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FIN 253

Fundamentals of Investment

TU BBS · Fourth Year · Four-year BBS curriculum

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elective
Full marks
100
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6 papers

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Fundamentals of Investment 2080 Board Question Paper

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Tribhuvan University

Faculty of Management

Office of the Dean

2080 BS / Regular Examination

Course: FIN 253 · Fundamentals of Investment

Level: Bachelor of Business Studies (BBS) · Fourth Year

Full Marks: 100

Time: 3 hrs.

Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

Section A

Brief Answer Questions : Attempt All questions .

[10*2=20]
  1. [2]

    Distinguish between investment and speculation.

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    Investment vs. Speculation

    • Investment: Commitment of funds based on thorough fundamental analysis to achieve steady return and capital preservation over a long horizon.
    • Speculation: High-risk trading targeting short-term capital windfalls based on market rumors and price volatility.
  2. [2]

    Who is an issue manager? List any three functions of issue manager.

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    Issue Manager & Three Key Functions

    An issue manager (merchant bank) manages securities issuance. Functions: (1) Due diligence and prospectus preparation, (2) Underwriting subscription risks, (3) Coordinating IPO allotments via C-ASBA.

  3. [2]

    What is long purchase? Illustrate with an example.

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    Long Purchase

    Buying a financial asset anticipating price appreciation (e.g., buying 100 shares of Nabil at Rs 500 expecting it to rise to Rs 650).

  4. [2]

    What is the expected return on a stock with a beta of 1.15, a market risk premium of 6 percent and a risk free return of 5 percent?

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    CAPM Expected Return:

    E(R)=Rf+β(MRP)=5%+1.15(6%)=5%+6.9%=11.90%E(R) = R_f + \beta (MRP) = 5\% + 1.15(6\%) = 5\% + 6.9\% = \mathbf{11.90\%}
  5. [2]

    Distinguish between cash dividend and stock dividend.

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    Cash Dividend vs. Stock Dividend

    • Cash Dividend: Direct monetary payout reducing cash and retained earnings.
    • Stock Dividend (Bonus Shares): Issuing additional shares pro-rata, capitalizing retained earnings into share capital without changing corporate asset base.
  6. [2]

    Assume a share of stock is selling at Rs. 200 per share. You buy 100 shares of stock on margin today. If the initial margin is 60 percent and maintenance margin is 40 percent, compute the margin call price.

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    Margin Call Price (Long Purchase):

    P∗=P0(1−IM)1−MM=200(1−0.60)1−0.40=800.60=Rs. 133.33P^* = \frac{P_0 (1 - IM)}{1 - MM} = \frac{200(1 - 0.60)}{1 - 0.40} = \frac{80}{0.60} = \mathbf{\text{Rs. } 133.33}
  7. [2]

    A well-known company has total assets of Rs. 400 million, total debt of Rs. 160 million, and Rs. 40 million of 10 percent preferred stock outstanding. If the company has 10,00,000 shares of common stock outstanding, what is the book value per share?

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    Book Value Per Share:

    Common Equity=Total Assets−Debt−Preferred Stock=400M−160M−40M=Rs. 200M\text{Common Equity} = \text{Total Assets} - \text{Debt} - \text{Preferred Stock} = 400\text{M} - 160\text{M} - 40\text{M} = \text{Rs. } 200\text{M}
    BVPS=200M1M=Rs. 200.00BVPS = \frac{200\text{M}}{1\text{M}} = \mathbf{\text{Rs. } 200.00}
  8. [2]

    Explain why bank discount yield is lower than bond equivalent yield.

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    Bank Discount Yield vs. Bond Equivalent Yield

    Bank discount yield understates true yield because it uses face value in the denominator rather than actual purchase price, and assumes a 360-day year instead of 365 days.

  9. [2]

    A bond has a Macaulay duration equal to 6 years and a yield to maturity of 9 percent. What is the percentage change in price of a bond if yield to maturity rises to 9.5 percent?

