Fundamentals of Finance 2022 Board Question Paper

Meaning of Business Finance:

• Definition: Business finance refers to the strategic management, acquisition, allocation, and monitoring of monetary resources by commercial enterprises.
• Core Scope: It encompasses three primary financial decisions: investment decisions (capital budgeting), financing decisions (capital structure), and dividend decisions (reinvestment vs. profit distribution) aimed at maximizing shareholder wealth.

Primary Market vs. Secondary Market:

Free Cash Flow (FCF):

• Definition: Free Cash Flow is the net cash generated by operations that remains available for distribution to all capital providers (both debtholders and equityholders) after the firm has paid operating expenses, taxes, and funded necessary net investments in operating working capital and fixed capital assets.
• Formula:
  $$FCF = \text{NOPAT} + \text{Depreciation} - \text{Net Capital Expenditures} - \Delta NOWC$$

Ordinary Annuity vs. Annuity Due:

1. Ordinary Annuity: A series of equal, periodic cash flows where payments occur at the end of each compounding period (e.g., standard mortgage payments, bond coupons).
2. Annuity Due: A series of equal, periodic cash flows where payments occur at the beginning of each compounding period (e.g., apartment leases, life insurance premiums).

• Relationship: Because each payment in an annuity due compounds for one additional period, its present and future value equals the ordinary annuity value multiplied by $(1 + r)$.

Meaning of a Bond:

• Definition: A bond is a formal, legally binding long-term debt security under which the borrower (issuer, such as a government or corporation) promises to pay fixed periodic interest payments (coupon payments) to the lender (investor) and repay the stated principal amount (face/par value) upon reaching maturity.

Weighted Average Cost of Capital (WACC):

• Definition: WACC is the overall weighted average after-tax required rate of return that an organization must earn on its total operating assets to satisfy the return expectations of all its long-term capital providers (creditors, preferred stockholders, and common shareholders).
• Formula:
  $$WACC = w_d \cdot r_d(1 - T) + w_p \cdot r_p + w_e \cdot r_s$$

Financial Securities and Instruments:

• Definition: Financial securities are tradable financial assets or legal contracts that represent a monetary claim on future cash flows or an ownership interest in a business entity.
• Common Instruments:
  1. Money Market Instruments (Short-term, < 1 year): Treasury Bills (T-bills), Commercial Paper, Certificates of Deposit (CDs).
  2. Capital Market Instruments (Long-term): Common Stock (equity ownership), Corporate Debentures/Bonds, and Preferred Stock.

Yield on Two-Year Treasury Securities:

Given:

• Real risk-free rate ($r^*$) = $3\%$
• Expected inflation Year 1 ($I_1$) = $2\%$
• Expected inflation Year 2 ($I_2$) = $4\%$
• Maturity risk premium ($MRP$) = $0\%$

Step 1: Compute Average Inflation Premium ($IP_2$)

$$IP_2 = \frac{I_1 + I_2}{2} = \frac{2\% + 4\%}{2} = \mathbf{3\%}$$

Step 2: Calculate 2-Year Treasury Yield ($T_2$)

$$T_2 = r^* + IP_2 + MRP = 3\% + 3\% + 0\% = \mathbf{6\%}$$

Final Answer: The yield on two-year Treasury securities is 6%.

Calculation of Depreciation and Amortization Charge:

Given:

• $EBITDA = \text{Rs } 7.5 \text{ million}$
• $\text{Net Income } (NI) = \text{Rs } 1.8 \text{ million}$
• $\text{Interest Expense } (I) = \text{Rs } 2.0 \text{ million}$
• $\text{Tax Rate } (T) = 40\% \implies (1 - T) = 0.60$

Step 1: Compute Earnings Before Taxes (EBT)

$$EBT = \frac{NI}{1 - T} = \frac{1.8}{0.60} = \text{Rs } 3.0 \text{ million}$$

Step 2: Compute Operating Income (EBIT)

$$EBIT = EBT + \text{Interest} = 3.0 + 2.0 = \text{Rs } 5.0 \text{ million}$$

Step 3: Compute Depreciation and Amortization (D&A)

$$D\&A = EBITDA - EBIT = 7.5 - 5.0 = \mathbf{Rs \; 2.5 \text{ million}}$$

Final Answer: The charge for depreciation and amortization is Rs 2.5 million.

