Fundamentals of Financial Management 2077 Board Question Paper

Financial management is the managerial activity concerned with the efficient planning, procurement, allocation, and control of a firm’s financial resources. It encompasses three core decision areas: investment decisions (capital budgeting), financing decisions (capital structure), and dividend decisions (reinvestment vs payout), with the ultimate objective of maximizing shareholder wealth.

The nominal rate (or APR) is the stated contractual annual interest rate that ignores the compounding of interest within the year. In contrast, the effective annual rate (EAR) reflects the actual economic annual rate earned or paid by explicitly taking into account the frequency of intra-year compounding ($m$):

$$\text{EAR} = \left(1 + \frac{r_{\text{Nom}}}{m}\right)^m - 1$$

Whenever compounding occurs more than once per year ($m > 1$), EAR is strictly greater than the nominal rate.

A portfolio is a collection or bundle of financial assets (such as stocks, bonds, treasury bills, and real estate) held concurrently by an investor or institution. The fundamental objective of constructing a portfolio is diversification—combining assets that are not perfectly positively correlated to eliminate unsystematic (firm-specific) risk and maximize return for a given risk level.

According to John Maynard Keynes, the three classic motives for holding cash are:

1. Transaction Motive: To bridge the gap between daily cash inflows and routine contractual outflows (payroll, supplier bills, taxes).
2. Precautionary Motive: To provide a liquidity cushion against unforeseen emergencies or sudden cash flow disruptions.
3. Speculative Motive: To exploit sudden attractive market opportunities, such as bargain asset purchases or bulk inventory discounts.

1. Stability of Sales: A firm with stable and predictable sales and cash flows faces lower operating risk and can comfortably commit to a higher and more consistent dividend payout ratio.
2. Growth of Sales: High-growth firms have abundant profitable capital investment opportunities, requiring internal financing; thus, they maintain a lower dividend payout (retaining most earnings). Conversely, mature low-growth firms distribute higher cash dividends.

The breakeven point (BEP) is the operational sales volume (in units or currency) at which a firm’s total revenues exactly equal its total operating costs (both fixed and variable), yielding an Operating Profit (EBIT) of zero:

$$\text{BEP (Units)} = \frac{\text{Total Fixed Operating Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}}$$

It represents the minimum sales threshold necessary to prevent operating losses.

Given:

• $\text{Risk-Free Rate } (R_f) = 6\%$
• $\text{Market Risk Premium } (R_m - R_f) = 8\%$
• $\text{Beta of Stock J } (\beta_J) = 1.5$

Capital Asset Pricing Model (CAPM):

$$E(R_J) = R_f + \beta_J \times (R_m - R_f)$$

$$E(R_J) = 6\% + 1.5 \times 8\% = 6\% + 12\% = \mathbf{18.00\%}$$

Given:

• $\text{Annual Demand } (A) = 10,000\text{ boxes}$
• $\text{Unit Purchase Cost } (C) = \text{Rs. } 200$
• $\text{Carrying Cost per unit } (c) = 10\% \text{ of Rs. } 200 = \text{Rs. } 20$
• $\text{Order Cost per order } (O) = \text{Rs. } 1,000$

Economic Order Quantity (EOQ):

$$\text{EOQ} = \sqrt{\frac{2AO}{c}} = \sqrt{\frac{2 \times 10,000 \times 1,000}{20}} = \sqrt{1,000,000} = \mathbf{1,000\text{ boxes}}$$

The firm should order 1,000 boxes per order.

Given:

• $\text{Initial Outlay } (I_0) = \text{Rs. } 400,000$
• $\text{Present Value of Future Inflows } (PV) = \text{Rs. } 300,000$

Step 1: Compute Profitability Index (PI):

$$\mathbf{\text{Profitability Index (PI)}} = \frac{PV}{I_0} = \frac{\text{Rs. } 300,000}{\text{Rs. } 400,000} = \mathbf{0.75}$$

Step 2: Decision Evaluation:

• Net Present Value: $NPV = 300,000 - 400,000 = -\text{Rs. } 100,000$.
• Conclusion: The project is not worthwhile because $PI < 1.0$ and $NPV < 0$, which would destroy shareholder wealth.