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    Percentage Change in Bond Price:

    D∗=D1+y=61.09=5.505 yearsD^* = \frac{D}{1 + y} = \frac{6}{1.09} = 5.505 \text{ years}
    %ΔP≈−D∗×Δy=−5.505×0.005=−0.0275=−2.75%\% \Delta P \approx -D^* \times \Delta y = -5.505 \times 0.005 = -0.0275 = \mathbf{-2.75\%}
  10. [2]

    Write the meaning of derivative securities.

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    Derivative Securities

    Financial contracts whose value derives from an underlying asset, benchmark, or index (e.g., options, futures).

Section B

Descriptive Answer Questions : Attempt any FIVE questions .

[5*10=50]
  1. [10]

    What is investment? Explain different types of investments.

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    What is Investment?

    Investment is the commitment of current funds to one or more assets with the expectation of earning future returns that compensate the investor for three things: (1) the time value of money (waiting), (2) expected inflation (erosion of purchasing power), and (3) risk and uncertainty (the possibility that actual returns differ from expected returns).

    1. Sacrifice now, benefit later: Consumption is postponed; funds are locked into assets.
    2. Return expectation: Investors demand interest, dividends, rent, or capital gains.
    3. Risk-return trade-off: Higher expected returns always accompany higher uncertainty.

    Types of Investments

    1. Direct vs. Indirect Investment: Direct means the investor personally buys securities (e.g. NEPSE-listed shares through a broker). Indirect means investing through intermediaries such as mutual funds or CIT schemes, which pool money and manage portfolios professionally.
    2. Financial vs. Real Assets: Financial assets are paper/electronic claims (shares, debentures, T-bills, mutual fund units). Real assets are tangible (land, buildings, gold, machinery).
    3. Fixed-Income vs. Variable-Return: Fixed-income promises scheduled payments (bank fixed deposits, debentures, government bonds). Variable-return securities (ordinary shares) pay uncertain dividends plus capital gains.
    4. Short-Term vs. Long-Term: Money-market instruments (T-bills, commercial paper) mature within a year; capital-market securities (shares, long debentures) fund long horizons.
    5. By Issuer: Government securities (NRB-issued T-bills and development bonds, near risk-free) vs. corporate securities (company shares and debentures carrying business and financial risk).
  2. [10]

    Assume that you sell short 500 shares of Nabil stock for Rs. 400 per share. The initial margin and maintenance margin requirements are 50 percent and 30 percent respectively.

    a. What is the initial value of debt and equity in your margin account?

    b. If the stock price increases to Rs. 450 per share, what will be the value of debt and equity in your margin account?

    c. Do you receive a margin call if the price of stock increases to Rs. 450?

    d. What will your rate of return be if Nabil stock is trading at Rs. 380?

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    Short Sale: 500 Nabil Shares at Rs. 400

    Short-sale proceeds =500×400=Rs. 200,000= 500 \times 400 = \mathbf{\text{Rs. } 200,000}

    Part (a): Initial Debt and Equity

    • Debt (market value of shares owed): Rs. 200,000
    • Equity (initial margin deposit): 50%×200,000=Rs. 100,00050\% \times 200,000 = \mathbf{\text{Rs. } 100,000}
    • Total margin account value =200,000+100,000=Rs. 300,000= 200,000 + 100,000 = \text{Rs. } 300,000

    Part (b): Price Rises to Rs. 450

    • Debt: 500×450=Rs. 225,000500 \times 450 = \mathbf{\text{Rs. } 225,000}
    • Equity: 300,000−225,000=Rs. 75,000300,000 - 225,000 = \mathbf{\text{Rs. } 75,000}
    • Actual margin =75,000/225,000=33.33%= 75,000 / 225,000 = \mathbf{33.33\%}

    Part (c): Margin Call?

    No margin call is received, because the actual margin of 33.33% exceeds the 30% maintenance margin requirement.

