Module 2: Numeric Questions

For students

Last updated: 11/08/2025 14:33

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)

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

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Answer the following questions based on the discussions in class.

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CAPM Cost of Capital

Suppose the market risk premium is 8.02% and the risk‑free interest rate is 4.99%.

1. What is the cost of capital of investing in a project with a beta of 0.73?

✅ Cost of capital = rf + β × mrp = 10.82.

Buy-hold Return

You bought a stock for $ 51.3 per share and sold it later for $ 56.04. It paid $ 2.44 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 = 14.02%.

Total and Annualized Return Over Multiple Years

You bought a stock for $97.88 per share and sold it for $113.82 after 1 years. You received $2.56 in dividends per year.

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

✅ Total return = (p2 − p1 + div × years)/p1 × 100 = 18.89%.

2. What was your annualized return (CAGR)?

✅ Annualized return (CAGR) = [((p2 + div × years)/p1)^(1/years) − 1] × 100 = 18.89%.

Average and Standard Deviation of Returns

The past five annual returns of a stock were (in %): 8.96, 11.52, 5.69, 8.08, 7.96

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

✅ Average return = mean(returns) = 8.44%.

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

✅ Standard deviation = sd(returns) = 2.1%.

Expected Return of a Mixed Portfolio

Suppose you invest 24.3% of your wealth in the market portfolio, which has an expected return of 8.19%, and the remainder in the risk‑free asset, which has a return of 2.57%.

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

✅ Expected portfolio return = rm * w + rf * (1-w)= 3.94%.

Portfolio Return from Two Stocks

You invested 31.9% of your capital in Stock A, which returned 6.36%, and the remainder in Stock B, which returned 9.87%.

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

✅ Portfolio return = w×rA + (1 − w)×rB = 8.75%.

Compounded Annual Return from Semi‑Annual Returns

A stock returned 1.08% in the first half of the year and 3.66% 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 = 4.79%.

Arithmetic vs. Geometric Average Return

A stock yielded returns of 11.42% and 10.82% over two consecutive years.

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

✅ Arithmetic average return = (r1 + r2)/2 = 11.12%.

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

✅ Geometric average return = [(1 + r1/100) × (1 + r2/100)]¹ᐟ² − 1 = 11.12%.

Market Risk Premium and Expected Return

The risk‑free rate is 2.65%, the expected market return is 9.74%, and the beta of a stock is 1.26.

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

✅ Market risk premium = rm − rf = 7.08%.

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

✅ Expected return = rf + β × (rm − rf) = 11.56%.