Calculation of Yield to Maturity (YTM):

a. Zero-Coupon Bond:

• Price ($P_0$) = $\text{Rs } 400$, Par Value ($M$) = $\text{Rs } 1,000$, Maturity ($n$) = $8 \text{ years}$$P_0 = \frac{M}{(1 + YTM)^n} \implies 400 = \frac{1000}{(1 + YTM)^8}$$
  $$(1 + YTM)^8 = \frac{1000}{400} = 2.50$$
  $$1 + YTM = (2.50)^{1/8} = (2.50)^{0.125} \approx 1.12135 \implies YTM = \mathbf{12.14\%}$$

b. Perpetual Bond:

• Par Value = $\text{Rs } 1,000$, Coupon Rate = $15\% \implies I = 1,000 \times 0.15 = \text{Rs } 150$
• Current Price ($P_0$) = $\text{Rs } 900$$YTM = \frac{I}{P_0} = \frac{150}{900} = \frac{1}{6} \approx \mathbf{16.67\%}$$

Final Answer:

• a. Zero-Coupon YTM: 12.14%
• b. Perpetual Bond YTM: 16.67%

Stock Valuation of Sagarmatha Company Using Gordon Growth Model:

Given Data:

• Last paid dividend ($D_0$) = $\text{Rs } 8.00$
• Constant dividend growth rate ($g$) = $10\% = 0.10$
• Current market price ($P_0$) = $\text{Rs } 176$

Next expected dividend ($D_1$):

$$D_1 = D_0(1 + g) = 8(1 + 0.10) = \mathbf{Rs \; 8.80}$$

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a. Expected Rate of Return ($\hat{r}_s$):

$$\hat{r}_s = \frac{D_1}{P_0} + g = \frac{8.80}{176} + 0.10 = 0.05 + 0.10 = 0.15 = \mathbf{15\%}$$

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b. Intrinsic Value of Stock Today ($V_0$) at $r_s = 14\%$:

$$V_0 = \frac{D_1}{r_s - g} = \frac{8.80}{0.14 - 0.10} = \frac{8.80}{0.04} = \mathbf{Rs \; 220}$$

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c. Investment Recommendation:

• Yes, you should invest your money in Sagarmatha Company.
• Rationale:
  1. The stock’s intrinsic value (Rs 220) is substantially higher than its current market price (Rs 176), indicating the stock is undervalued by the market.
  2. The expected rate of return (15%) exceeds your required rate of return (14%), providing a favorable margin of safety.

Effective Annual Rate (EAR) Computations for Credit Card APR = 19.5%:

Given:

• Nominal Annual Percentage Rate ($APR$ or $r$) = $19.5\% = 0.195$

General EAR Formula:

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

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1. Daily Compounding ($m = 365$):

$$EAR_{\text{daily}} = \left(1 + \frac{0.195}{365}\right)^{365} - 1 = (1 + 0.0005342466)^{365} - 1$$

$$EAR_{\text{daily}} = (1.0005342466)^{365} - 1 \approx 1.21526 - 1 = 0.21526 = \mathbf{21.53\%}$$

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2. Monthly Compounding ($m = 12$):

$$EAR_{\text{monthly}} = \left(1 + \frac{0.195}{12}\right)^{12} - 1 = (1 + 0.01625)^{12} - 1$$

$$EAR_{\text{monthly}} = (1.01625)^{12} - 1 \approx 1.21346 - 1 = 0.21346 = \mathbf{21.35\%}$$

Final Answer:

• EAR under Daily Compounding: 21.53%
• EAR under Monthly Compounding: 21.35%

The Statement of Cash Flows and Its Four Core Sections:

1. Definition

The Statement of Cash Flows is a primary financial report that tracks and details the gross inflows and outflows of cash and cash equivalents over a specific accounting period, categorizing cash flows according to business purpose.