Given:

• $\text{Total Capital Budget} = \text{Rs. } 8,000,000$
• $\text{Target Equity Proportion } (w_e) = 30\%$
• $\text{Net Income} = \text{Rs. } 5,000,000$

Calculations under Residual Dividend Policy:

1. $\text{Equity Needed for New Investments} = 30\% \times \text{Rs. } 8,000,000 = \text{Rs. } 2,400,000$
2. $\text{Residual Cash Dividends} = \text{Net Income} - \text{Equity Needed} = 5,000,000 - 2,400,000 = \text{Rs. } 2,600,000$
3. $\mathbf{\text{Dividend Payout Ratio}} = \frac{\text{Dividends}}{\text{Net Income}} = \frac{\text{Rs. } 2,600,000}{\text{Rs. } 5,000,000} \times 100 = \mathbf{52.00\%}$

Wealth Maximization vs. Profit Maximization

Concept of Wealth Maximization

Wealth maximization (also known as Net Present Worth Maximization) is the foundational operational goal of modern financial management. It states that financial managers should make decisions that maximize the total present market value of the firm’s equity shares.

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

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Why Wealth Maximization is Superior to Profit Maximization

1. Recognizes the Time Value of Money (TVM): Profit maximization measures accounting profit without considering when the cash is received. In contrast, wealth maximization discounts future cash flows at the firm’s cost of capital, reflecting that a rupee received today is worth more than a rupee in the future.

2. Explicitly Accounts for Risk and Uncertainty: Accounting profit treats safe cash flows and highly speculative ventures identically if they report the same projected net income. Wealth maximization integrates risk via higher discount rates (cost of equity), directly penalizing excessively risky ventures.

3. Focuses on Cash Flows rather than Accounting Book Profits: Profits can be manipulated through accounting conventions (depreciation methods, inventory valuation). Wealth maximization is anchored on verifiable, discounted free cash flows.

4. Incorporates Dividend Policy and Market Expectations: It recognizes that market share price reflects investor perceptions of dividend consistency, capital structure quality, and strategic longevity.

5. Avoids Short-Termism: Profit maximization often tempts managers to cut essential R&D, maintenance, or employee training to inflate quarterly earnings. Wealth maximization demands investments in long-term enterprise value.

Portfolio Risk and Return Computations

(a) Risk Evaluation and Stock Preference

To evaluate relative risk per unit of return, calculate the Coefficient of Variation (CV):

$$CV = \frac{\sigma}{\bar{R}}$$

• Stock A: $CV_A = \frac{6\%}{12\%} = 0.50$

• Stock B: $CV_B = \frac{8\%}{18\%} = 0.444$

• Absolute Risk: Stock B has higher standard deviation ($8\% > 6\%$), making it more risky in absolute terms.

• Relative Risk: Stock A has a higher CV ($0.50 > 0.444$).

• Preference: A risk-averse investor prioritizing capital preservation prefers Stock A ($6\%$ risk), while an investor seeking return efficiency per unit of risk prefers Stock B (lower CV of 0.444 with higher return of $18\%$).

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

• Expected Portfolio Return ($R_p$):

  $$R_p = (w_A \times R_A) + (w_B \times R_B) = (0.60 \times 12\%) + (0.40 \times 18\%) = 7.2\% + 7.2\% = \mathbf{14.40\%}$$

• Portfolio Variance ($\sigma_p^2$):

  $$\sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \text{Cov}(A, B)$$
  $$\sigma_p^2 = (0.60)^2(6)^2 + (0.40)^2(8)^2 + 2(0.60)(0.40)(-38.4)$$
  $$\sigma_p^2 = (0.36 \times 36) + (0.16 \times 64) + (0.48 \times -38.4)$$
  $$\sigma_p^2 = 12.96 + 10.24 - 18.432 = 4.768$$

• Portfolio Standard Deviation ($\sigma_p$):

  $$\mathbf{\sigma_p} = \sqrt{4.768} = \mathbf{2.18\%}$$
  (Remark: Due to strong negative correlation $-0.80$, portfolio risk drops dramatically to $2.18\%$ while yielding $14.40\%$ return).

