Financial Management 2024 Board Question Paper

Meaning of Social Responsibility

Corporate Social Responsibility (CSR) refers to a corporation’s voluntary commitment and ethical obligation to operate in an economically, socially, and environmentally sustainable manner while balancing the interests of all stakeholders—including employees, customers, suppliers, local communities, and the environment—rather than exclusively pursuing shareholder wealth maximization.

• Core Dimensions:
  1. Environmental Stewardship: Reducing carbon footprint, adopting green energy, and minimizing pollution.
  2. Ethical Labor Practices: Providing fair wages, workplace safety, and gender equality.
  3. Community Development: Funding local education, healthcare, and infrastructure.
• Nepalese Regulatory Context: Under the Industrial Enterprises Act, 2076 (2020) of Nepal, medium, large, and cottage industries with an annual turnover exceeding NPR 150 million are legally mandated to allocate at least 1% of their annual net profit to designated CSR activities.

Causes of Agency Problem Between Shareholders and Managers

The agency problem arises due to the separation of ownership (shareholders/principals) and management control (managers/agents) in modern corporations. The primary causes include:

1. Divergence of Goals and Interests: Shareholders seek long-term maximization of the market value of common stock, whereas managers may prioritize personal wealth, job security, status, power, and prestige.
2. Information Asymmetry: Managers possess deeper, real-time insider knowledge about company operations and investment risks, which they may withhold or manipulate to mask poor performance.
3. Horizon Asymmetry (Short-Term Bias): Managers often focus on short-term quarterly accounting earnings to maximize annual bonuses, sacrificing value-creating long-term research and capital projects.
4. Empire Building and Perquisite Consumption: Managers may pursue unprofitable mergers or lavish perquisites (e.g., luxury corporate jets, opulent executive offices) that increase corporate size and managerial perks at the expense of shareholder wealth.
5. Differential Risk Tolerance: Managers hold concentrated firm-specific human capital risk and tend to be excessively risk-averse, avoiding positive NPV projects that carry career risk, while shareholders hold well-diversified portfolios.

Meaning of Financial Plan

A financial plan is a formal, comprehensive operational statement detailing an enterprise’s future financial goals, capital requirements, financing strategy, and resource allocation policies over a defined planning horizon (typically 1 to 5 years).

• Core Components:
  1. Pro-forma Financial Statements: Projected income statements, balance sheets, and cash flow statements derived from sales forecasts.
  2. Capital Expenditure Budget: Scheduled outlays for fixed assets and expansion projects.
  3. Financing Requirements (External Financing Needed): Exact debt and equity funding needed to support projected asset growth.
  4. Working Capital Policy: Target levels and financing of cash, receivables, and inventory.
• Primary Objective: Ensuring adequate liquidity to meet maturing obligations while optimizing capital structure to minimize the firm’s Weighted Average Cost of Capital (WACC).

Payback Period vs. Discounted Payback Period

Calculation of Required Rate of Return on Stock X

1. Given Data:

• Risk-free rate of return ($R_f$) = $4\% = 0.04$
• Market risk premium ($R_m - R_f$) = $6\% = 0.06$
• Systematic risk / Beta coefficient of Stock X ($\beta_X$) = $1.5$

---

2. Theoretical Formula:

According to the Capital Asset Pricing Model (CAPM):

$$E(R_X) = R_f + \beta_X \cdot (R_m - R_f)$$

---

3. Step-by-Step Calculation:

$$E(R_X) = 4\% + 1.5 \imes 6\%$$

$$E(R_X) = 4\% + 9.0\% = \mathbf{13.0\%}$$

---

4. Financial Interpretation:

Stock X carries $50\%$ more systematic market risk than the overall market ($\beta = 1.5 > 1.0$). Therefore, rational investors demand a required return of $13.0\%$ (consisting of a $4\%$ baseline risk-free compensation plus a $9\%$ systematic risk premium) to hold Stock X.

Dividend Calculation Under Residual Dividend Policy

1. Given Data:

• Net Income ($NI$) = Rs 15,000,000 (Rs 15 million)
• Target Debt Ratio ($w_d$) = $40\% = 0.40$
• Target Equity Ratio ($w_e$) = $1 - w_d = 1 - 0.40 = 60\% = 0.60$
• Total Capital Budget / Investment Opportunity ($I$) = Rs 20,000,000 (Rs 20 million)

---

2. Mathematical Formula:

Under the Residual Dividend Policy, dividends are paid only after all positive NPV capital budgeting projects are financed according to the target capital structure:

$$\ext{Equity Required} = I \imes w_e$$

$$\ext{Dividend} = \ext{Net Income} - \ext{Equity Required}$$

(Subject to a non-negativity constraint; if Equity Required $> NI$, Dividend $= 0$).

---

3. Step-by-Step Calculation:

1. Calculate Equity Capital Needed for Investment:
   $$\ext{Equity Required} = \ext{Rs } 20,000,000 \imes 0.60 = \mathbf{\ext{Rs } 12,000,000} \ext{ (Rs 12 million)}$$
2. Calculate Residual Dividend Amount:
   $$\ext{Dividend} = \ext{Rs } 15,000,000 - \ext{Rs } 12,000,000 = \mathbf{\ext{Rs } 3,000,000} \ext{ (Rs 3 million)}$$

---

4. Final Answer & Conclusion:

The firm will distribute Rs 3 million as cash dividends to shareholders. The resulting dividend payout ratio is $\frac{\ext{Rs } 3\ext{M}}{\ext{Rs } 15\ext{M}} = 20\%$, while Rs 12 million is retained for capital investment.