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2. Four Sections of the Statement of Cash Flows:

1. Operating Activities:
   • Encompasses cash generated or used in the core revenue-producing operations of the firm.
   • Items: Cash received from customers, cash paid to suppliers and employees, income taxes paid, adjusted for non-cash expenses (depreciation) and working capital changes.
2. Investing Activities:
   • Reflects cash flows associated with the acquisition and disposal of long-term productive assets and financial investments.
   • Items: Purchase or sale of property, plant, and equipment (CapEx), and purchase/sale of corporate securities.
3. Financing Activities:
   • Captures transactions between the enterprise and its long-term capital providers (creditors and equity shareholders).
   • Items: Issuance of common stock, proceeds from issuing bonds or bank borrowings, principal debt repayments, and cash dividend distributions.
4. Reconciliation Summary (Net Increase/Decrease in Cash):
   • Combines net cash from the three operating, investing, and financing tiers with the opening cash balance to determine the closing balance of cash and cash equivalents reported on the Balance Sheet.

Financial Ratio Computations for Sitalpati Company:

Balance Sheet Aggregates:

• Current Assets ($CA$): $\text{Cash } (50,000) + \text{AR } (100,000) + \text{Inventory } (400,000) = \mathbf{Rs \; 550,000}$
• Quick Assets ($QA$): $CA - \text{Inventory} = 550,000 - 400,000 = \mathbf{Rs \; 150,000}$
• Current Liabilities ($CL$): $\text{AP } (50,000) + \text{Accrued Exp } (50,000) + \text{Deferred Taxes } (50,000) = \mathbf{Rs \; 150,000}$
• Long-Term Debt ($LTD$): $\text{Debentures } (50,000) + \text{Long Term Loan } (150,000) = \mathbf{Rs \; 200,000}$
• Total Debt ($TD$): $CL + LTD = 150,000 + 200,000 = \mathbf{Rs \; 350,000}$
• Total Equity ($TE$): $\text{Common Stock } (500,000) + \text{Retained Earnings } (150,000) = \mathbf{Rs \; 650,000}$
• Total Assets ($TA$): $\mathbf{Rs \; 1,000,000}$

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Ratio Calculations:

a. Current Ratio:

$$\frac{CA}{CL} = \frac{550,000}{150,000} = \mathbf{3.67 : 1}$$

b. Quick Ratio:

$$\frac{QA}{CL} = \frac{150,000}{150,000} = \mathbf{1.00 : 1}$$

c. Debt Ratio:

$$\frac{\text{Total Debt}}{TA} = \frac{350,000}{1,000,000} = \mathbf{35\%} \quad (0.35)$$

d. Debt-Equity Ratio:

$$\frac{\text{Total Debt}}{TE} = \frac{350,000}{650,000} = \mathbf{0.538 : 1} \quad (53.85\%)$$

e. Equity Multiplier:

$$\frac{TA}{TE} = \frac{1,000,000}{650,000} = \mathbf{1.538}$$

f. Long-Term Debt to Total Assets Ratio:

$$\frac{LTD}{TA} = \frac{200,000}{1,000,000} = \mathbf{20\%} \quad (0.20)$$

Tuition Deposit and Account Balance Computations:

Given:

• Annual withdrawal ($PMT$) = $\text{Rs } 10,000$ per year
• Duration ($n$) = $4 \text{ years}$ (starting at the end of Year 1 — ordinary annuity)
• Interest rate ($i$) = $7\% = 0.07$

