Test 14: answer key

Question 1 · 2 marks · Cost of Capital · medium

Scenario. Royal Hospitality Ltd has 12% irredeemable debentures of face value ₹100 each with book value ₹8,00,000 and market price ₹96 per debenture. It has 10% preference shares of face value ₹100 each with book value ₹4,00,000 and market price ₹105 per share. Equity shares of face value ₹10 each have book value ₹12,00,000 and market price ₹42 per share. The next expected equity dividend is ₹4.20 per share and dividend growth is 6% p.a. Corporate tax is 30%. The company is examining cost of capital using book value and market value weights.

What is the post-tax cost of irredeemable debentures for Royal Hospitality Ltd based on current market price?

1. 8.40%
2. 8.75% (correct answer)
3. 12.00%
4. 10.00%

Answer: B — 8.75%

Working. Kd = I(1 - t)/NP = 12*(1 - 0.30)/96 = 8.4/96 = 0.0875 = 8.75%.

Explanation. The post-tax cost of irredeemable debentures is annual interest after tax divided by net proceeds or current market price. Interest is ₹12 per debenture and net proceeds are ₹96. Hence Kd = 12(1 - 0.30)/96 = 8.75%. Option a ignores the market price and uses face value. Option c ignores tax. Option d is an intermediate figure and not the post-tax market-price based cost.

Where it goes wrong. Students may use face value ₹100 instead of market price ₹96, or may forget the tax shield.

Authority. Chapter 4: Cost of Capital - Cost of Long-Term Debt

Question 2 · 2 marks · Cost of Capital · medium

What is the cost of equity of Royal Hospitality Ltd using the dividend growth model?

1. 16.00% (correct answer)
2. 10.00%
3. 15.00%
4. 12.00%

Answer: A — 16.00%

Working. Ke = 4.20/42 + 0.06 = 0.10 + 0.06 = 0.16 = 16.00%.

Explanation. Using the Gordon growth model, Ke = D1/P0 + g. D1 is ₹4.20, P0 is ₹42 and g is 6%. Thus Ke = 4.20/42 + 0.06 = 16.00%. Option b is the dividend yield only. Option c and option d are not supported by the data.

Where it goes wrong. Students may omit growth or may divide by face value ₹10 instead of market price ₹42.

Authority. Chapter 4: Cost of Capital - Cost of Equity Share Capital

Question 3 · 2 marks · Cost of Capital · hard

What is the approximate weighted average cost of capital using market value weights?

1. 13.42%
2. 15.20%
3. 14.67% (correct answer)
4. 12.95%

Answer: C — 14.67%

Working. MV debentures = 8,000*96 = 7,68,000; MV preference = 4,000*105 = 4,20,000; MV equity = 1,20,000*42 = 50,40,000; total = 62,28,000. WACC = 8.75*(7,68,000/62,28,000) + 9.5238*(4,20,000/62,28,000) + 16*(50,40,000/62,28,000) = 14.67% approximately.

Explanation. Market values are debentures 8,000 × 96 = ₹7,68,000; preference shares 4,000 × 105 = ₹4,20,000; equity shares 1,20,000 × 42 = ₹50,40,000; total ₹62,28,000. Costs are Kd 8.75%, Kp 10/105 = 9.5238% and Ke 16%. Weighted average is approximately 14.67%. Other options arise from incorrect weights or omitted tax adjustment.

Where it goes wrong. Students may use book value weights instead of market value weights or may use preference dividend divided by face value.

Authority. Chapter 4: Cost of Capital - Weighted Average Cost of Capital

Question 4 · 2 marks · Dividend Decisions · medium

Scenario. Beta Ltd has earnings per share of ₹10. Its cost of equity is 12%. The company is evaluating Gordon growth model outcomes under different internal rates of return and retention ratios. In each case the payout ratio is 40%, except where the question states otherwise. The relationship g = b*r is to be applied.

If Beta Ltd has internal rate of return r = 15%, cost of equity Ke = 12%, retention ratio b = 0.60 and EPS = ₹10, what is the Gordon model market price per share?

1. ₹100.00
2. ₹166.67
3. ₹80.00
4. ₹133.33 (correct answer)

Answer: D — ₹133.33

Working. P0 = 10*(1 - 0.60)/(0.12 - 0.60*0.15) = 4/(0.12 - 0.09) = 4/0.03 = 133.33.