    Part (d): Rate of Return at Rs. 380

    • Profit =(400−380)×500=Rs. 10,000= (400 - 380) \times 500 = \text{Rs. } 10,000
    • Rate of return =10,000/100,000=10%= 10,000 / 100,000 = \mathbf{10\%}
  3. [10]

    Consider the following stock price and no. of shares information:

    Stock No. of shares outstanding Stock prices at the end of 2022 (Rs) Stock prices at the end of 2023 (Rs)
    A 2,000 400 380
    B 1,000 150 165
    C 5,000 700 720

    a. Construct a price-weighted index for 2022 and 2023 and compute the percentage change in series for the period from 2022 to 2023.

    b. Construct a market value weighted index 2023 and compute the percentage change in the period from 2022 to 2023.

    c. Construct equally-weighted index for 2023 and compute the percentage change in series for the period from 2022 and 2023.

    d. Briefly discuss the difference in the results for three stock indexes.

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    Part (a): Price-Weighted Index (PWI)

    PWI2022=400+150+7003=1,2503=416.67\text{PWI}_{2022} = \frac{400 + 150 + 700}{3} = \frac{1,250}{3} = \mathbf{416.67}
    PWI2023=380+165+7203=1,2653=421.67\text{PWI}_{2023} = \frac{380 + 165 + 720}{3} = \frac{1,265}{3} = \mathbf{421.67}

    Percentage change =(421.67−416.67)/416.67=+1.20%= (421.67 - 416.67) / 416.67 = \mathbf{+1.20\%}

    Part (b): Market Value Weighted Index (VWI, base 2022 = 100)

    • MV(2022) =2,000(400)+1,000(150)+5,000(700)=Rs. 4,450,000= 2,000(400) + 1,000(150) + 5,000(700) = \text{Rs. } 4,450,000
    • MV(2023) =2,000(380)+1,000(165)+5,000(720)=Rs. 4,525,000= 2,000(380) + 1,000(165) + 5,000(720) = \text{Rs. } 4,525,000
    • VWI(2023) =100×4,525,000/4,450,000=101.69= 100 \times 4,525,000 / 4,450,000 = \mathbf{101.69}, i.e. +1.69%

    Part (c): Equally-Weighted Index (EWI, base 2022 = 100)

    • Relatives: A =380/400=0.9500= 380/400 = 0.9500, B =165/150=1.1000= 165/150 = 1.1000, C =720/700=1.0286= 720/700 = 1.0286
    • EWI(2023) =100×(0.9500+1.1000+1.0286)/3=102.62= 100 \times (0.9500 + 1.1000 + 1.0286) / 3 = \mathbf{102.62}, i.e. +2.62%

    Part (d): Why the Results Differ

    • EWI (+2.62%) is highest because it gives small Stock B’s +10% gain the same weight as the giants.
    • VWI (+1.69%) is dominated by Stock C, the largest capitalization, which rose only 2.86%.
    • PWI (+1.20%) weights by price level, so high-priced Stock C again dominates while Stock B’s move barely registers.
  4. [10]

    Consider the following subjective probability distribution of returns on Stock X and Stock Y for a potential investment.

    State of economy Probability Estimated rate of returns
    Stock X Stock Y
    Strong growth 0.1 -10% 20%
    Moderate growth 0.4 5% 15%
    Weak growth 0.4 15% 10%
    Recession 0.1 30% -10%

    a. Which stock would you select on the basis of expected [return]?

    b. Calculate standard deviation of the returns of Stock X and S[tock Y]. What purpose does standard deviation service for an investor?

    c. Calculate coefficient of variation for each stock. What purpose does coefficient of variation serve?

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    Part (a): Expected Returns

    • E(X) =0.1(−10)+0.4(5)+0.4(15)+0.1(30)=−1+2+6+3=10%= 0.1(-10) + 0.4(5) + 0.4(15) + 0.1(30) = -1 + 2 + 6 + 3 = \mathbf{10\%}
    • E(Y) =0.1(20)+0.4(15)+0.4(10)+0.1(−10)=2+6+4−1=11%= 0.1(20) + 0.4(15) + 0.4(10) + 0.1(-10) = 2 + 6 + 4 - 1 = \mathbf{11\%}

    On expected return alone, select Stock Y (11% > 10%).

