Dean's Office Official Model Question Paper

Answer: Agency Problem: A conflict of interest inherent in any relationship where one party (the agent, such as corporate management) is expected to act in the best interests of another (the principal, such as equity shareholders). Because ownership is separated from control in modern corporations, managers may pursue personal perquisites, empire building, or job security rather than shareholder wealth maximization.

Governance Mechanisms:

1. Performance-Based Compensation: Aligning executive incentives via stock options, restricted equity grants, and performance bonuses tied to Economic Value Added (EVA) or earnings milestones.
2. Board Oversight and Threat of Takeover: Active monitoring by an independent Board of Directors and the external discipline of hostile corporate takeovers in competitive capital markets.

Answer: Effective Annual Rate (EAR): The actual annualized rate of interest earned or paid on an investment or loan, reflecting the compounding of interest over multiple compounding periods within a year.

Calculation:

$$\text{Given: } r_{\text{nom}} = 12\% = 0.12, \quad m = 4 \text{ compounding periods per year}$$

$$\text{EAR} = \left(1 + \frac{r_{\text{nom}}}{m}\right)^m - 1 = \left(1 + \frac{0.12}{4}\right)^4 - 1 = (1 + 0.03)^4 - 1$$

$$\text{EAR} = (1.03)^4 - 1 = 1.1255088 - 1 = 0.1255088 \approx \mathbf{12.55\%}$$

Answer:

• Systematic Risk (Market / Non-Diversifiable Risk): Risk that affects the entire market or economy as a whole (e.g., changes in GDP, interest rates, inflation, political shocks). It cannot be eliminated through diversification and is measured by Beta ($\beta$).
• Unsystematic Risk (Firm-Specific / Diversifiable Risk): Risk unique to an individual company or narrow industry (e.g., labor strikes, management errors, patent loss). It can be eliminated through well-constructed portfolio diversification.

Risk Rewarded: Under the Capital Asset Pricing Model (CAPM), investors are compensated with a risk premium only for Systematic Risk, because unsystematic risk can be diversified away at zero cost.

Answer: Two Components of Total Stock Return:

1. Dividend Yield: The expected cash dividend per share relative to the current market price: $\frac{D_1}{P_0}$.
2. Capital Gains Yield: The expected percentage rate of price appreciation over the holding period: $\frac{P_1 - P_0}{P_0} = g$.

Gordon’s Constant Growth Model Formula:

$$P_0 = \frac{D_1}{k_s - g} = \frac{D_0(1 + g)}{k_s - g}$$

Where $P_0$ is intrinsic value, $D_1$ is next year’s expected dividend, $k_s$ is the required rate of return on equity, and $g$ is the perpetual dividend growth rate (assuming $k_s > g$).

Answer:

• Operating Cycle (OC): The total elapsed time between purchasing raw materials/inventory and collecting cash proceeds from the sale of finished goods:
  $$\text{Operating Cycle} = \text{Inventory Conversion Period (ICP)} + \text{Receivables Collection Period (RCP)}$$
• Cash Conversion Cycle (CCC): The net duration for which a firm’s cash remains tied up in working capital operations before cash is collected from customers:
  $$\text{CCC} = \text{Operating Cycle} - \text{Payables Deferral Period (PDP)} = \text{ICP} + \text{RCP} - \text{PDP}$$
  A shorter CCC improves corporate liquidity and minimizes short-term financing costs.

Solution: Loan Amortization Schedule

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Part (a): Annual Installment Payment (3 Marks)

The loan represents the present value of an ordinary annuity ($PVA_n$):

$$PVA_n = PMT \times PVIFA_{k, n}$$

Where:

• Present Value of Loan ($PVA$) = Rs. 2,000,000
• Annual Interest Rate ($k$) = 10% = 0.10
• Term ($n$) = 5 years

$$PVIFA_{10\%, 5} = \frac{1 - (1 + k)^{-n}}{k} = \frac{1 - (1.10)^{-5}}{0.10} = \frac{1 - 0.6209213}{0.10} = 3.790787$$

$$\text{Annual Installment } (PMT) = \frac{\text{Loan Amount}}{PVIFA_{10\%, 5}} = \frac{2,000,000}{3.790787} = \mathbf{\text{Rs. } 527,595.00}$$

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Part (b): 5-Year Loan Amortization Schedule (5 Marks)

(Note: In Year 5, installment is adjusted by -Rs. 0.23 due to cumulative penny rounding).

