ACCA FM · Chapter 11
Cost of capital MCQs with Answers
11 multiple-choice questions on Cost of capital for ACCA FM Financial Management. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
A company is about to pay a dividend of $0.40 per share. Its share price is $6.00 cum div. Dividends are expected to grow at 5% a year. Using the dividend valuation model, what is the cost of equity (to 2 decimal places)?
- A) 11.67%
- B) 12.00%
- C) 12.14%
- D) 12.50%
Show answer & explanation
Answer: D) 12.50%
The ex-div price is 6.00 - 0.40 = $5.60. Ke = D0(1 + g)/P0 + g = 0.40 x 1.05 / 5.60 + 0.05 = 0.42 / 5.60 + 0.05 = 0.075 + 0.05 = 12.50%. Using the cum-div price gives 12.00%, and failing to grow the dividend gives 12.14%.
Question 2
A company retains 60% of its earnings each year and earns a return of 15% on reinvested funds. Using Gordon's growth model, what is the expected dividend growth rate?
- A) 6.0%
- B) 9.0%
- C) 15.0%
- D) 25.0%
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Answer: B) 9.0%
Gordon's growth model: g = r x b, where b is the proportion of earnings retained and r the return on reinvested funds. g = 15% x 0.60 = 9.0%. Using the payout ratio (40%) instead of the retention ratio gives 6.0%.
Question 3
A company's dividend per share was $0.30 four years ago and is $0.42 this year. What is the historical average annual dividend growth rate (to 2 decimal places)?
- A) 8.78%
- B) 10.00%
- C) 11.87%
- D) 40.00%
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Answer: A) 8.78%
There are four years of growth between the two dividends. g = (0.42 / 0.30)^(1/4) - 1 = 1.4^(0.25) - 1 = 8.78%. Dividing the total growth of 40% by four (10.00%) ignores compounding, and using a cube root counts only three years of growth.
Question 4
The risk-free rate is 4%, the expected return on the market portfolio is 11% and a company's equity beta is 1.3. Using the capital asset pricing model (CAPM), what is the company's cost of equity?
- A) 11.0%
- B) 13.1%
- C) 14.3%
- D) 18.3%
Show answer & explanation
Answer: B) 13.1%
CAPM: Ke = Rf + beta x (Rm - Rf) = 4% + 1.3 x (11% - 4%) = 4% + 1.3 x 7% = 13.1%. A common error is to multiply beta by the market return rather than by the market risk premium, giving 18.3%.
Question 5
A company has irredeemable bonds with a coupon rate of 8% on a nominal value of $100. They are trading at $96 ex interest. Corporation tax is 25%. What is the after-tax cost of the debt (to 2 decimal places)?
- A) 5.77%
- B) 6.00%
- C) 6.25%
- D) 8.33%
Show answer & explanation
Answer: C) 6.25%
For irredeemable debt, Kd (after tax) = I(1 - T) / P0 = 8 x (1 - 0.25) / 96 = 6 / 96 = 6.25%. Ignoring tax gives the pre-tax cost of 8.33%, 6.00% wrongly uses nominal value rather than market value, and 5.77% wrongly adds the interest to the ex-interest price.
Question 6
A company's bonds pay a 6% coupon annually on a $100 nominal value and are redeemable at par in five years. They currently trade at $95 ex interest. Corporation tax is 20%. Using linear interpolation between discount rates of 5% and 7%, what is the after-tax cost of debt (to 1 decimal place)?
- A) 5.1%
- B) 6.0%
- C) 6.3%
- D) 7.2%
Show answer & explanation
Answer: B) 6.0%
After-tax interest = 6 x (1 - 0.20) = 4.80 a year. The after-tax cost of debt is the IRR of: time 0 -95; years 1-5 +4.80; year 5 +100. At 5%: -95 + 4.80 x 4.329 + 100 x 0.784 = +4.18. At 7%: -95 + 4.80 x 4.100 + 100 x 0.713 = -4.02. Kd = 5% + 4.18 / (4.18 + 4.02) x 2% = 6.02%, i.e. 6.0% to 1 decimal place (the exact IRR is 5.99%). 7.2% is the pre-tax yield to maturity, 6.3% is the pre-tax coupon divided by the price (6/95), and 5.1% ignores the gain on redemption (4.80/95).