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a. Size of Deposit Required Today ($PV$):

$$PV = PMT \times PVIFA(7\%, 4) = PMT \times \left[\frac{1 - (1 + i)^{-n}}{i}\right]$$

$$PV = 10,000 \times \left[\frac{1 - (1.07)^{-4}}{0.07}\right] = 10,000 \times \left[\frac{1 - 0.762895}{0.07}\right] = 10,000 \times 3.38721 = \mathbf{Rs \; 33,872.11}$$

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b. Balance Immediately After the First Withdrawal:

At the end of Year 1, before withdrawal, the deposit earns 7% interest:

$$\text{Balance before withdrawal} = 33,872.11 \times (1 + 0.07) = \text{Rs } 36,243.16$$

$$\text{Balance after first withdrawal} = 36,243.16 - 10,000 = \mathbf{Rs \; 26,243.16}$$

(Verification: Present value of the remaining 3 payments of Rs 10,000: $10,000 \times PVIFA(7\%, 3) = 10,000 \times 2.62432 = \text{Rs } 26,243.20$).

Final Answer:

• a. Deposit required today: Rs 33,872.11
• b. Account balance after first withdrawal: Rs 26,243.16

Portfolio Expected Return and Risk (Standard Deviation):

Given Data:

• Stock X: $E(R_X) = 10\%$, $\sigma_X = 5\%$, Weight ($w_X$) = $0.60$
• Stock Y: $E(R_Y) = 6\%$, $\sigma_Y = 4\%$, Weight ($w_Y$) = $0.40$
• Correlation coefficient ($r_{XY}$) = $-0.35$

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

$$E(R_p) = w_X E(R_X) + w_Y E(R_Y)$$

$$E(R_p) = (0.60 \times 10\%) + (0.40 \times 6\%) = 6.0\% + 2.4\% = \mathbf{8.4\%}$$

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

$$\sigma_p^2 = w_X^2 \sigma_X^2 + w_Y^2 \sigma_Y^2 + 2 w_X w_Y \sigma_X \sigma_Y r_{XY}$$

$$\sigma_p^2 = (0.60)^2(5)^2 + (0.40)^2(4)^2 + 2(0.60)(0.40)(5)(4)(-0.35)$$

$$\sigma_p^2 = 0.36(25) + 0.16(16) + 2(0.24)(20)(-0.35)$$

$$\sigma_p^2 = 9.00 + 2.56 - 3.36 = \mathbf{8.20}$$

$$\sigma_p = \sqrt{8.20} \approx \mathbf{2.86\%}$$

Final Answer:

• Expected Portfolio Return: 8.4%
• Portfolio Risk (Standard Deviation): 2.86% (Note: Because of negative correlation, portfolio risk is reduced below either individual stock’s risk).

Cost of Capital Computations for Garudnahani and Bhedetar Companies:

Part (a): Garudnahani Company — After-Tax Cost of Debt

• Maturity ($n$) = $10 \text{ years}$, Price ($P_0$) = $\text{Rs } 500$, Par Value ($M$) = $\text{Rs } 1,000$, Tax Rate ($T$) = $40\%$
• Pre-tax cost of debt ($r_d$):
  $$P_0 = \frac{M}{(1 + r_d)^n} \implies 500 = \frac{1000}{(1 + r_d)^{10}} \implies (1 + r_d)^{10} = 2.00$$
  $$1 + r_d = (2.00)^{1/10} = 1.07177 \implies r_d = 7.177\%$$
• After-Tax Cost of Debt:
  $$r_d(1 - T) = 7.177\% \times (1 - 0.40) = 7.177\% \times 0.60 = \mathbf{4.31\%}$$

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Part (b): Bhedetar Company — Cost of Equity