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Part (c): Loan Payoff at End of Year 3 (2 Marks)

At the end of Year 3, immediately following the third installment payment:

• The outstanding principal balance remaining is the ending balance of Year 3:
  $$\text{Payoff Amount} = \mathbf{\text{Rs. } 915,660.55}$$

Alternatively, this equals the present value of the remaining 2 payments of Rs. 527,595 at 10%:

$$\text{Remaining Balance} = 527,595 \times PVIFA_{10\%, 2} = 527,595 \times 1.735537 = \mathbf{\text{Rs. } 915,660.55}$$

Solution: Risk and Return & Portfolio Analysis

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Part (a): Expected Return & Standard Deviation (4 Marks)

1. Stock A:

$$E(R_A) = \sum P_i R_{Ai} = 0.30(25\%) + 0.50(15\%) + 0.20(-5\%) = 7.5\% + 7.5\% - 1.0\% = \mathbf{14.0\%}$$

$$\sigma_A^2 = \sum P_i [R_{Ai} - E(R_A)]^2$$

$$\sigma_A^2 = 0.30(25 - 14)^2 + 0.50(15 - 14)^2 + 0.20(-5 - 14)^2$$

$$\sigma_A^2 = 0.30(121) + 0.50(1) + 0.20(361) = 36.3 + 0.5 + 72.2 = 109.0\%^2$$

$$\sigma_A = \sqrt{109.0} = \mathbf{10.44\%}$$

2. Stock B:

$$E(R_B) = \sum P_i R_{Bi} = 0.30(35\%) + 0.50(15\%) + 0.20(-15\%) = 10.5\% + 7.5\% - 3.0\% = \mathbf{15.0\%}$$

$$\sigma_B^2 = 0.30(35 - 15)^2 + 0.50(15 - 15)^2 + 0.20(-15 - 15)^2$$

$$\sigma_B^2 = 0.30(400) + 0.50(0) + 0.20(900) = 120.0 + 0 + 180.0 = 300.0\%^2$$

$$\sigma_B = \sqrt{300.0} = \mathbf{17.32\%}$$

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Part (b): Covariance and Correlation Coefficient (3 Marks)

$$Cov(A, B) = \sum P_i [R_{Ai} - E(R_A)][R_{Bi} - E(R_B)]$$

$$Cov(A, B) = 0.30(25 - 14)(35 - 15) + 0.50(15 - 14)(15 - 15) + 0.20(-5 - 14)(-15 - 15)$$

$$Cov(A, B) = 0.30(11)(20) + 0.50(1)(0) + 0.20(-19)(-30)$$

$$Cov(A, B) = 0.30(220) + 0 + 0.20(570) = 66.0 + 114.0 = \mathbf{180.0\%^2}$$

$$\rho_{AB} = \frac{Cov(A, B)}{\sigma_A \times \sigma_B} = \frac{180.0}{10.4403 \times 17.3205} = \frac{180.0}{180.831} = \mathbf{+0.9954}$$

The two stocks exhibit an almost perfectly positive linear correlation ($\rho \approx +1.0$).