    Part (b): Standard Deviations

    • Var(X) =0.1(−10−10)2+0.4(5−10)2+0.4(15−10)2+0.1(30−10)2= 0.1(-10-10)^2 + 0.4(5-10)^2 + 0.4(15-10)^2 + 0.1(30-10)^2
    • Var(X) =0.1(400)+0.4(25)+0.4(25)+0.1(400)=10+10+10+40=80= 0.1(400) + 0.4(25) + 0.4(25) + 0.1(400) = 10 + 10 + 10 + 40 = 80
    • SD(X) =80=8.94%= \sqrt{80} = \mathbf{8.94\%}
    • Var(Y) =0.1(20−11)2+0.4(15−11)2+0.4(10−11)2+0.1(−10−11)2= 0.1(20-11)^2 + 0.4(15-11)^2 + 0.4(10-11)^2 + 0.1(-10-11)^2
    • Var(Y) =0.1(81)+0.4(16)+0.4(1)+0.1(441)=8.1+6.4+0.4+44.1=59= 0.1(81) + 0.4(16) + 0.4(1) + 0.1(441) = 8.1 + 6.4 + 0.4 + 44.1 = 59
    • SD(Y) =59=7.68%= \sqrt{59} = \mathbf{7.68\%}

    Purpose: Standard deviation measures total risk — the dispersion of possible returns around the expected return. A larger SD means more volatile, less predictable outcomes.

    Part (c): Coefficients of Variation

    • CV(X) =8.94/10=0.89= 8.94 / 10 = \mathbf{0.89}
    • CV(Y) =7.68/11=0.70= 7.68 / 11 = \mathbf{0.70}

    Purpose: CV measures risk per unit of expected return, allowing fair comparison of assets with different return levels. Stock Y is also superior here (0.70 < 0.89) — it offers higher return at lower relative risk.

  5. [10]

    ** (**a) City fund had average daily assets of Rs. 1800 million in the past year. The Fund sold Rs. 600 million and purchased Rs. 500 million worth of stock during the year.

    i) What was the portfolio turnover rate?

    ii) If City Fund’s expense ratio was 1.2 percent and the management fee was 0.8 percent, what were the total fees paid to the fund’s investment managers during the year? What were the other administrative expenses?

    (b) Assume the average return on portfolio P was 35 percent and that of the market was 28 percent. The beta coefficient of portfolio P was 1.2 and that of the market was 1.0. Standard deviation of portfolio P and the market was 42 percent and 30 percent respectively. The T-bill rate during the period was 6 percent.

    i) Calculate the Treynor and Sharpe measures for both portfolio P and the market.

    ii) Briefly explain whether portfolio P underperformed, equated, or outperformed the market. Why these two measures may produce conflicting results?

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    Part (a): City Fund Turnover and Fees

    i) Portfolio turnover rate uses the lesser of purchases and sales over average assets:

    Turnover=min⁡(600,500)1,800=5001,800=27.78%\text{Turnover} = \frac{\min(600, 500)}{1,800} = \frac{500}{1,800} = \mathbf{27.78\%}

    ii) Fees:

    • Management fee paid =0.8%×1,800=Rs. 14.40 million= 0.8\% \times 1,800 = \mathbf{\text{Rs. } 14.40 \text{ million}}
    • Total expenses =1.2%×1,800=Rs. 21.60 million= 1.2\% \times 1,800 = \text{Rs. } 21.60 \text{ million}
    • Other administrative expenses =21.60−14.40=Rs. 7.20 million= 21.60 - 14.40 = \mathbf{\text{Rs. } 7.20 \text{ million}}

    Part (b): Treynor and Sharpe Measures

    i) Treynor (excess return per unit of beta):