Motives of Holding Cash

According to John Maynard Keynes and modern corporate financial management, firms hold liquid cash and marketable securities for four primary motives:

1. Transaction Motive: To meet routine, day-to-day synchronized cash disbursements (e.g., payment of wages, purchases of raw materials, trade taxes, interest, and utility bills) arising in the normal course of business.
2. Precautionary Motive: To act as a financial safety cushion against unexpected contingencies, seasonal shocks, sudden supply chain disruptions, or customer default risks.
3. Speculative Motive: To exploit unexpected lucrative, bargain investment opportunities, such as buying distress inventory at deep discounts or acquiring undervalued assets during market downturns.
4. Compensating Balance Motive: To satisfy minimum non-interest-bearing deposit balances required by commercial banks in exchange for credit lines, loan syndications, and clearing facilities.

Calculation of Accounts Receivable for Beta Company

1. Given Data:

• Credit terms = Net 30 days
• Accounts past due on average = 40 days
• Annual credit sales ($S$) = Rs 18,000,000 (Rs 18 million)
• Days in a year ($D$) = 360 days

---

2. Step-by-Step Mathematical Derivation:

1. Determine Days Sales Outstanding (DSO) / Average Collection Period (ACP):
   $$DSO = \ext{Credit Terms} + \ext{Average Past Due Days}$$
   $$DSO = 30 + 40 = \mathbf{70 \ext{ days}}$$
2. Calculate Average Daily Sales (ADS):
   $$ADS = \frac{\ext{Annual Credit Sales}}{D} = \frac{\ext{Rs } 18,000,000}{360} = \mathbf{\ext{Rs } 50,000 \ext{ per day}}$$
3. Compute Accounts Receivable ($AR$):
   $$AR = ADS \imes DSO = \ext{Rs } 50,000 \imes 70 = \mathbf{\ext{Rs } 3,500,000}$$

---

3. Final Answer:

Beta Company’s balance of accounts receivable is Rs 3,500,000 (Rs 3.5 million).

Meaning of Stock Repurchase

A stock repurchase (or share buyback) is a corporate financial transaction in which a company buys back its own outstanding common stock from open-market investors, through a tender offer, or via negotiated private transactions, utilizing available retained earnings or cash reserves.

• Key Financial Impacts:
  1. Reduction in Outstanding Shares: Decreases the total share count, which mechanically increases Earnings Per Share (EPS) and Book Value Per Share (BVPS).
  2. Alternative to Cash Dividends: Distributes excess corporate liquidity to shareholders in a tax-efficient manner (benefiting from capital gains tax treatment).
  3. Market Signaling: Signals to the capital market that corporate management believes the company’s stock is undervalued.

Exchange Rate Determination via Purchasing Power Parity (PPP)

1. Given Data:

• Price of Apple Laptop in Japan ($P_{\ext{Japan}}$) = $\yen 160,000$
• Price of the same Apple Laptop in Nepal ($P_{\ext{Nepal}}$) = $\ext{NPR } 120,000$

---

2. Theoretical Formula:

Under the Absolute Purchasing Power Parity (Law of One Price):

$$P_{\ext{Nepal}} = S(\ext{NPR}/\yen) \imes P_{\ext{Japan}}$$

$$S(\ext{NPR}/\yen) = \frac{P_{\ext{Nepal}}}{P_{\ext{Japan}}}$$

---

3. Step-by-Step Calculation:

$$S(\ext{NPR}/\yen) = \frac{\ext{NPR } 120,000}{\yen 160,000} = \mathbf{0.75 \ext{ NPR per Japanese Yen}}$$

• Expressed per 10 Japanese Yen:
  $$\ext{NPR } 0.75 \imes 10 = \mathbf{\ext{NPR } 7.50 \ext{ per } 10 \ext{ JPY}}$$
• Expressed in JPY per NPR:
  $$S(\yen/\ext{NPR}) = \frac{1}{0.75} = \mathbf{1.3333 \ext{ JPY per NPR}}$$

---

4. Final Answer:

As per Purchasing Power Parity, the equilibrium exchange rate is NPR 0.75 per Japanese Yen (or NPR 75 per 100 Japanese Yen).

Comprehensive Overview of Financial Management Decisions

In modern corporate finance, the financial manager makes three interrelated, value-maximizing decisions:

                          Financial Management Decisions
                                        │
         ┌──────────────────────────────┼──────────────────────────────┐
         ▼                              ▼                              ▼
 1. Investment Decision        2. Financing Decision         3. Dividend Decision
(Capital Budgeting & CA)      (Capital Structure & WACC)    (Payout Policy & Retained Earn.)

---

1. Investment Decisions (Capital Budgeting & Asset Allocation)

• Long-Term Investment Decisions (Capital Budgeting): Involves committing funds into long-term capital projects, technological upgrades, plants, or M&A whose cash inflows will materialize over multiple future years. Techniques utilized include Net Present Value ($NPV$), Internal Rate of Return ($IRR$), and Profitability Index ($PI$).
• Short-Term Investment Decisions (Working Capital Management): Involves managing the day-to-day composition of current assets (cash, receivables, inventories) to maintain adequate operational liquidity while avoiding idle capital.

---

2. Financing Decisions (Capital Structure Selection)

• Deals with determining the optimal financing mix between debt capital (bank loans, debentures) and equity capital (common stock, preferred stock, retained earnings).
• Objective: Achieving an optimal capital structure that balances tax-shield benefits of debt against financial distress/bankruptcy costs, thereby minimizing the Weighted Average Cost of Capital (WACC) and maximizing firm value.