Explanation. Under Gordon model P0 = E1(1 - b)/(Ke - br). Here E1 = ₹10, payout = 0.40, D1 = ₹4, br = 0.60 × 0.15 = 0.09. Therefore P0 = 4/(0.12 - 0.09) = ₹133.33. Option a ignores growth and retention. Option b uses an incorrect denominator. Option c is not supported.

Where it goes wrong. Students may use D0 or may compute br incorrectly as b + r or r only.

Authority. Chapter 8: Dividend Decisions - Gordon's Model

Question 5 · 2 marks · Dividend Decisions · medium

If Beta Ltd has r = 8%, Ke = 12%, retention ratio b = 0.60 and EPS = ₹10, what is the Gordon model market price per share?

1. ₹55.56 (correct answer)
2. ₹66.67
3. ₹50.00
4. ₹40.00

Answer: A — ₹55.56

Working. P0 = 10*(1 - 0.60)/(0.12 - 0.60*0.08) = 4/(0.12 - 0.048) = 4/0.072 = 55.56.

Explanation. P0 = E1(1 - b)/(Ke - br). D1 = 10 × 0.40 = ₹4; br = 0.60 × 0.08 = 0.048. Hence P0 = 4/(0.12 - 0.048) = ₹55.56. Option b uses an incorrect growth term. Option c and option d do not follow from the stated data.

Where it goes wrong. Students may wrongly use r = Ke or may ignore the retention ratio while computing growth.

Authority. Chapter 8: Dividend Decisions - Gordon's Model

Question 6 · 2 marks · Dividend Decisions · medium

Under Gordon model, which statement is correct when internal rate of return r equals cost of equity Ke?

1. The optimum payout ratio is zero.
2. Dividend policy does not affect market price. (correct answer)
3. The optimum payout ratio is zero only when r is less than Ke.
4. The company should adopt 100 percent payout when r exceeds Ke.

Answer: B — Dividend policy does not affect market price.

Working. Conceptual comparison: r greater than Ke favours zero payout; r less than Ke favours full payout; r equal to Ke makes dividend policy irrelevant to price.

Explanation. When r = Ke, the Gordon model shows that market price is not affected by retention or payout because the return available internally equals the shareholders required return. Option a is true for r greater than Ke. Option c misstates the r less than Ke case. Option d is not the Gordon conclusion.

Where it goes wrong. Students may confuse the r greater than Ke case with the r equal to Ke case.

Authority. Chapter 8: Dividend Decisions - Gordon's Model

Question 7 · 2 marks · Cost of Capital · medium

Scenario. Alpha Ltd has cost of equity of 15%. An investor faces personal tax at 20% on dividends and incurs brokerage of 2% on reinvestment. The finance team is computing cost of retained earnings using the adjustment for personal taxes and brokerage. The finance manager also wants to know the directional effect of an increase in personal tax rate on cost of retained earnings, other things remaining equal.

What is the cost of retained earnings if Ke is 15%, personal tax is 20% and brokerage is 2%?

1. 12.00%
2. 15.00%
3. 11.76% (correct answer)
4. 10.50%

Answer: C — 11.76%

Working. Kr = 15*(1 - 0.20)*(1 - 0.02) = 15*0.80*0.98 = 11.76%.

Explanation. Kr = Ke(1 - Tp)(1 - B). Substituting Ke = 15%, Tp = 20% and B = 2% gives 15 × 0.80 × 0.98 = 11.76%. Option a ignores brokerage. Option b ignores both personal tax and brokerage. Option d is not supported.

Where it goes wrong. Students may deduct tax and brokerage additively instead of multiplying the adjustment factors.

Authority. Chapter 4: Cost of Capital - Cost of Retained Earnings

Question 8 · 1 marks · Cost of Capital · medium

If personal tax rate on dividends increases, what happens to cost of retained earnings under the adjustment formula, other things remaining equal?

1. It increases.
2. It remains unchanged.
3. It becomes equal to Ke.
4. It decreases. (correct answer)

Answer: D — It decreases.

Working. Directional check: higher Tp reduces the factor (1 - Tp), so Kr decreases.

Explanation. The formula Kr = Ke(1 - Tp)(1 - B) shows that a higher personal tax rate reduces the after-tax opportunity cost of retained earnings. Therefore Kr decreases. Option a reverses the direction. Option b ignores the adjustment. Option c is not a necessary result.

Where it goes wrong. Students may confuse the tax shield on debt with the personal tax adjustment for retained earnings.

Authority. Chapter 4: Cost of Capital - Cost of Retained Earnings