    • Portfolio P: (35−6)/1.2=29/1.2=24.17%(35 - 6) / 1.2 = 29 / 1.2 = \mathbf{24.17\%}
    • Market: (28−6)/1.0=22.00%(28 - 6) / 1.0 = \mathbf{22.00\%}

    Sharpe (excess return per unit of total risk):

    • Portfolio P: (35−6)/42=29/42=0.69(35 - 6) / 42 = 29 / 42 = \mathbf{0.69}
    • Market: (28−6)/30=22/30=0.73(28 - 6) / 30 = 22 / 30 = \mathbf{0.73}

    ii) Interpretation: The measures conflict — Treynor ranks P above the market (24.17 > 22.00) while Sharpe ranks the market above P (0.73 > 0.69). Portfolio P earned high returns but carried very large total volatility (42% SD), most of it diversifiable risk. Treynor credits only systematic (beta) risk and ignores that extra volatility, whereas Sharpe penalizes it. Conflict arises whenever a portfolio is poorly diversified: Treynor suits a portfolio held as part of a larger diversified fund, while Sharpe suits a stand-alone portfolio.

  6. [10]

    Assume that risk free rate is currently 6 percent. The expected return on the average stocks in the market is 12 percent. You are evaluating the prospect of ABC stock which is currently paying Rs 20 per share in dividend. The stock has a beta coefficient of 1.5. Currently, the aggressive marketing campaign launched by the company will enhance its earnings significantly. As a result the growth rate of dividends is expected to be 20 percent for the next two year. After this period, the growth rate is expected to slow down to a normal rate of 5 percent indefinitely.

    a. Calculate the required rate of return on ABC stock.

    b. What is the expected dividends per share on ABC stock for next two years?

    c. At what price the stock is expected to sell at the end of year 2?

    d. What is the intrinsic value of this stock today?

    e. If the stock is currently trading in Rs. 260 per share, is the stock underpriced or overpriced? Would you prefer to buy the stock?

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    Part (a): Required Rate of Return (CAPM)

    k=6%+1.5(12%−6%)=6%+9%=15%k = 6\% + 1.5(12\% - 6\%) = 6\% + 9\% = \mathbf{15\%}

    Part (b): Expected Dividends

    • D1 =20×1.20=Rs. 24.00= 20 \times 1.20 = \mathbf{\text{Rs. } 24.00}
    • D2 =24×1.20=Rs. 28.80= 24 \times 1.20 = \mathbf{\text{Rs. } 28.80}

    Part (c): Expected Price at End of Year 2

    • D3 =28.80×1.05=Rs. 30.24= 28.80 \times 1.05 = \text{Rs. } 30.24
    • P2 =D3/(k−g)=30.24/(0.15−0.05)=30.24/0.10=Rs. 302.40= D3 / (k - g) = 30.24 / (0.15 - 0.05) = 30.24 / 0.10 = \mathbf{\text{Rs. } 302.40}

    Part (d): Intrinsic Value Today

    V0=241.15+28.801.152+302.401.152=20.87+21.78+228.65=Rs. 271.30V0 = \frac{24}{1.15} + \frac{28.80}{1.15^2} + \frac{302.40}{1.15^2} = 20.87 + 21.78 + 228.65 = \mathbf{\text{Rs. } 271.30}

    Part (e): Investment Decision

    The market price of Rs. 260 is below the intrinsic value of Rs. 271.30, so the stock is underpriced (undervalued). Yes, buy the stock — it offers an expected return above the 15% required rate.

Section C

Analytical Answer Questions : Attempt any TWO questions .

[2*15=30]
  1. [15]

    What is fixed income security? Explain different types of fixed income securities.

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    What is a Fixed Income Security?

    A fixed income security is a debt contract under which the issuer promises to pay the holder a specified, scheduled stream — periodic interest (coupons) plus repayment of principal at maturity. Its defining features are:

    1. Contractual cash flows: Amounts and dates are fixed at issue, unlike uncertain equity dividends.
    2. Maturity date: A stated redemption point (short money-market to long capital-market).
    3. Priority of claim: Debtholders are paid before shareholders in distress or liquidation.
    4. Lower risk, lower return: Certainty of income trades off against limited upside.