---

3. Dividend Decisions (Profit Allocation)

• Determines how corporate net earnings after tax should be distributed: paying out cash dividends to shareholders versus retaining earnings for internal reinvestment.
• The financial manager must balance shareholder preferences for current dividend income against the firm’s growth opportunities and capital expenditure requirements.

Impact of Profit Size, Liquidity Position, and Investment Opportunities on Dividend Policy

A company’s dividend policy represents the strategic decision to divide net earnings between dividend payouts and internal retention. Three pivotal determinants govern this policy:

---

1. Size and Stability of Profit

• Baseline Determinant: Corporate law and prudence dictate that cash dividends can only be paid out of accumulated accounting earnings. Larger net profits expand the pool of funds available for distribution.
• Earnings Stability: A corporation with stable, predictable annual earnings can safely commit to a high, regular dividend payout ratio (e.g., mature commercial banks like Nabil Bank). Conversely, firms with volatile, cyclical earnings maintain conservative baseline payouts to prevent costly dividend cuts.

---

2. Liquidity Position of the Firm

• Cash vs. Profit Disconnect: Accounting profit represents accrual revenue minus expenses; it does not equal liquid cash. A firm may exhibit high accounting net income while experiencing an acute cash shortage due to funds tied up in receivables and inventory.
• Direct Impact: Because dividends are paid strictly in cash, a strong liquidity buffer (cash and marketable securities) is required to sustain cash distributions. A highly profitable but illiquid company must pay stock dividends (bonus shares) or conserve cash rather than paying cash dividends.

---

3. Availability of Investment Opportunities

• The Residual Dividend Framework: According to financial theory, if a firm possesses profitable investment opportunities with expected returns exceeding the cost of capital ($r > k$), shareholder wealth is maximized by retaining earnings to finance these positive NPV projects.
• Firm Life Cycle Impact:
  • Rapidly Growing Firms: Face extensive capital investment opportunities (e.g., Nepalese hydropower companies during construction); hence, they maintain low dividend payouts or zero dividends.
  • Mature / Saturated Firms: Have limited internal reinvestment avenues; hence, they distribute excess free cash flow as dividends.

Features of an Optimal Capital Structure

The optimal capital structure is that dynamic combination of debt, preferred stock, and common equity that minimizes the firm’s Weighted Average Cost of Capital (WACC) while simultaneously maximizing the market value of the firm ($V$).

---

Key Features and Principles:

1. Minimization of Overall Cost of Capital (WACC):

   • Takes advantage of the lower cost of debt and the interest tax-shield benefit:
     $$k_d(\text{after-tax}) = k_d(1 - T)$$
   • Optimizes the leverage ratio where the marginal benefit of tax shields exactly equals the marginal cost of expected financial distress (Static Trade-off Theory).

2. Maintenance of Financial Solvency and Safety:

   • Excessive debt introduces fixed financial obligations. An optimal capital structure avoids excessive leverage, ensuring that the Times Interest Earned (TIE) and debt-service coverage ratios remain well above danger thresholds even during severe economic downturns.

3. Adequate Financial Flexibility:

   • Preserves spare borrowing capacity so the firm can access external debt markets swiftly during unforeseen emergencies or attractive unexpected expansion opportunities without paying punitive yields.

4. Profitability and EPS Enhancement (Favorable Leverage):

   • Employs debt trading on equity when Return on Investment exceeds the cost of debt ($ROI > k_d$), boosting Return on Equity (ROE) and Earnings Per Share (EPS) for common stockholders.

5. Protection of Managerial and Ownership Control:

   • Avoids issuing new common equity when doing so would dilute the voting control of existing majority shareholders or expose the company to hostile acquisition.

Comprehensive Inventory Management Analysis for KCFC

1. Given Data:

• Annual Demand ($D$) = $3,380,000$ bags
• Ordering cost per order ($S$) = Rs 480
• Purchase price per bag ($C$) = Rs 600
• Carrying cost percentage ($I$) = $20\% = 0.20$
• Annual carrying cost per bag ($H = C \times I$) = $\text{Rs } 600 \times 0.20 = \mathbf{\text{Rs } 120 \text{ per bag/year}}$
• Safety stock ($SS$) = $15,000$ bags
• Lead time ($L$) = $2$ weeks (out of $52$ weeks per year)

---

Part a: Economic Order Quantity (EOQ)

$$EOQ = \sqrt{\frac{2 \cdot D \cdot S}{H}}$$

$$EOQ = \sqrt{\frac{2 \times 3,380,000 \times 480}{120}} = \sqrt{\frac{3,244,800,000}{120}} = \sqrt{27,040,000} = \mathbf{5,200 \text{ bags}}$$

---

Part b: Total Inventory Cost (TIC)

Total inventory cost consists of annual ordering costs plus annual carrying costs of both cycle inventory and safety stock:

1. Annual Ordering Cost:
   $$\text{Ordering Cost} = \left(\frac{D}{EOQ}\right) \times S = \left(\frac{3,380,000}{5,200}\right) \times 480 = 650 \times 480 = \mathbf{\text{Rs } 312,000}$$
2. Annual Carrying Cost of Cycle Inventory:
   $$\text{Carrying Cost}_{\text{cycle}} = \left(\frac{EOQ}{2}\right) \times H = \left(\frac{5,200}{2}\right) \times 120 = 2,600 \times 120 = \mathbf{\text{Rs } 312,000}$$
3. Annual Carrying Cost of Safety Stock:
   $$\text{Carrying Cost}_{\text{safety}} = SS \times H = 15,000 \times 120 = \mathbf{\text{Rs } 1,800,000}$$
4. Total Inventory Management Cost:
   $$TIC = 312,000 + 312,000 + 1,800,000 = \mathbf{\text{Rs } 2,424,000}$$
   (Note: Excluding safety stock carrying costs, basic $TIC = 312,000 + 312,000 = \text{Rs } 624,000$).

