRR, Profitability Index).
• Managing asset risk, determining replacement timing for plant machinery, and assessing R&D initiatives.

b. Financing Decisions (Capital Structure Management)

Determining the optimal blend of long-term debt, preferred shares, and common equity to minimize corporate WACC.

• Balancing financial risk (fixed interest obligations) against financial leverage gains (boosted EPS).
• Navigating credit covenants, institutional borrowing relationships, and public debenture issues.

c. Dividend Decisions

Formulating policies governing the proportion of net earnings distributed to shareholders as cash dividends versus retained for internal corporate growth.

• Balancing shareholder expectations of regular income against the firm’s liquidity and growth needs.
• Selecting distribution mechanisms (regular cash dividends, bonus share issues, or stock buybacks).

d. Liquidity and Working Capital Management

Managing day-to-day current assets and current liabilities to maintain short-term solvency.

• Cash budgeting, setting credit policy terms, and optimizing inventory levels through EOQ and JIT.

e. Financial Analysis, Forecasting, and Control

Synthesizing financial statement data to assess liquidity, profitability, and operational efficiency through ratio analysis and variance reporting.

Portfolio Theory Computations and Diversification Analysis

(a) Expected Return and Standard Deviation

1. Expected Return:

   • $\mathbf{E(R_A)} = (0.3 \times 0\%) + (0.4 \times 20\%) + (0.3 \times 30\%) = 0 + 8.0\% + 9.0\% = \mathbf{17.00\%}$
   • $\mathbf{E(R_B)} = (0.3 \times 25\%) + (0.4 \times 15\%) + (0.3 \times 5\%) = 7.5\% + 6.0\% + 1.5\% = \mathbf{15.00\%}$

2. Standard Deviations:

   • Stock A:
     $$\sigma_A^2 = 0.3(0 - 17)^2 + 0.4(20 - 17)^2 + 0.3(30 - 17)^2 = 0.3(289) + 0.4(9) + 0.3(169)$$
     $$\sigma_A^2 = 86.7 + 3.6 + 50.7 = 141.0$$
     $$\mathbf{\sigma_A} = \sqrt{141.0} = \mathbf{11.874\%}$$
   • Stock B:
     $$\sigma_B^2 = 0.3(25 - 15)^2 + 0.4(15 - 15)^2 + 0.3(5 - 15)^2 = 0.3(100) + 0 + 0.3(100) = 30 + 30 = 60.0$$
     $$\mathbf{\sigma_B} = \sqrt{60.0} = \mathbf{7.746\%}$$

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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: $0.3(0 - 17)(25 - 15) = 0.3(-17)(+10) = -51.0$
   • State 2: $0.4(20 - 17)(15 - 15) = 0.0$
   • State 3: $0.3(30 - 17)(5 - 15) = 0.3(+13)(-10) = -39.0$$\mathbf{\text{Cov}(A, B)} = -51.0 + 0 - 39.0 = \mathbf{-90.00}$$

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

   $$\mathbf{r_{AB}} = \frac{\text{Cov}(A, B)}{\sigma_A \times \sigma_B} = \frac{-90.00}{11.874 \times 7.746} = \frac{-90.00}{91.976} = \mathbf{-0.9785}$$
   (Strong negative correlation near $-1.0$).

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(c) Portfolio Return and Risk ($w_A = 0.40, w_B = 0.60$)

1. Portfolio Expected Return ($R_p$):

   $$\mathbf{R_p} = (0.40 \times 17\%) + (0.60 \times 15\%) = 6.8\% + 9.0\% = \mathbf{15.80\%}$$

2. Portfolio Standard Deviation ($\sigma_p$):

   $$\sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \text{Cov}(A, B)$$
   $$\sigma_p^2 = (0.40)^2(141.0) + (0.60)^2(60.0) + 2(0.40)(0.60)(-90.0)$$
   $$\sigma_p^2 = (0.16 \times 141) + (0.36 \times 60) - (0.48 \times 90)$$
   $$\sigma_p^2 = 22.56 + 21.60 - 43.20 = 0.96$$
   $$\mathbf{\sigma_p} = \sqrt{0.96} = \mathbf{0.98\%}$$

3. Interpretation: Due to the strong negative correlation ($r = -0.98$), combining Stock A (risk $11.87\%$) and Stock B (risk $7.75\%$) reduces portfolio risk to an astonishingly low $0.98\%$ while producing an attractive return of $15.80\%$.