Question 7
A company's 8% convertible bonds ($100 nominal) are trading at $102 ex interest. In four years' time each bond can be converted into 25 ordinary shares or redeemed at par. The current share price is $3.50 and is expected to grow at 5% a year. Corporation tax is 25%. Using linear interpolation between discount rates of 5% and 8%, what is the after-tax cost of the convertible debt (to 1 decimal place)?
- A) 5.5%
- B) 5.9%
- C) 6.9%
- D) 8.7%
Show answer & explanation
Answer: C) 6.9%
Conversion value in 4 years = 25 x 3.50 x 1.05^4 = $106.36, which exceeds the redemption value of $100, so investors are expected to convert. After-tax interest = 8 x 0.75 = 6. Cash flows: time 0 -102; years 1-4 +6; year 4 +106.36. NPV at 5% = -102 + 6 x 3.546 + 106.36 x 0.823 = +6.81; NPV at 8% = -102 + 6 x 3.312 + 106.36 x 0.735 = -3.95. Kd = 5% + 6.81 / (6.81 + 3.95) x 3% = 6.90%, i.e. 6.9% (exact IRR 6.85%). Assuming redemption at par gives 5.5%, ignoring tax relief on interest gives 8.7%, and 5.9% is simply after-tax interest divided by price (6/102).
Question 8
A company has 10 million ordinary shares with a market price of $3.00 (book value of equity $15m) and a cost of equity of 12%. It also has $10m nominal of bonds quoted at $105 per $100, with an after-tax cost of 5%. What is the weighted average cost of capital using market values (to 2 decimal places)?
- A) 8.50%
- B) 9.20%
- C) 10.19%
- D) 10.25%
Show answer & explanation
Answer: C) 10.19%
Market value of equity = 10m x $3.00 = $30m; market value of debt = $10m x 105/100 = $10.5m; total $40.5m. WACC = (30 x 12% + 10.5 x 5%) / 40.5 = (3.60 + 0.525) / 40.5 = 10.19%. Using book values gives 9.20%, and using the nominal value of the debt gives 10.25%.
Question 9
A company has 7% irredeemable preference shares with a nominal value of $1, currently quoted at $0.875 ex div. What is the cost of the preference shares?
- A) 5.6%
- B) 6.1%
- C) 7.0%
- D) 8.0%
Show answer & explanation
Answer: D) 8.0%
Kp = preference dividend / ex-div market price = $0.07 / $0.875 = 8.0%. Preference dividends are paid out of post-tax profits, so no adjustment for tax is made. 7.0% is the coupon rate on nominal value, and 5.6% wrongly deducts tax relief at 20%.
Question 10
A company has a bank loan with an interest rate of 7% a year. Corporation tax is 20%. What is the after-tax cost of the bank loan?
- A) 1.4%
- B) 5.6%
- C) 7.0%
- D) 8.4%
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Answer: B) 5.6%
A bank loan is not traded, so its cost is based on the interest rate. Because interest is tax deductible, the after-tax cost = 7% x (1 - 0.20) = 5.6%. 1.4% is the value of the tax relief, not the cost.
Question 11
According to portfolio theory and the CAPM, which type of risk is rewarded by a higher expected return?
- A) Systematic risk, because it cannot be eliminated by diversification
- B) Unsystematic risk, because it is specific to each company
- C) Business risk, because it can be eliminated by diversification
- D) Total risk, measured by the standard deviation of returns
Show answer & explanation
Answer: A) Systematic risk, because it cannot be eliminated by diversification
Unsystematic (specific) risk can be diversified away by holding a well-diversified portfolio, so investors are not rewarded for bearing it. Systematic (market) risk affects all companies and cannot be diversified away. The CAPM measures systematic risk by beta and sets the required return accordingly.