---

Part c: Re-Order Point (ROP)

$$\text{Weekly Demand } (d) = \frac{D}{52} = \frac{3,380,000}{52} = 65,000 \text{ bags per week}$$

$$\text{Lead Time Demand} = d \times L = 65,000 \times 2 = 130,000 \text{ bags}$$

$$ROP = \text{Lead Time Demand} + \text{Safety Stock} = 130,000 + 15,000 = \mathbf{145,000 \text{ bags}}$$

---

Summary of Final Answers:

• EOQ: 5,200 bags (placing 650 orders per year).
• Total Inventory Cost: Rs 2,424,000 per annum.
• Re-order Level: 145,000 bags.

Evaluation of Proposed Credit Policy Change for Birat Trading Company (BTC)

1. Given Financial Parameters:

• Current Sales ($S_0$) = Rs 6,000,000; Proposed Sales ($S_1$) = Rs 7,200,000
• Incremental Sales ($\Delta S$) = Rs 1,200,000
• Variable cost ratio ($v$) = $70\% = 0.70$; Contribution margin ratio ($1 - v$) = $30\% = 0.30$
• Current Average Collection Period ($ACP_0$) = $45$ days; Proposed $ACP_1 = 60$ days
• Current Bad Debt rate ($b_0$) = $2.0\%$; Proposed Bad Debt rate ($b_1$) = $2.5\%$
• Opportunity cost of funds in receivables ($k$) = $10\% = 0.10$
• Corporate tax rate ($T$) = $30\% = 0.30$; Days in year = $360$ days

---

2. Incremental Cash Flow & Profit Analysis:

Step 1: Incremental Contribution Margin

$$\Delta CM = \Delta S \times (1 - v) = \text{Rs } 1,200,000 \times 0.30 = \mathbf{+\text{Rs } 360,000}$$

Step 2: Incremental Bad Debt Losses

• Current Bad Debts = $S_0 \times b_0 = \text{Rs } 6,000,000 \times 0.02 = \text{Rs } 120,000$
• Proposed Bad Debts = $S_1 \times b_1 = \text{Rs } 7,200,000 \times 0.025 = \text{Rs } 180,000$$\Delta \text{Bad Debts} = 180,000 - 120,000 = \mathbf{+\text{Rs } 60,000}$$

Step 3: Incremental Cost of Funds Invested in Accounts Receivable

Using the standard variable cost basis:

• Current AR Investment = $\left(\frac{S_0}{360} \times ACP_0\right) \times v = \left(\frac{6,000,000}{360} \times 45\right) \times 0.70 = 750,000 \times 0.70 = \text{Rs } 525,000$
• Proposed AR Investment = $\left(\frac{S_1}{360} \times ACP_1\right) \times v = \left(\frac{7,200,000}{360} \times 60\right) \times 0.70 = 1,200,000 \times 0.70 = \text{Rs } 840,000$$\Delta \text{Investment in AR} = 840,000 - 525,000 = \text{Rs } 315,000$$
  $$\Delta \text{Carrying Cost of AR} = \Delta \text{Investment} \times k = \text{Rs } 315,000 \times 0.10 = \mathbf{+\text{Rs } 31,500}$$
  (Note: If calculated on sales basis: $\Delta AR = 1,200,000 - 750,000 = 450,000$, Cost $= 450,000 \times 0.10 = \text{Rs } 45,000$).

Step 4: Incremental Pre-Tax & After-Tax Profit

$$\Delta \text{Profit Before Tax} = \Delta CM - \Delta \text{Bad Debts} - \Delta \text{Carrying Cost}$$

$$\Delta EBT = 360,000 - 60,000 - 31,500 = \mathbf{\text{Rs } 268,500}$$

$$\Delta \text{Net Profit After Tax} = \Delta EBT \times (1 - T) = 268,500 \times (1 - 0.30) = \mathbf{+\text{Rs } 187,950}$$

(On sales basis: $\Delta EAT = (360,000 - 60,000 - 45,000) \times 0.70 = \mathbf{+\text{Rs } 178,500}$).

---

3. Recommendation & Decision:

BTC should change its credit terms from ‘net 40’ to ‘net 50’. Financial Justification: The additional contribution margin (Rs 360,000) substantially surpasses the combined incremental bad debt expenses (Rs 60,000) and opportunity carrying costs (Rs 31,500), generating a net positive after-tax benefit of Rs 187,950 annually.