    Types of Fixed Income Securities

    1. Treasury Bills (T-Bills): Short-term government papers (91/182/364 days in Nepal, auctioned via NRB), sold at a discount with no coupons — the safest money-market asset.
    2. Government/Development Bonds: Long-term sovereign debt funding public projects; near-zero default risk.
    3. Corporate Debentures: Company-issued bonds (secured or unsecured) paying fixed coupons; many trade on NEPSE with credit ratings.
    4. Municipal/Local Bonds: Issued by local bodies for infrastructure, sometimes with tax advantages.
    5. Preferred Shares (hybrid): Fixed preferential dividends with priority over ordinary shares, though junior to debentures; usually non-voting.
    6. Bank Fixed Deposits & CIT Schemes: Retail fixed-income staples in Nepal — guaranteed interest over a chosen tenure, the default safe asset for households.
  2. [15]

    You have been provided the following returns data of three assets for your advice in selecting a portfolio of assets:

    Year Rate of return: Asset A Asset B Asset C
    2019 10% 18% 10%
    2020 12% 16% 12%
    2021 14% 14% 14%
    2022 16% 12% 16%
    2023 18% 10% 16%

    You have been told that you can create two portfolios - one consisting of assets A and B, and other consisting of assets A and C - by investing equal proportions in each of the two component assets.

    a. Calculate average return and standard deviation for each of the three assets.

    b. Calculate the covariance between the returns of assets A and B, and assets A and C.

    c. Calculate the return and standard deviation of the portfolios consisting of assets A and B, and assets A and C.

    d. Which portfolio do you recommend? Why?

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    Part (a): Average Returns and Standard Deviations

    (Historical series use the sample divisor n−1=4n - 1 = 4.)

    • Mean A =(10+12+14+16+18)/5=14%= (10+12+14+16+18)/5 = \mathbf{14\%}; Var A =(16+4+0+4+16)/4=10= (16+4+0+4+16)/4 = 10; SD(A) =3.16%= \mathbf{3.16\%}
    • Mean B =(18+16+14+12+10)/5=14%= (18+16+14+12+10)/5 = \mathbf{14\%}; Var B =(16+4+0+4+16)/4=10= (16+4+0+4+16)/4 = 10; SD(B) =3.16%= \mathbf{3.16\%}
    • Mean C =(10+12+14+16+16)/5=13.60%= (10+12+14+16+16)/5 = \mathbf{13.60\%}; Var C =(12.96+2.56+0.16+5.76+5.76)/4=6.80= (12.96+2.56+0.16+5.76+5.76)/4 = 6.80; SD(C) =2.61%= \mathbf{2.61\%}

    Part (b): Covariances

    • Cov(A,B) =[(−4)(4)+(−2)(2)+(0)(0)+(2)(−2)+(4)(−4)]/4=−40/4=−10= [(-4)(4) + (-2)(2) + (0)(0) + (2)(-2) + (4)(-4)] / 4 = -40/4 = \mathbf{-10}
    • Cov(A,C) =[(14.40)+(3.20)+(0)+(4.80)+(9.60)]/4=32/4=8= [(14.40) + (3.20) + (0) + (4.80) + (9.60)] / 4 = 32/4 = \mathbf{8}
    • Correlation: ρAB=−10/(3.16×3.16)=−1.0\rho_{AB} = -10 / (3.16 \times 3.16) = \mathbf{-1.0} (perfect negative); ρAC=8/(3.16×2.61)=0.97\rho_{AC} = 8 / (3.16 \times 2.61) = \mathbf{0.97} (strong positive).