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(c) Beta and Required Return on Stock A

• Given: $\text{Cov}(A, M) = 54$, $\sigma_M^2 = 36$, $R_f = 8\%$, $R_m = 15\%$.
• Beta of Stock A ($\beta_A$):
  $$\mathbf{\beta_A} = \frac{\text{Cov}(A, M)}{\sigma_M^2} = \frac{54}{36} = \mathbf{1.50}$$
• Required Rate of Return (CAPM):
  $$E(R_A) = R_f + \beta_A (R_m - R_f) = 8\% + 1.50 \times (15\% - 8\%) = 8\% + (1.50 \times 7\%) = 8\% + 10.5\% = \mathbf{18.50\%}$$

Bond Valuation Computations

(a) Present Value of Bond ($k_d = 10\%, n = 7, M = \text{Rs. } 1,000, I = 8\% \times 1,000 = \text{Rs. } 80$)

$$V_0 = I \times \text{PVIFA}_{k_d, n} + M \times \text{PVIF}_{k_d, n}$$

• $\text{PVIFA}_{10\%, 7} = \frac{1 - (1 + 0.10)^{-7}}{0.10} = 4.8684$

• $\text{PVIF}_{10\%, 7} = (1 + 0.10)^{-7} = 0.5132$$V_0 = (80 \times 4.8684) + (1,000 \times 0.5132) = 389.47 + 513.16 = \mathbf{\text{Rs. } 902.63}$$

• Investment Recommendation: The intrinsic value of the bond is Rs. 902.63. Because the current market price is Rs. 900.00, which is less than intrinsic value ($P_0 < V_0$), the bond is undervalued (underpriced). Recommendation: Yes, the investor should purchase the bond as it offers a yield higher than the required $10\%$.

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(b) Impact of Market Interest Rates on Bond Value

There is an inverse relationship between bond prices and market interest rates:

1. Interest Rates Rise ($k_d > \text{Coupon Rate}$): The bond offers an uncompetitive coupon relative to newly issued bonds, forcing its price to drop below par (trading at a discount).
2. Interest Rates Fall ($k_d < \text{Coupon Rate}$): The bond’s fixed coupon is more attractive, driving its price above par (trading at a premium).
3. Interest Rates Equal Coupon ($k_d = \text{Coupon Rate}$): The bond trades exactly at par (Rs. 1,000).
4. Maturity Sensitivity: Longer-term bonds exhibit higher price volatility in response to interest rate changes than shorter-term bonds.

Stock Valuation using Gordon Constant Growth Model

Given:

• $\text{Current Dividend Just Paid } (D_0) = \text{Rs. } 30$
• $\text{Constant Growth Rate } (g) = 6\% = 0.06$
• $\text{Required Rate of Return } (k_s) = 16\% = 0.16$

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a. Present Value of Stock ($P_0$)

$$\text{Expected Dividend Next Year } (D_1) = D_0(1 + g) = 30 \times (1 + 0.06) = \text{Rs. } 31.80$$

$$\mathbf{P_0} = \frac{D_1}{k_s - g} = \frac{\text{Rs. } 31.80}{0.16 - 0.06} = \frac{\text{Rs. } 31.80}{0.10} = \mathbf{\text{Rs. } 318.00}$$

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b. Dividend Yield for the First Year

$$\mathbf{\text{Dividend Yield}} = \frac{D_1}{P_0} = \frac{\text{Rs. } 31.80}{\text{Rs. } 318.00} = \mathbf{10.00\%}$$

(Note: Capital gains yield equals $g = 6\%$; Total return $= 10\% + 6\% = 16\% = k_s$).

