Module 2: Numeric Questions

For students

Last updated: 17/08/2025 09:49

The questions are based on or inspired by the following references:

• Berk & DeMarzo, Corporate Finance, 5th ed. (2020)
  
• Brealey & Myers, Principles of Corporate Finance, 13th ed. (2020)

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💡 You can also press Ctrl + P (or Cmd + P on Mac) to print or save your responses as a .pdf file.

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⚠️ These exercises are powered by AI-assisted technologies and may contain occasional formatting or logic errors. Please report any issues you encounter so I can improve the experience.

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📘 Part 1 (until Midterm)

Module	Chapter	Slides	T/F	MCQ	Numeric	Long
2	ch10	🎞️	✅	❓	🔢	📝

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Answer the following questions based on the discussions in class.

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Q1.

CAPM Cost of Capital

Suppose the market risk premium is 8.01% and the risk‑free interest rate is 5%.

1. What is the cost of capital of investing in a project with a beta of 0.96?

✅ Cost of capital = rf + β × mrp = 12.69.

Q2.

Buy-hold Return

You bought a stock for $ 51.11 per share and sold it later for $ 63.96. It paid $ 2.03 in dividends over the period.

1. What was your holding period return (in %)?

✅ Holding period return = (p_sell − p_buy + div_yield)/p_buy × 100 = 29.12%.

Q3.

Total and Annualized Return Over Multiple Years

You bought a stock for $90.95 per share and sold it for $138.14 after 5 years. You received $4.71 in dividends per year.

1. What was your total return over the period (in %)?

✅ Total return = (p2 − p1 + div × years)/p1 × 100 = 77.79%.

2. What was your annualized return (CAGR)?

✅ Annualized return (CAGR) = [((p2 + div × years)/p1)^(1/years) − 1] × 100 = 12.2%.

Q4.

Average and Standard Deviation of Returns

The past five annual returns of a stock were (in %): 8.07, 9.08, 9.57, 4.68, 4.78

1. What was the average return (in %)?

✅ Average return = mean(returns) = 7.24%.

2. What was the standard deviation of the returns (in %)?

✅ Standard deviation = sd(returns) = 2.35%.

Q5.

Expected Return of a Mixed Portfolio

Suppose you invest 4% of your wealth in the market portfolio, which has an expected return of 9.2%, and the remainder in the risk‑free asset, which has a return of 3.04%.

1. What is the expected return of your portfolio (in %)?

✅ Expected portfolio return = rm * w + rf * (1-w)= 3.28%.

Q6.

Portfolio Return from Two Stocks

You invested 27.3% of your capital in Stock A, which returned 7.98%, and the remainder in Stock B, which returned 5.94%.

1. What is your portfolio’s return (in %)?

✅ Portfolio return = w×rA + (1 − w)×rB = 6.5%.

Q7.

Compounded Annual Return from Semi‑Annual Returns

A stock returned 3.41% in the first half of the year and 7.17% in the second half of the year.

1. What is the total annual return (in %)?

✅ Total annual return = (1 + r₁/100) × (1 + r₂/100) − 1 = 10.82%.

Q8.

Arithmetic vs. Geometric Average Return

A stock yielded returns of 3.29% and 13.59% over two consecutive years.

1. What is the arithmetic average return (in %)?

✅ Arithmetic average return = (r1 + r2)/2 = 8.44%.

2. What is the geometric average return (in %)?

✅ Geometric average return = [(1 + r1/100) × (1 + r2/100)]¹ᐟ² − 1 = 8.31%.

Q9.

Market Risk Premium and Expected Return

The risk‑free rate is 2.56%, the expected market return is 10.66%, and the beta of a stock is 1.19.

1. What is the market risk premium (in %)?

✅ Market risk premium = rm − rf = 8.1%.

2. What is the expected return of this stock (in %)?

✅ Expected return = rf + β × (rm − rf) = 12.2%.