• Next expected dividend ($D_1$) = $\text{Rs } 3.18$
• Constant growth rate ($g$) = $6\% = 0.06$
• Current stock price ($P_0$) = $\text{Rs } 36.00$
• Net price of new stock ($P_n$) = $\text{Rs } 32.40$

a. Cost of Retained Earnings ($r_s$):

$$r_s = \frac{D_1}{P_0} + g = \frac{3.18}{36.00} + 0.06 = 0.08833 + 0.06 = \mathbf{14.83\%}$$

b. Percentage Flotation Cost ($F$):

$$F = \frac{P_0 - P_n}{P_0} = \frac{36.00 - 32.40}{36.00} = \frac{3.60}{36.00} = 0.10 = \mathbf{10\%}$$

c. Cost of New Common Stock ($r_e$):

$$r_e = \frac{D_1}{P_n} + g = \frac{3.18}{32.40} + 0.06 = 0.09815 + 0.06 = \mathbf{15.82\%}$$

Summary of Answers:

• Part (a): After-tax cost of debt = 4.31%
• Part (b): Cost of retained earnings = 14.83%, Flotation cost = 10%, Cost of new equity = 15.82%

Balance Sheet Overview and Financial Flow Analysis for Horleri Company:

Part (a): The Balance Sheet

• Definition: The Balance Sheet is a snapshot financial statement that reports a company’s financial position at a specific point in time. It details what the firm owns (Assets), what it owes to external creditors (Liabilities), and the residual ownership stake belonging to shareholders (Stockholders’ Equity).
• Fundamental Equation:
  $$\text{Assets} = \text{Liabilities} + \text{Stockholders' Equity}$$

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Part (b): Financial Computations for Horleri Company

Given:

• $EBIT = \text{Rs } 5 \text{ million}$, $D\&A = \text{Rs } 1 \text{ million}$, $\text{Interest} = \text{Rs } 1 \text{ million}$, $T = 40\%$
• $CA = \text{Rs } 14 \text{ million}$, $NIBCL = \text{Rs } 4 \text{ million}$, $\text{Net Plant \& Equip} = \text{Rs } 15 \text{ million}$
• Cost of Capital ($WACC$) = $10\%$, Previous Year Operating Capital ($TOC_{t-1}$) = $\text{Rs } 24 \text{ million}$

i. Net Income:

$$EBT = EBIT - \text{Interest} = 5.0 - 1.0 = \text{Rs } 4.0 \text{ million}$$

$$\text{Taxes} = 4.0 \times 0.40 = \text{Rs } 1.6 \text{ million}$$

$$\text{Net Income} = 4.0 - 1.6 = \mathbf{Rs \; 2.4 \text{ million}}$$

ii. Net Cash Flow:

$$\text{Net Cash Flow} = \text{Net Income} + \text{Depreciation} = 2.4 + 1.0 = \mathbf{Rs \; 3.4 \text{ million}}$$

iii. Net Operating Profit After Taxes (NOPAT):

$$NOPAT = EBIT \times (1 - T) = 5.0 \times (1 - 0.40) = 5.0 \times 0.60 = \mathbf{Rs \; 3.0 \text{ million}}$$

iv. Operating Cash Flow (OCF):

$$OCF = NOPAT + \text{Depreciation} = 3.0 + 1.0 = \mathbf{Rs \; 4.0 \text{ million}}$$

v. Free Cash Flow (FCF):

• Current Net Operating Working Capital: $NOWC_t = CA - NIBCL = 14.0 - 4.0 = \text{Rs } 10.0 \text{ million}$
• Total Net Operating Capital: $TOC_t = NOWC_t + \text{Net Fixed Assets} = 10.0 + 15.0 = \text{Rs } 25.0 \text{ million}$
• Net Capital Investment: $\Delta TOC = TOC_t - TOC_{t-1} = 25.0 - 24.0 = \text{Rs } 1.0 \text{ million}$$FCF = NOPAT - \Delta TOC = 3.0 - 1.0 = \mathbf{Rs \; 2.0 \text{ million}}$$

vi. Economic Value Added (EVA):

$$EVA = NOPAT - (TOC_{t-1} \times WACC) = 3.0 - (24.0 \times 0.10) = 3.0 - 2.4 = \mathbf{Rs \; 0.6 \text{ million (Rs 600,000)}}$$