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c. Stock Worth at the End of Third Year ($P_3$)

Under constant growth, the stock price grows at the constant dividend growth rate $g$:

$$\mathbf{P_3} = P_0 \times (1 + g)^3 = \text{Rs. } 318.00 \times (1 + 0.06)^3 = 318.00 \times 1.191016 = \mathbf{\text{Rs. } 378.74}$$

(Alternatively: $D_4 = D_0(1+g)^4 = 30(1.06)^4 = 37.874 \implies P_3 = \frac{37.874}{0.10} = \text{Rs. } 378.74$).

Cost of Capital Computations for Gandaki Cement

Given:

• $\text{Debt} = \text{Rs. } 80\text{M} \implies w_d = \frac{80}{200} = 0.40$ ($40\%$)
• $\text{Equity} = \text{Rs. } 120\text{M} \implies w_e = \frac{120}{200} = 0.60$ ($60\%$)
• $\text{Pre-tax Cost of Debt } (r_d) = 10\%$, $\text{Tax Rate } (t) = 30\%$
• $D_0 = \text{Rs. } 30$, $g = 6\%$, $P_0 = \text{Rs. } 400$

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(a) Component Costs of Capital

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 Common Equity from Retained Earnings ($k_s$):

   $$D_1 = D_0(1 + g) = 30 \times (1 + 0.06) = \text{Rs. } 31.80$$
   $$\mathbf{k_s} = \frac{D_1}{P_0} + g = \frac{\text{Rs. } 31.80}{\text{Rs. } 400} + 0.06 = 0.0795 + 0.06 = 0.1395 = \mathbf{13.95\%}$$

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(b) Weighted Average Cost of Capital (WACC)

$$\text{WACC} = [w_d \times k_d] + [w_e \times k_s]$$

$$\mathbf{\text{WACC}} = [0.40 \times 7.00\%] + [0.60 \times 13.95\%]$$

$$\text{WACC} = 2.80\% + 8.37\% = \mathbf{11.17\%}$$

(a) Financial Ratios for Hi-Tech Company (in '000 Rs.)

1. Accounts Receivable:

   $$\text{DSO} = \frac{\text{Receivables}}{\text{Sales} / 360} \implies 40 = \frac{\text{Receivables}}{1,000 / 360}$$
   $$\mathbf{\text{Receivables}} = 40 \times 2.7778 = \mathbf{\text{Rs. } 111.11\text{ thousand}}$$

2. Current Liabilities (CL): Quick Assets $= \text{Cash (100)} + \text{Receivables (111.11)} = \text{Rs. } 211.11$$\text{Quick Ratio} = \frac{\text{Quick Assets}}{\text{CL}} \implies 2.0 = \frac{211.11}{\text{CL}} \implies \mathbf{\text{CL}} = \frac{211.11}{2.0} = \mathbf{\text{Rs. } 105.56\text{ thousand}}$$

3. Current Assets (CA):

   $$\text{Current Ratio} = \frac{\text{CA}}{\text{CL}} \implies 3.0 = \frac{\text{CA}}{105.56} \implies \mathbf{\text{CA}} = 3.0 \times 105.56 = \mathbf{\text{Rs. } 316.67\text{ thousand}}$$

4. Total Assets (TA):

   $$\mathbf{\text{Total Assets}} = \text{CA} + \text{Fixed Assets} = 316.67 + 283.50 = \mathbf{\text{Rs. } 600.17\text{ thousand}}$$

5. Return on Assets (ROA):

   $$\mathbf{\text{ROA}} = \frac{\text{Net Income}}{\text{Total Assets}} = \frac{\text{Rs. } 50}{\text{Rs. } 600.17} \times 100 = \mathbf{8.33\%}$$

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(b) Kathmandu Gift Center Breakeven and Leverage

• $SPPU = \text{Rs. } 80$, $VCPU = \text{Rs. } 50$, $CMPU = 80 - 50 = \text{Rs. } 30$
• $Fixed Cost (FC) = \text{Rs. } 300,000$

1. Break-Even Point in Units:

   $$\mathbf{\text{BEP (Units)}} = \frac{FC}{CMPU} = \frac{\text{Rs. } 300,000}{\text{Rs. } 30} = \mathbf{10,000\text{ units}}$$