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Part (c): Portfolio Return, Risk & Diversification (3 Marks)

1. Portfolio Expected Return ($w_A = 0.60, w_B = 0.40$):

$$E(R_p) = w_A E(R_A) + w_B E(R_B) = 0.60(14.0\%) + 0.40(15.0\%) = 8.4\% + 6.0\% = \mathbf{14.4\%}$$

2. Portfolio Standard Deviation:

$$\sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B Cov(A, B)$$

$$\sigma_p^2 = (0.60)^2(109.0) + (0.40)^2(300.0) + 2(0.60)(0.40)(180.0)$$

$$\sigma_p^2 = (0.36)(109.0) + (0.16)(300.0) + (0.48)(180.0) = 39.24 + 48.00 + 86.40 = 173.64\%^2$$

$$\sigma_p = \sqrt{173.64} = \mathbf{13.18\%}$$

3. Interpretation of Diversification:

• Weighted average standard deviation: $0.60(10.44\%) + 0.40(17.32\%) = 6.264\% + 6.928\% = 13.192\%$.
• Actual portfolio standard deviation: $\sigma_p = 13.18\%$.
• Conclusion: Because the correlation coefficient is near $+1.0$ ($\rho = 0.9954$), the diversification benefit is virtually negligible (reducing risk by a mere $0.012\%$). Significant portfolio risk reduction occurs only when asset correlation is low or negative.

Solution: Bond and Common Stock Valuation

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Part (a): Bond Valuation & YTM (5 Marks)

1. Intrinsic Value of Bond at $k_d = 10\%$:

• Face Value ($M$) = Rs. 1,000
• Annual Coupon ($I$) = $8\% \times 1,000 = \text{Rs. } 80$
• Maturity ($n$) = 10 years, Required Yield ($k_d$) = 10%

$$V_B = I \times PVIFA_{k_d, n} + M \times PVIF_{k_d, n}$$

$$PVIFA_{10\%, 10} = 6.144567, \quad PVIF_{10\%, 10} = 0.385543$$

$$V_B = 80(6.144567) + 1,000(0.385543) = 491.565 + 385.543 = \mathbf{\text{Rs. } 877.11}$$

Conclusion: Since the intrinsic value (Rs. 877.11) is below the face value (Rs. 1,000), the bond sells at a discount, because the market requires a 10% yield which exceeds the bond’s 8% contractual coupon rate.

2. Approximate Yield to Maturity (YTM) at Current Price $P_0 = \text{Rs. } 885$:

$$YTM \approx \frac{I + \frac{M - P_0}{n}}{\frac{M + 2P_0}{3}} = \frac{80 + \frac{1,000 - 885}{10}}{\frac{1,000 + 2(885)}{3}} = \frac{80 + \frac{115}{10}}{\frac{1,000 + 1,770}{3}} = \frac{80 + 11.5}{\frac{2,770}{3}} = \frac{91.5}{923.333} = \mathbf{9.91\%}$$

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Part (b): Supernormal Growth Common Stock Valuation (5 Marks)

• Given: $D_0 = \text{Rs. } 15.00, \quad g_1 = g_2 = 20\%, \quad g_n = 6\%, \quad k_s = 12\%$

1. Forecast Dividends during Supernormal Period:

• $D_1 = D_0(1 + g_1) = 15.00(1 + 0.20) = \mathbf{\text{Rs. } 18.00}$
• $D_2 = D_1(1 + g_2) = 18.00(1 + 0.20) = \mathbf{\text{Rs. } 21.60}$
• $D_3 = D_2(1 + g_n) = 21.60(1 + 0.06) = \mathbf{\text{Rs. } 22.896}$

2. Horizon / Terminal Value at End of Year 2 ($P_2$):

$$P_2 = \frac{D_3}{k_s - g_n} = \frac{22.896}{0.12 - 0.06} = \frac{22.896}{0.06} = \mathbf{\text{Rs. } 381.60}$$

3. Present Value of Cash Flows:

• $PV(D_1) = \frac{18.00}{(1.12)^1} = \text{Rs. } 16.071$
• $PV(D_2) = \frac{21.60}{(1.12)^2} = \frac{21.60}{1.2544} = \text{Rs. } 17.220$
• $PV(P_2) = \frac{381.60}{(1.12)^2} = \frac{381.60}{1.2544} = \text{Rs. } 304.209$

4. Intrinsic Value per Share ($P_0$):

$$P_0 = PV(D_1) + PV(D_2) + PV(P_2) = 16.071 + 17.220 + 304.209 = \mathbf{\text{Rs. } 337.50 \text{ per share}}$$

