Question 2 (b)
WACC at book-value and market-value weights
11 marks
- Time to write
- About 22 minutes
From an older CBCS paper
Question
Question 2 (b) · 11 marksPQR Ltd.'s capital structure is as below:
| Equity share capital (face value Rs. 10 each) | Rs. 18,00,000 |
| 8% Debentures (face value Rs 100) | Rs. 4,80,000 |
| 12% Preference shares (face value Rs. 100) | Rs. 4,80,000 |
| 10% Term loan | Rs. 8,40,000 |
| Rs. 36,00,000 |
Last year the company paid a dividend of Rs. 3 per share, and dividends are expected to grow at 5% per annum. The company's applicable tax rate is 30%. All the securities are traded in the capital market, at these recent market prices:
| Equity Shares | Rs. 15 |
| Debentures | Rs. 80 |
| Preference Shares | Rs. 100 |
Using book value weights and market value weights, find out the weighted average cost of capital.
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- find outFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The term loan has no market quote; its book value is used in the market value weights. The equity dividend grows from last year's Rs. 3, so next year's dividend is Rs. 3 × 1.05. Debentures and preference shares are treated as irredeemable.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Cost of equity 2 marks 4 min
- 2 Costs of debentures, preference shares and term loan 3 marks 6 min
- 3 WACC at book-value weights 3 marks 5 min
- 4 WACC at market-value weights 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 22 minutes for 11 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
- Equity: Ke = D1 ÷ P0 + g, with D1 = D0(1 + g). D1 = 3 × 1.05 = ₹3.15 (paper note); Ke = 3.15 ÷ 15 + 0.05 = 0.21 + 0.05 = 26%.
- 8% debentures (irredeemable, paper note): Kd = I(1 − t) ÷ NP, interest being tax-deductible; at the market price of ₹80, Kd = 8 × 0.70 ÷ 80 = 7%.
- 12% preference shares (irredeemable): Kp = D ÷ NP, with no tax adjustment; Kp = 12 ÷ 100 = 12%.
- 10% term loan: 10% × (1 − 0.30) = 7%.
(a) WACC at book-value weights
| Source | Book value (₹) | After-tax cost | Book value × cost (₹) |
|---|---|---|---|
| Equity share capital | 18,00,000 | 26% | 4,68,000 |
| 8% Debentures | 4,80,000 | 7% | 33,600 |
| 12% Preference shares | 4,80,000 | 12% | 57,600 |
| 10% Term loan | 8,40,000 | 7% | 58,800 |
| Total | 36,00,000 | 6,18,000 |
WACC (book) = 6,18,000 ÷ 36,00,000 = 17.17%.
(b) WACC at market-value weights. Market value weights reflect current prices and are preferred. Market values: equity 1,80,000 shares × ₹15; debentures 4,800 × ₹80; preference shares 4,800 × ₹100; the term loan has no market quote and is taken at book value (paper note).
| Source | Market value (₹) | After-tax cost | Market value × cost (₹) |
|---|---|---|---|
| Equity shares (1,80,000 × 15) | 27,00,000 | 26% | 7,02,000 |
| 8% Debentures (4,800 × 80) | 3,84,000 | 7% | 26,880 |
| 12% Preference shares (4,800 × 100) | 4,80,000 | 12% | 57,600 |
| 10% Term loan (book value) | 8,40,000 | 7% | 58,800 |
| Total | 44,04,000 | 8,45,280 |
WACC (market) = 8,45,280 ÷ 44,04,000 = 19.19%.
The market-value WACC is higher because the costliest source, equity, trades well above its book value.
Where the 11 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Cost of equity | 2 |
| 2 | Costs of debentures, preference shares and term loan | 3 |
| 3 | WACC at book-value weights | 3 |
| 4 | WACC at market-value weights | 3 |
| Total | 11 |
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