Comparative Analysis: Stock Dividend vs. Stock Split for XYZ Company

1. Initial Position:

• Existing shares outstanding ($N_0$) = $100,000$ shares
• Current market price per share ($P_0$) = Rs 300
• Par value per share = Rs 100
• Total Initial Market Capitalization = $100,000 \times \text{Rs } 300 = \mathbf{\text{Rs } 30,000,000}$

---

Part a: 10 Percent Stock Dividend

1. New Number of Shares ($N_1$):
   $$N_1 = N_0 \times (1 + \%SD) = 100,000 \times (1 + 0.10) = \mathbf{110,000 \text{ shares}}$$
   (New bonus shares issued = $10,000$ shares).
2. New Market Price Per Share ($P_1$):
   $$P_1 = \frac{P_0}{1 + \%SD} = \frac{\text{Rs } 300}{1.10} = \mathbf{\text{Rs } 272.73 \text{ per share}}$$
   (Par value remains Rs 100 per share).
3. Verification of Total Equity Value:
   $$V_1 = 110,000 \times \text{Rs } 272.727 = \text{Rs } 30,000,000 \quad \text{(Total market value is conserved)}.$$

---

Part b: 2-for-1 Stock Split

1. New Number of Shares ($N_2$):
   $$N_2 = N_0 \times 2 = 100,000 \times 2 = \mathbf{200,000 \text{ shares}}$$
2. New Market Price Per Share ($P_2$):
   $$P_2 = \frac{P_0}{2} = \frac{\text{Rs } 300}{2} = \mathbf{\text{Rs } 150.00 \text{ per share}}$$
3. New Par Value Per Share:
   $$\text{New Par Value} = \frac{\text{Old Par Value}}{2} = \frac{\text{Rs } 100}{2} = \mathbf{\text{Rs } 50.00 \text{ per share}}$$
4. Verification of Total Equity Value:
   $$V_2 = 200,000 \times \text{Rs } 150 = \text{Rs } 30,000,000 \quad \text{(Total market value is conserved)}.$$

---

Summary Table:

Cross Exchange Rate Calculation and Financial Interpretation

1. Given Currency Quotations:

• Exchange rate between US Dollar and Indian Rupee:
  $$S(\text{INR}/\text{USD}) = \text{INR } 83.22 \text{ per USD}$$
• Exchange rate between Nepalese Rupee and Indian Rupee:
  $$S(\text{NPR}/\text{INR}) = \text{NPR } 1.60 \text{ per INR}$$

---

2. Mathematical Cross-Rate Formulation:

$$\text{Cross Rate } S(\text{NPR}/\text{USD}) = S(\text{NPR}/\text{INR}) \times S(\text{INR}/\text{USD})$$

---

3. Step-by-Step Calculation:

$$S(\text{NPR}/\text{USD}) = 1.60 \times 83.22 = \mathbf{\text{NPR } 133.152 \text{ per USD}}$$

---

4. Financial Interpretation:

1. Direct Rate: Exactly NPR 133.152 is required to purchase one US Dollar in the foreign exchange market.
2. Institutional Pegging Mechanism in Nepal: The Nepalese Rupee is officially pegged to the Indian Rupee at a fixed parity of NPR 1.60 per INR (a fixed exchange rate regime maintained since 1993 by Nepal Rastra Bank). Consequently, the NPR does not float independently against the US Dollar; rather, the NPR/USD exchange rate fluctuates in exact lockstep with international movements between the US Dollar and the Indian Rupee.

Multinational Financial Management vs. Domestic Financial Management

1. Meaning of Multinational Financial Management

Multinational Financial Management (MNC/MNE Finance) involves the strategic planning, acquisition, allocation, and controlling of financial resources within multinational corporations operating across multiple sovereign national borders. It builds upon domestic financial principles but must navigate distinct political environments, multiple currencies, varied tax codes, and international capital markets.

---

2. Key Differences Between Domestic and Multinational Financial Management

---

3. Relevance in the Nepalese Economy:

Multinational firms operating in Nepal (e.g., Unilever Nepal, Standard Chartered Bank Nepal) face strict regulatory oversight by Nepal Rastra Bank regarding foreign currency repatriation under the Foreign Investment and Technology Transfer Act (FITTA), 2075.

Comprehensive Financial Forecasting and AFN Analysis — Hulas Metal Company (HMC)

1. Given Financial Data (2023 Baseline):

• Baseline Sales ($S_0$) = Rs 1,000,000
• Projected Sales Growth ($g$) = $25\% = 0.25$
• Projected 2024 Sales ($S_1$) = $\text{Rs } 1,000,000 \times 1.25 = \mathbf{\text{Rs } 1,250,000}$
• Sales Increase ($\Delta S$) = $\text{Rs } 250,000$
• Profit Margin on Sales ($M$) = $8\% = 0.08$
• Retention Ratio ($RR$) = $40\% = 0.40$
• All assets are operated at full capacity $\implies$ Spontaneous Assets ($A^*$) = Total Assets = Rs 500,000
• Spontaneous Liabilities ($L^*$): Accounts payable (Rs 60,000) + Accruals (Rs 50,000) = Rs 110,000 (Notes payable is a negotiated financing source and does not increase spontaneously).

---

Part a: Estimation of Additional Funds Needed (AFN) Using AFN Formula

$$AFN = \left(\frac{A^*}{S_0}\right)\Delta S - \left(\frac{L^*}{S_0}\right)\Delta S - M \cdot S_1 \cdot RR$$

1. Required Increase in Assets:
   $$\left(\frac{A^*}{S_0}\right)\Delta S = \left(\frac{\text{Rs } 500,000}{\text{Rs } 1,000,000}\right) \times \text{Rs } 250,000 = 0.50 \times 250,000 = \mathbf{\text{Rs } 125,000}$$
2. Spontaneous Increase in Current Liabilities:
   $$\left(\frac{L^*}{S_0}\right)\Delta S = \left(\frac{\text{Rs } 110,000}{\text{Rs } 1,000,000}\right) \times \text{Rs } 250,000 = 0.11 \times 250,000 = \mathbf{\text{Rs } 27,500}$$
3. Internal Addition to Retained Earnings:
   $$\Delta RE = M \times S_1 \times RR = 0.08 \times \text{Rs } 1,250,000 \times 0.40 = \text{Rs } 100,000 \times 0.40 = \mathbf{\text{Rs } 40,000}$$
4. Calculated AFN:
   $$AFN = \text{Rs } 125,000 - \text{Rs } 27,500 - \text{Rs } 40,000 = \mathbf{\text{Rs } 57,500}$$