2. Degree of Operating Leverage (DOL) at 15,000 units:

   • $\text{Total Contribution Margin} = 15,000 \times \text{Rs. } 30 = \text{Rs. } 450,000$
   • $\text{EBIT} = 450,000 - 300,000 = \text{Rs. } 150,000$$\mathbf{\text{DOL}_{15,000}} = \frac{\text{Total Contribution Margin}}{\text{EBIT}} = \frac{\text{Rs. } 450,000}{\text{Rs. } 150,000} = \mathbf{3.0\text{ times}}$$

Concept and Strategic Importance of Working Capital Management

1. The Concept of Working Capital

Working capital represents the liquid financial lifeblood required to fund the day-to-day operating cycle of an enterprise. It is viewed through two primary concepts:

1. Gross Working Capital: The total monetary investment in current assets (cash, marketable securities, receivables, inventories).
2. Net Working Capital (NWC): The excess of current assets over current liabilities ($NWC = CA - CL$). A positive NWC indicates sound liquidity and short-term solvency.

Working Capital Management is the managerial discipline focused on optimizing the relationship between current assets and current liabilities so that the firm operates smoothly without the twin perils of insolvency (illiquidity) and unproductive asset accumulation (idle funds).

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2. Importance in Manufacturing Industries

Manufacturing firms face a long operating cycle ($RM \to WIP \to FG \to Receivables \to Cash$):

1. Uninterrupted Production Scheduling: Ensures raw material inventories are adequate, preventing factory downtime.
2. Financing Work-in-Progress (WIP): Sustains multi-stage processing costs where substantial cash is locked up in factory labor and energy.
3. Capacity Utilization: Enables high factory utilization by smoothing out seasonal supply shortages.

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3. Importance in Trading Industries

Trading organizations do not manufacture goods; their operating cycle is shorter and dominated by inventory turnover:

1. Rapid Inventory Turnover and Stock Freshness: Prevents inventory obsolescence in fast-moving consumer markets.
2. Managing Trade Receivables: Enables offering competitive credit terms to retail stockists while enforcing sound collection policies.
3. Exploiting Supplier Trade Discounts: Sufficient liquidity allows capturing cash discounts (e.g., $2/10, \text{ net } 30$).

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Conclusion

Effective working capital management achieves the classic financial trade-off: optimizing liquidity without compromising profitability.

Time Value of Money Calculations

Parameters:

• Initial Deposit on January 1, 2021 $= \text{Rs. } 100,000$
• Terminal Date $= \text{January 1, 2024}$
• Time elapsed ($n$) $= 3\text{ years}$ (Jan 1, 2021 to Jan 1, 2024).
• Stated Interest Rate ($i$) $= 10\% = 0.10$.

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a. Future Value with Annual Compounding

$$FV_3 = PV \times (1 + i)^n = \text{Rs. } 100,000 \times (1 + 0.10)^3$$

$$\mathbf{FV_3} = 100,000 \times 1.331 = \mathbf{\text{Rs. } 133,100}$$

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b. Future Value with Quarterly Compounding ($m = 4$)

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

$$\text{Quarterly Rate } \left(\frac{i}{m}\right) = \frac{10\%}{4} = 2.5\% = 0.025$$

$$FV_3 = PV \times \left(1 + \frac{i}{m}\right)^{n \times m} = \text{Rs. } 100,000 \times (1 + 0.025)^{12}$$

$$\mathbf{FV_3} = 100,000 \times 1.344889 = \mathbf{\text{Rs. } 134,488.90}$$

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c. Future Value of 4 Installments of Rs. 25,000 Each (Annuity Due / Exact Cash Flow Timing)

Payments occur on:

• Jan 1, 2021 (compounds for 3 years): $25,000 \times (1.10)^3 = 25,000 \times 1.331 = \text{Rs. } 33,275$
• Jan 1, 2022 (compounds for 2 years): $25,000 \times (1.10)^2 = 25,000 \times 1.21 = \text{Rs. } 30,250$
• Jan 1, 2023 (compounds for 1 year): $25,000 \times (1.10)^1 = 25,000 \times 1.10 = \text{Rs. } 27,500$
• Jan 1, 2024 (deposited on terminal day, 0 years): $25,000 \times 1 = \text{Rs. } 25,000$$\mathbf{\text{Total Balance on Jan 1, 2024}} = 33,275 + 30,250 + 27,500 + 25,000 = \mathbf{\text{Rs. } 116,025}$$