    Part (c): Equal-Weight Portfolios

    • Portfolio AB: E(R) =(14+14)/2=14%= (14+14)/2 = \mathbf{14\%}; Var =0.25(10)+0.25(10)+2(0.5)(0.5)(−10)=2.5+2.5−5=0= 0.25(10) + 0.25(10) + 2(0.5)(0.5)(-10) = 2.5 + 2.5 - 5 = 0; SD =0%= \mathbf{0\%}
    • Portfolio AC: E(R) =(14+13.6)/2=13.80%= (14+13.6)/2 = \mathbf{13.80\%}; Var =0.25(10)+0.25(6.8)+2(0.5)(0.5)(8)=2.5+1.7+4=8.2= 0.25(10) + 0.25(6.8) + 2(0.5)(0.5)(8) = 2.5 + 1.7 + 4 = 8.2; SD =2.86%= \mathbf{2.86\%}

    Part (d): Recommendation

    Recommend Portfolio AB. It delivers a higher expected return (14% vs 13.80%) at zero risk, because Assets A and B move in perfect opposition (ρ=−1\rho = -1): every loss on one is exactly offset by a gain on the other. Portfolio AC merely diversifies partially since A and C move together (ρ=0.97\rho = 0.97).

  3. [15]

    Assume that you are an aggressive bond trader and therefore, want to speculate on interest rate swing. Market interest rates are currently 9 percent, but you expect the interest rates to fall to 7 percent within a year. You are thinking of buying either a 25-year, zero coupon bond or a 20-year, 5.5 percent bond. Both bonds have Rs. 1000 par values and carry same agency rating**.**

    a. If you want to maximize capital gain income, which of the two bonds should you select? Show your calculation.

    b. If you want to maximize total return from your investment, which of the two bonds should you select?

    c. Why did one bond provide better capital gains than the other?

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    Part (a): Maximizing Capital Gain

    25-year zero-coupon bond:

    • Buy today (25-yr @ 9%): P0 =1,000/1.0925=Rs. 115.97= 1,000 / 1.09^{25} = \text{Rs. } 115.97
    • Sell in 1 year (24-yr @ 7%): P1 =1,000/1.0724=Rs. 197.15= 1,000 / 1.07^{24} = \text{Rs. } 197.15
    • Capital gain =(197.15−115.97)/115.97=70.00%= (197.15 - 115.97) / 115.97 = \mathbf{70.00\%}

    20-year 5.5% coupon bond (Rs. 55 annual coupon):

    • Buy today @ 9%: P0 =55×PVIFA(9%,20)+1,000/1.0920=55(9.1286)+178.43=Rs. 680.50= 55 \times PVIFA(9\%, 20) + 1,000 / 1.09^{20} = 55(9.1286) + 178.43 = \text{Rs. } 680.50
    • Sell in 1 year (19-yr @ 7%): P1 =55×PVIFA(7%,19)+1,000/1.0719=55(10.3356)+276.51=Rs. 844.97= 55 \times PVIFA(7\%, 19) + 1,000 / 1.07^{19} = 55(10.3356) + 276.51 = \text{Rs. } 844.97
    • Capital gain =(844.97−680.50)/680.50=24.17%= (844.97 - 680.50) / 680.50 = \mathbf{24.17\%}

    Select the 25-year zero-coupon bond (70.00% vs 24.17%).

    Part (b): Maximizing Total Return

    • Zero-coupon (no interim coupon): total return =70.00%= \mathbf{70.00\%}
    • Coupon bond (collects Rs. 55): total return =(844.97+55−680.50)/680.50=219.47/680.50=32.25%= (844.97 + 55 - 680.50) / 680.50 = 219.47 / 680.50 = \mathbf{32.25\%}

    The zero-coupon bond still wins on total return.

    Part (c): Why the Zero Wins

    Bond price sensitivity rises with duration, and the zero-coupon bond has the maximum possible duration (25 years — all cash arrives at maturity, nothing earlier to cushion the rate fall). The coupon bond’s earlier Rs. 55 receipts shorten its duration, so the same 9%-to-7% swing lifts its price far less. Longer maturity plus zero coupons equals maximum interest-rate leverage.