---

Part b: Projected Balance Sheet Method (Verification)

Assets and spontaneous liabilities expand by $25\%$ in tandem with sales:

Projected Assets (2024):

• Cash: $\text{Rs } 50,000 \times 1.25 = \text{Rs } 62,500$
• Accounts Receivable: $\text{Rs } 70,000 \times 1.25 = \text{Rs } 87,500$
• Inventories: $\text{Rs } 130,000 \times 1.25 = \text{Rs } 162,500$
• Total Current Assets: $\mathbf{\text{Rs } 312,500}$
• Net Fixed Assets: $\text{Rs } 250,000 \times 1.25 = \mathbf{\text{Rs } 312,500}$
• Total Projected Assets: $\mathbf{\text{Rs } 625,000}$

Projected Liabilities & Equity (2024 Before AFN):

• Accounts Payable: $\text{Rs } 60,000 \times 1.25 = \text{Rs } 75,000$
• Accruals: $\text{Rs } 50,000 \times 1.25 = \text{Rs } 62,500$
• Notes Payable (remains constant): $\text{Rs } 40,000$
• Total Current Liabilities: $\mathbf{\text{Rs } 177,500}$
• Common Stock (remains constant): $\mathbf{\text{Rs } 200,000}$
• Retained Earnings: $\text{Rs } 150,000 + \text{Rs } 40,000 (\Delta RE) = \mathbf{\text{Rs } 190,000}$
• Total Liabilities & Equity Before External Financing:
  $$177,500 + 200,000 + 190,000 = \mathbf{\text{Rs } 567,500}$$

Verification of AFN:

$$AFN = \text{Total Projected Assets} - \text{Total Liabilities \& Equity Before AFN}$$

$$AFN = \text{Rs } 625,000 - \text{Rs } 567,500 = \mathbf{\text{Rs } 57,500}$$

---

Pro-Forma Balance Sheet as on December 31, 2024:

Rigorous Statistical and Portfolio Analysis for Stock X and Stock Y

1. Given Probability Distribution:

---

Part a: Expected Rate of Return

$$E(R) = \sum_{i=1}^{n} P_i \cdot R_i$$

• For Stock X:
  $$E(R_X) = (0.30 \times 10) + (0.40 \times 15) + (0.30 \times 20) = 3.0 + 6.0 + 6.0 = \mathbf{15.0\%}$$
• For Stock Y:
  $$E(R_Y) = (0.30 \times 30) + (0.40 \times 20) + (0.30 \times 10) = 9.0 + 8.0 + 3.0 = \mathbf{20.0\%}$$

---

Part b: Standard Deviation of Returns

$$\sigma^2 = \sum_{i=1}^{n} P_i \cdot [R_i - E(R)]^2, \quad \sigma = \sqrt{\sigma^2}$$

• For Stock X:

  $$\sigma_X^2 = 0.30(10 - 15)^2 + 0.40(15 - 15)^2 + 0.30(20 - 15)^2$$
  $$\sigma_X^2 = 0.30(25) + 0.40(0) + 0.30(25) = 7.5 + 0 + 7.5 = 15.0\%^2$$
  $$\sigma_X = \sqrt{15.0} = \mathbf{3.87298\%} \approx \mathbf{3.87\%}$$

• For Stock Y:

  $$\sigma_Y^2 = 0.30(30 - 20)^2 + 0.40(20 - 20)^2 + 0.30(10 - 20)^2$$
  $$\sigma_Y^2 = 0.30(100) + 0.40(0) + 0.30(100) = 30.0 + 0 + 30.0 = 60.0\%^2$$
  $$\sigma_Y = \sqrt{60.0} = \mathbf{7.74597\%} \approx \mathbf{7.75\%}$$

---

Part c: Covariance and Correlation Coefficient

$$\text{Cov}(X, Y) = \sum_{i=1}^{n} P_i \cdot [R_{Xi} - E(R_X)] \cdot [R_{Yi} - E(R_Y)]$$

1. Condition 1: $0.30 \times (10 - 15) \times (30 - 20) = 0.30 \times (-5) \times (+10) = -15.0$
2. Condition 2: $0.40 \times (15 - 15) \times (20 - 20) = 0.40 \times (0) \times (0) = 0.0$
3. Condition 3: $0.30 \times (20 - 15) \times (10 - 20) = 0.30 \times (+5) \times (-10) = -15.0$$\text{Cov}(X, Y) = -15.0 + 0.0 - 15.0 = \mathbf{-30.0\%^2} \quad (\text{or } -0.0030)$$

• Correlation Coefficient ($r_{XY}$):
  $$r_{XY} = \frac{\text{Cov}(X, Y)}{\sigma_X \cdot \sigma_Y} = \frac{-30.0}{\sqrt{15} \times \sqrt{60}} = \frac{-30.0}{\sqrt{900}} = \frac{-30.0}{30.0} = \mathbf{-1.0}$$
  (Stock X and Stock Y exhibit perfect negative correlation).

---

Part d: Portfolio Expected Return and Risk (50% in X, 50% in Y)

Given weights: $w_X = 0.50$, $w_Y = 0.50$.