Solution: Weighted Average Cost of Capital (WACC)

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Part (a): Component Costs of Capital (6 Marks)

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

• Par Value ($M$) = Rs. 1,000, Coupon = $8\% \times 1,000 = \text{Rs. } 80$
• Net Issue Price ($P_{\text{net}}$) = Selling Price - Flotation Cost = $960 - 20 = \text{Rs. } 940$
• Maturity ($n$) = 10 years, Tax Rate ($T$) = 25%

$$\text{Pre-Tax Cost of Debt } (k_d) \approx \frac{I + \frac{M - P_{\text{net}}}{n}}{\frac{M + 2P_{\text{net}}}{3}} = \frac{80 + \frac{1,000 - 940}{10}}{\frac{1,000 + 2(940)}{3}} = \frac{80 + 6}{\frac{2,880}{3}} = \frac{86}{960} = 8.9583\%$$

$$\text{After-Tax Cost of Debt } = k_d(1 - T) = 8.9583\% \times (1 - 0.25) = \mathbf{6.72\%}$$

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

• Par Value = Rs. 100, Dividend ($D_p$) = $9\% \times 100 = \text{Rs. } 9.00$
• Net Proceeds ($P_{\text{net}}$) = $95 - 5 = \text{Rs. } 90.00$$k_p = \frac{D_p}{P_{\text{net}}} = \frac{9.00}{90.00} = \mathbf{10.00\%}$$

3. Cost of Retained Earnings / Internal Equity ($k_s$):

• $P_0 = \text{Rs. } 250, \quad D_1 = \text{Rs. } 18.00, \quad g = 7\% = 0.07$$k_s = \frac{D_1}{P_0} + g = \frac{18.00}{250.00} + 0.07 = 0.072 + 0.07 = 0.1420 = \mathbf{14.20\%}$$

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Part (b): Weighted Average Cost of Capital (WACC) (2 Marks)

$$\mathbf{WACC = 11.54\%}$$

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Part (c): External Common Equity and Revised WACC (2 Marks)

1. Cost of External Equity ($k_e$):

• Flotation cost percentage ($F$) = 10% = 0.10
• Net Proceeds: $P_{\text{net}} = P_0(1 - F) = 250(1 - 0.10) = \text{Rs. } 225.00$$k_e = \frac{D_1}{P_0(1 - F)} + g = \frac{18.00}{225.00} + 0.07 = 0.080 + 0.07 = \mathbf{15.00\%}$$

2. Revised WACC:

$$WACC_{\text{revised}} = (0.30 \times 6.72\%) + (0.10 \times 10.00\%) + (0.60 \times 15.00\%)$$

$$WACC_{\text{revised}} = 2.016\% + 1.000\% + 9.000\% = \mathbf{12.02\%}$$

Case Solution: Annapurna Beverages Nepal Ltd. (ABNL)

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Part (a): Net Initial Cash Outlay ($CF_0$) at Year 0 (5 Marks)

1. Capitalized Cost of New Equipment:

   $$\text{Purchase Price} + \text{Installation/Freight} = 9,200,000 + 800,000 = \text{Rs. } 10,000,000$$

2. Salvage of Old Machine and Tax Liability on Gain:

   • Market Selling Price of Old Asset = Rs. 2,000,000
   • Book Value of Old Asset = Rs. 1,500,000
   • Taxable Gain on Disposal = $2,000,000 - 1,500,000 = \text{Rs. } 500,000$
   • Tax Liability on Disposal Gain = $500,000 \times 25\% = \text{Rs. } 125,000$
   • Net Cash Proceeds from Old Asset = $2,000,000 - 125,000 = \text{Rs. } 1,875,000$

3. Initial Working Capital Investment: +Rs. 1,000,000

$$\text{Net Initial Outlay } (CF_0) = \text{Cost of New Asset} + \Delta NWC - \text{Net Salvage Proceeds of Old Asset}$$

$$CF_0 = 10,000,000 + 1,000,000 - 1,875,000 = \mathbf{\text{Rs. } 9,125,000}$$

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Part (b): Operating & Terminal Cash Flows (5 Marks)