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d. Equal Annual Payments (PMT) to Accumulate Rs. 133,100 by Jan 1, 2024

The total future value factor for the 4 payments at Jan 1, 2024 is:

$$\text{Factor} = (1.10)^3 + (1.10)^2 + (1.10)^1 + 1 = 1.331 + 1.210 + 1.100 + 1.000 = 4.641$$

$$PMT \times 4.641 = \text{Rs. } 133,100$$

$$\mathbf{PMT} = \frac{\text{Rs. } 133,100}{4.641} = \mathbf{\text{Rs. } 28,679.16}$$

Each payment must be Rs. 28,679.16.

Comprehensive Capital Budgeting Analysis

Given Parameters:

• Initial Outlay ($I_0$) $= \text{Rs. } 1,000,000$
• Cash Flows: Year 1 = Rs. 400,000; Year 2 = Rs. 400,000; Year 3 = Rs. 600,000; Year 4 = Rs. 500,000
• Cost of Capital ($k$) $= 12\%$

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(a) Payback Period (PBP)

Definition: The Payback Period is the exact time period (in years) required for the cumulative cash inflows from a project to recover the initial capital investment outlay.

• Cumulative Cash Flows:
  • Year 1: Rs. 400,000
  • Year 2: Rs. 800,000
  • Year 3: Rs. 1,400,000
• The Rs. 1,000,000 investment is recovered between Year 2 and Year 3:
  $$\mathbf{\text{PBP}} = 2 + \frac{1,000,000 - 800,000}{600,000} = 2 + \frac{200,000}{600,000} = \mathbf{2.33\text{ years (2 years and 4 months)}}$$

Decision: Because the project’s PBP of 2.33 years is well within the maximum recovery limit of 3 years, the company should run the tourist bus.

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(b) Net Present Value (NPV)

Definition: The Net Present Value (NPV) is the difference between the present value of future cash inflows discounted at the required rate of return and the initial cost outlay.

Decision: Because $NPV = +\text{Rs. } 420,870 > 0$, running the tourist bus will add substantial wealth to the company’s equity value. Accept the project.

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(c) Internal Rate of Return (IRR)

Definition: The Internal Rate of Return (IRR) is the break-even discount rate that equates the present value of future cash inflows to the initial cost outlay ($NPV = 0$).

• At $k = 12\%$, $NPV = +\text{Rs. } 420,870$. Try higher discount rate $r = 30\%$:
  • Y1: $400,000 \times 0.7692 = 307,680$
  • Y2: $400,000 \times 0.5917 = 236,680$
  • Y3: $600,000 \times 0.4552 = 273,120$
  • Y4: $500,000 \times 0.3501 = 175,050$
  • Total PV at $30\% = \text{Rs. } 992,530 \implies NPV_{30\%} = 992,530 - 1,000,000 = -\text{Rs. } 7,470$.
• Try $r = 28\%$:
  • Y1: $400k \times 0.7813 = 312,520$
  • Y2: $400k \times 0.6104 = 244,160$
  • Y3: $600k \times 0.4768 = 286,080$
  • Y4: $500k \times 0.3725 = 186,250$
  • Total PV at $28\% = \text{Rs. } 1,029,010 \implies NPV_{28\%} = +\text{Rs. } 29,010$.

Interpolation:

$$\mathbf{\text{IRR}} = 28\% + \frac{29,010}{29,010 - (-7,470)} \times (30\% - 28\%) = 28\% + \left(\frac{29,010}{36,480} \times 2\%\right) = 28\% + 1.59\% = \mathbf{29.59\%}$$

Decision: Because $IRR = 29.59\%$, which significantly exceeds the cost of capital ($12\%$), the company should run the tourist bus.