1. Portfolio Expected Return ($E(R_p)$):

   $$E(R_p) = w_X E(R_X) + w_Y E(R_Y) = 0.50(15\%) + 0.50(20\%) = 7.5\% + 10.0\% = \mathbf{17.5\%}$$

2. Portfolio Variance ($\sigma_p^2$):

   $$\sigma_p^2 = w_X^2 \sigma_X^2 + w_Y^2 \sigma_Y^2 + 2 w_X w_Y \text{Cov}(X, Y)$$
   $$\sigma_p^2 = (0.50)^2 (15) + (0.50)^2 (60) + 2(0.50)(0.50)(-30)$$
   $$\sigma_p^2 = 0.25(15) + 0.25(60) + 0.50(-30) = 3.75 + 15.00 - 15.00 = \mathbf{3.75\%^2}$$

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

   $$\sigma_p = \sqrt{3.75} = \mathbf{1.9365\%} \approx \mathbf{1.94\%}$$

---

Key Financial Interpretation:

Because the correlation is perfectly negative ($r = -1.0$), diversification reduces total portfolio risk to $1.94\%$, which is substantially lower than Stock X alone ($3.87\%$) and Stock Y alone ($7.75\%$), while generating an attractive expected return of $17.5\%$.

Comprehensive Leverage and Break-Even Analysis — Delta Manufacturing Company (DMC)

1. Given Baseline Income Statement Data:

• Sales Volume ($Q$) = $10,000$ units
• Selling Price per unit ($P$) = Rs 40; Total Sales ($S$) = Rs 400,000
• Variable Cost per unit ($V$) = Rs 20; Total Variable Cost ($VC$) = Rs 200,000
• Unit Contribution Margin ($P - V$) = Rs 20; Total Contribution Margin ($CM$) = Rs 200,000
• Fixed Operating Costs ($FC$) = Rs 100,000
• Operating Income ($EBIT$) = $200,000 - 100,000 = \text{Rs } 100,000$
• Interest Expense ($I$) = Rs 20,000
• Earnings Before Tax ($EBT$) = $100,000 - 20,000 = \text{Rs } 80,000$
• Tax Expense ($T = 30\%$) = Rs 24,000
• Net Income ($NI$) = Rs 56,000
• Number of Common Shares Outstanding ($N$) = $10,000$ shares

---

Part a: Earnings Per Share (EPS)

$$EPS = \frac{\text{Net Income}}{N} = \frac{\text{Rs } 56,000}{10,000 \text{ shares}} = \mathbf{\text{Rs } 5.60 \text{ per share}}$$

---

Part b: Operating Break-Even Point

1. Break-Even Quantity in Units ($Q_{BEP}$):
   $$Q_{BEP} = \frac{FC}{P - V} = \frac{\text{Rs } 100,000}{\text{Rs } 40 - \text{Rs } 20} = \frac{100,000}{20} = \mathbf{5,000 \text{ units}}$$
2. Break-Even Revenue in Rupees ($S_{BEP}$):
   $$S_{BEP} = Q_{BEP} \times P = 5,000 \times \text{Rs } 40 = \mathbf{\text{Rs } 200,000}$$

---

Part c: Degree of Operating, Financial, and Combined Leverage

1. Degree of Operating Leverage (DOL at 10,000 units):
   $$DOL = \frac{\text{Contribution Margin}}{EBIT} = \frac{\text{Rs } 200,000}{\text{Rs } 100,000} = \mathbf{2.00}$$
2. Degree of Financial Leverage (DFL at EBIT of Rs 100,000):
   $$DFL = \frac{EBIT}{EBT} = \frac{\text{Rs } 100,000}{\text{Rs } 80,000} = \mathbf{1.25}$$
3. Degree of Combined Leverage (DCL / DTL):
   $$DCL = DOL \times DFL = 2.00 \times 1.25 = \mathbf{2.50}$$
   (Alternatively: $DCL = \frac{CM}{EBT} = \frac{200,000}{80,000} = 2.50$).

---

Part d: Percentage Increase in Net Profit for a 20% Increase in Sales

$$\% \Delta NI = DCL \times \% \Delta \text{Sales}$$

$$\% \Delta NI = 2.50 \times 20\% = \mathbf{50.0\%}$$

Rigorous Verification:

• New Sales ($+20\%$) = $12,000 \text{ units} \times \text{Rs } 40 = \text{Rs } 480,000$
• Less: Variable Costs ($12,000 \times \text{Rs } 20$) = $\text{Rs } 240,000$
• New Contribution Margin = $\text{Rs } 240,000$
• Less: Fixed Costs = $\text{Rs } 100,000$
• New EBIT = $\text{Rs } 140,000$ ($+40\%$, matching $DOL \times 20\%$)
• Less: Interest = $\text{Rs } 20,000$
• New EBT = $\text{Rs } 120,000$
• Less: Tax ($30\%$) = $\text{Rs } 36,000$
• New Net Income ($NI_1$) = $\text{Rs } 84,000$$\% \Delta NI = \frac{\text{Rs } 84,000 - \text{Rs } 56,000}{\text{Rs } 56,000} = \frac{28,000}{56,000} = \mathbf{50.0\%}$$

Comprehensive Capital Budgeting Case Analysis — Gandaki Hydropower Company (GTC)

1. Case Background & Projected Cash Flows:

• Initial Capital Investment ($I_0$):
  $$\text{Project X} = -\text{Rs } 500,000, \quad \text{Project Y} = -\text{Rs } 500,000$$
• Cost of Capital ($k$) = $10\% = 0.10$
• Projected Net Cash Inflows ($CF_t$):