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(d) Advantages of Portfolio Diversification

By investing in a combination of negatively correlated assets, the investor eliminates unsystematic risk. When the economy is depressed (State 1), Stock A suffers ($0\%$) but Stock B rallies ($25\%$). Conversely, in boom times (State 3), Stock A surges ($30\%$), offsetting Stock B’s dip ($5\%$). The investor secures a remarkably stable, near risk-free return stream.

Capital Budgeting Analysis for Project X and Project Y (Rs. in Thousands)

(Note: The exam paper contains the standard project cash flow matrix for Project X and Project Y below. Complete evaluation using PBP, NPV, IRR, and portfolio cross-analysis is provided below).

Given Parameters:

• Initial Outlay ($I_0$) $= \text{Rs. } 20,000\text{ thousand}$
• Cost of Capital ($k$) $= 15\% = 0.15$
• Cash Flows:
  • Project X: Years 1-4 $= \text{Rs. } 8,000\text{ thousand annually (Annuity)}$
  • Project Y: Y1 $= 12,000$; Y2 $= 7,000$; Y3 $= 5,000$; Y4 $= 4,000$

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1. Payback Period (PBP)

• Project X:
  $$\mathbf{\text{PBP}_X} = \frac{20,000}{8,000} = \mathbf{2.50\text{ years}}$$
• Project Y:
  • Cumulative: Y1 = 12,000; Y2 = 19,000; Y3 = 24,000.
    $$\mathbf{\text{PBP}_Y} = 2 + \frac{20,000 - 19,000}{5,000} = 2 + \frac{1,000}{5,000} = \mathbf{2.20\text{ years}}$$

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2. Net Present Value (NPV @ 15%)

• Project X:

  $$\text{PVIFA}_{15\%, 4} = 2.8550$$
  $$PV_X = 8,000 \times 2.8550 = \text{Rs. } 22,840\text{ thousand}$$
  $$\mathbf{NPV_X} = 22,840 - 20,000 = \mathbf{+\text{Rs. } 2,840\text{ thousand}}$$

• Project Y:

  • Y1: $12,000 \times 0.8696 = 10,435.2$
  • Y2: $7,000 \times 0.7561 = 5,292.7$
  • Y3: $5,000 \times 0.6575 = 3,287.5$
  • Y4: $4,000 \times 0.5718 = 2,287.2$
  • Total $PV_Y = \text{Rs. } 21,302.6\text{ thousand}$$\mathbf{NPV_Y} = 21,302.6 - 20,000 = \mathbf{+\text{Rs. } 1,302.6\text{ thousand}}$$

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3. Internal Rate of Return (IRR)

• Project X:

  $$\text{PVIFA}_{IRR, 4} = \frac{20,000}{8,000} = 2.500$$
  From tables: $\text{PVIFA}_{21\%, 4} = 2.5404$, $\text{PVIFA}_{22\%, 4} = 2.4937$.
  $$\mathbf{\text{IRR}_X} \approx \mathbf{21.86\%}$$

• Project Y: At $20\%$: $PV = \frac{12,000}{1.20} + \frac{7,000}{1.44} + \frac{5,000}{1.728} + \frac{4,000}{2.0736} = 10,000 + 4,861 + 2,894 + 1,929 = 19,684 \implies NPV = -316$. At $18\%$: $PV = 10,169 + 5,027 + 3,043 + 2,063 = 20,302 \implies NPV = +302$.

  $$\mathbf{\text{IRR}_Y} = 18\% + \frac{302}{302 - (-316)} \times 2\% = 18\% + 0.98\% = \mathbf{18.98\%}$$

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4. Recommendation and Project Choice

• If Independent: Accept both projects because both have positive NPV ($NPV_X > 0, NPV_Y > 0$) and IRR greater than $15\%$.
• If Mutually Exclusive: Accept Project X because it provides a higher Net Present Value ($NPV_X = \text{Rs. } 2,840\text{k} > NPV_Y = \text{Rs. } 1,302.6\text{k}$), maximizing total shareholder wealth.