1. Annual Depreciation:

$$\text{Annual Depreciation} = \frac{\text{Capitalized Cost}}{5} = \frac{10,000,000}{5} = \text{Rs. } 2,000,000 \text{ per year}$$

2. Annual Operating Cash Flow (OCF) for Years 1 to 5:

3. Terminal Non-Operating Cash Flow (End of Year 5):

• Market Salvage Value of New Asset = Rs. 1,200,000
• Book Value at Year 5 = Rs. 0.00
• Tax on Salvage Gain = $1,200,000 \times 25\% = \text{Rs. } 300,000$
• After-Tax Salvage Value = $1,200,000 - 300,000 = \text{Rs. } 900,000$
• Full Recovery of Working Capital = +Rs. 1,000,000
• Total Terminal Non-Operating Cash Flow: $900,000 + 1,000,000 = \mathbf{\text{Rs. } 1,900,000}$

Total Cash Flow at Year 5: $3,875,000 + 1,900,000 = \mathbf{\text{Rs. } 5,775,000}$.

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Part (c): Evaluation Metrics — NPV, PI, and IRR (6 Marks)

1. Present Value of Inflows ($k = 12\%$):

• $PVIFA_{12\%, 5} = \frac{1 - (1.12)^{-5}}{0.12} = 3.604776$
• $PVIF_{12\%, 5} = (1.12)^{-5} = 0.567427$$PV(\text{OCF Years 1–5}) = 3,875,000 \times 3.604776 = \text{Rs. } 13,968,507.00$$
  $$PV(\text{Terminal Cash Flow Year 5}) = 1,900,000 \times 0.567427 = \text{Rs. } 1,078,111.30$$
  $$\text{Total Present Value of Inflows (PV)} = 13,968,507.00 + 1,078,111.30 = \mathbf{\text{Rs. } 15,046,618.30}$$

2. Net Present Value (NPV):

$$NPV = PV - CF_0 = 15,046,618.30 - 9,125,000.00 = \mathbf{+\text{Rs. } 5,921,618.30}$$

3. Profitability Index (PI):

$$PI = \frac{PV}{CF_0} = \frac{15,046,618.30}{9,125,000.00} = \mathbf{1.649}$$

4. Internal Rate of Return (IRR):

• At $r = 12\%$, $NPV = +5,921,618.30$
• Test at $r = 35\%$:
  • $PVIFA_{35\%, 5} = \frac{1 - (1.35)^{-5}}{0.35} = \frac{1 - 0.223019}{0.35} = 2.219946$
  • $PVIF_{35\%, 5} = 0.223019$
  • $PV_{35\%} = (3,875,000 \times 2.219946) + (1,900,000 \times 0.223019) = 8,602,291 + 423,736 = \text{Rs. } 9,026,027$
  • $NPV_{35\%} = 9,026,027 - 9,125,000 = -\text{Rs. } 98,973$

Using linear interpolation:

$$IRR = 12\% + \left[\frac{5,921,618}{5,921,618 - (-98,973)}\right] \times (35\% - 12\%) = 12\% + \left[\frac{5,921,618}{6,020,591}\right] \times 23\% = 12\% + 22.62\% = \mathbf{34.62\%}$$

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Part (d): Managerial Recommendation & Strategic Justification (4 Marks)

1. Investment Decision: Firm Accept Recommendation.
   • The project generates an extraordinarily positive Net Present Value of +Rs. 5,921,618, indicating that undertaking this investment will expand the equity value of ABNL by nearly Rs. 6 million above its capital costs.
   • The Profitability Index is 1.649, showing that every rupee of capital invested produces Rs. 1.65 in present value terms.
2. Margin of Safety Analysis:
   • The project’s Internal Rate of Return of 34.62% far exceeds the firm’s required cost of capital of 12.00%, providing a substantial safety cushion of 22.62 percentage points (2,262 basis points).
   • Operating cash flows could decline by over 40% before the project becomes unprofitable, confirming that modernizing the bottling line is financially sound and strategically robust.