  Year ($t$)	Project X (Rs)	Project Y (Rs)
  1	200,000	300,000
  2	200,000	200,000
  3	200,000	200,000
  4	200,000	100,000

---

Part a: Payback Period (PBP)

• Concept: The payback period is the exact number of years required for an enterprise to recoup its original capital outlay from cumulative undiscounted net cash inflows.
• Calculation for Project X (Equal Annual Inflows):
  $$PBP_X = \frac{\text{Initial Outlay}}{\text{Annual Cash Inflow}} = \frac{\text{Rs } 500,000}{\text{Rs } 200,000} = \mathbf{2.50 \text{ years}}$$
• Calculation for Project Y (Unequal Cash Inflows):
  • Year 1: Cumulative Cash Flow = Rs 300,000
  • Year 2: Cumulative Cash Flow = $300,000 + 200,000 = \text{Rs } 500,000$ (Exactly reaches initial cost).
    $$PBP_Y = \mathbf{2.00 \text{ years}}$$

---

Part b: Net Present Value (NPV at k = 10%)

$$NPV = \sum_{t=1}^{n} \frac{CF_t}{(1 + k)^t} - I_0$$

• Present Value Factors at $10\%$: $PVIF_{10\%, 1} = 0.90909$, $PVIF_{10\%, 2} = 0.82645$, $PVIF_{10\%, 3} = 0.75131$, $PVIF_{10\%, 4} = 0.68301$, $PVIFA_{10\%, 4} = 3.16987$.

1. Project X (4-year annuity of Rs 200,000):

   $$PV_X = \text{Rs } 200,000 \times PVIFA_{10\%, 4} = 200,000 \times 3.169865 = \text{Rs } 633,973$$
   $$NPV_X = \text{Rs } 633,973 - \text{Rs } 500,000 = \mathbf{+\text{Rs } 133,973}$$

2. Project Y (Year-by-year discounting):

   • Year 1: $\text{Rs } 300,000 \times 0.909091 = \text{Rs } 272,727$
   • Year 2: $\text{Rs } 200,000 \times 0.826446 = \text{Rs } 165,289$
   • Year 3: $\text{Rs } 200,000 \times 0.751315 = \text{Rs } 150,263$
   • Year 4: $\text{Rs } 100,000 \times 0.683013 = \text{Rs } 68,301$
   • Total Present Value ($PV_Y$): $272,727 + 165,289 + 150,263 + 68,301 = \text{Rs } 656,580$$NPV_Y = \text{Rs } 656,580 - \text{Rs } 500,000 = \mathbf{+\text{Rs } 156,580}$$

---

Part c: Decision Under Independent Projects

• Decision Criterion: Accept all projects that add value ($NPV > 0$ or $IRR > k$).
• Conclusion: Since $NPV_X = +\text{Rs } 133,973 > 0$ and $NPV_Y = +\text{Rs } 156,580 > 0$, both Project X and Project Y should be accepted (provided GTC has sufficient capital budget of Rs 1,000,000).

---

Part d: Decision Under Mutually Exclusive Projects

• Decision Criterion: Select the single project that maximizes absolute shareholder wealth (the highest positive NPV).
• Comparison:
  $$NPV_Y (\text{Rs } 156,580) > NPV_X (\text{Rs } 133,973)$$
• Recommendation: Project Y must be chosen.
• Managerial Justification:
  1. Project Y delivers an extra Rs 22,607 in net shareholder wealth compared to Project X.
  2. Project Y recovers initial capital faster ($2.0$ years vs $2.5$ years), front-loading cash generation in Year 1 (Rs 300,000) and minimizing project liquidity risk.

---

Part e: Internal Rate of Return (IRR)

1. Project X:

$$PVIFA_{IRR, 4} = \frac{I_0}{CF} = \frac{500,000}{200,000} = 2.5000$$

• At $21\%$: $PVIFA_{21\%, 4} = 2.5404$
• At $22\%$: $PVIFA_{22\%, 4} = 2.4937$
• Interpolation:
  $$IRR_X = 21\% + \left(\frac{2.5404 - 2.5000}{2.5404 - 2.4937}\right) \times (22\% - 21\%) = 21\% + \left(\frac{0.0404}{0.0467}\right) \times 1\% = \mathbf{21.86\%}$$

2. Project Y:

• At $k = 25\%$:
  $$PV = \frac{300,000}{1.25} + \frac{200,000}{1.25^2} + \frac{200,000}{1.25^3} + \frac{100,000}{1.25^4}$$
  $$PV = 240,000 + 128,000 + 102,400 + 40,960 = \text{Rs } 511,360 \implies NPV = +\text{Rs } 11,360$$
• At $k = 27\%$:
  $$PV = \frac{300,000}{1.27} + \frac{200,000}{1.27^2} + \frac{200,000}{1.27^3} + \frac{100,000}{1.27^4}$$
  $$PV = 236,220 + 124,000 + 97,640 + 38,440 = \text{Rs } 496,300 \implies NPV = -\text{Rs } 3,700$$
• Interpolation:
  $$IRR_Y = 25\% + \left(\frac{11,360}{11,360 - (-3,700)}\right) \times (27\% - 25\%) = 25\% + \left(\frac{11,360}{15,060}\right) \times 2\% = 25\% + 1.51\% = \mathbf{26.51\%}$$

---

Consolidated Master Comparison Table: