Question 1 OR (b)
Weighted average cost of capital: book-value and market-value weights
12 marks
- Time to write
- About 24 minutes
- Topic
- Cost of capital
Question
Question 1 OR (b) · 12 marksThe capital structure of Saransh Ltd. is as follows:
| Sources | Amount (₹) | Specific c/c (cost of capital) |
|---|---|---|
| Equity share capital (3,00,000 shares of ₹ 10 each) | 30,00,000 | 11% |
| Preference share capital (75,000 shares of ₹ 10 each) | 7,50,000 | 8% |
| Retained earnings | 15,00,000 | 11% |
| 7.5% Debenture of ₹ 1000 each | 22,50,000 | 4.5% |
Currently the debentures are being traded at 94%, the Preference shares at par, while the Equity shares are at ₹13 per share. 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).
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Method and book-value weights table 4 marks 7 min
- 2 WACC on book-value weights 1 mark 2 min
- 3 Market values: debentures at 94%, preference at par, equity apportioned to retained earnings 3 marks 5 min
- 4 Market-value weights table and WACC 3 marks 5 min
- 5 Comment on the difference 1 mark 1 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 24 minutes for 12 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.
Method. The weighted average cost of capital is Kw = ΣXW ÷ ΣW: each source's specific cost (X) is weighted by its amount (W), and the total is divided by the total amount. The weights may be book values or market values, and the two give different results. The specific costs are given by the question, so only the weights change between the two calculations.
| Source | Amount (₹) | Weight | Specific cost | Weighted cost (₹) |
|---|---|---|---|---|
| Equity share capital | 30,00,000 | 0.40 | 11% | 3,30,000 |
| Preference share capital | 7,50,000 | 0.10 | 8% | 60,000 |
| Retained earnings | 15,00,000 | 0.20 | 11% | 1,65,000 |
| 7.5% Debentures | 22,50,000 | 0.30 | 4.5% | 1,01,250 |
| Total | 75,00,000 | 1.00 | 6,56,250 |
WACC (book) = 6,56,250 ÷ 75,00,000 = 8.75%.
- Debentures are traded at 94%: 22,50,000 × 94% = ₹21,15,000.
- Preference shares are at par: ₹7,50,000.
- Equity shares: 3,00,000 shares × ₹13 = ₹39,00,000. There is no separate market value for retained earnings: the market value of the equity shares covers both the paid-up capital and the retained earnings. So it is apportioned between them in the ratio of their book values, 30,00,000: 15,00,000 = 2: 1. That gives ₹26,00,000 (equity share capital) and ₹13,00,000 (retained earnings).
| Source | Market value (₹) | Weight | Specific cost | Weighted cost (₹) |
|---|---|---|---|---|
| Equity share capital | 26,00,000 | 0.3843 | 11% | 2,86,000 |
| Preference share capital | 7,50,000 | 0.1109 | 8% | 60,000 |
| Retained earnings | 13,00,000 | 0.1922 | 11% | 1,43,000 |
| 7.5% Debentures | 21,15,000 | 0.3126 | 4.5% | 95,175 |
| Total | 67,65,000 | 1.0000 | 5,84,175 |
WACC (market) = 5,84,175 ÷ 67,65,000 = 8.64% (8.635%).
Comment. Market-value weights give a slightly lower WACC here. The costliest funds, equity capital and retained earnings at 11%, have a market value (₹39,00,000) below their book value (₹45,00,000), so their weight falls from 0.60 to 0.5765; the debentures' weight rises from 0.30 to 0.3126. Because equity capital and retained earnings both cost 11% here, taking the whole ₹39,00,000 at 11% without apportioning gives the same 8.64%. Market-value weights reflect current conditions and the true value to investors; book-value weights are easier to obtain and more stable.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Method and book-value weights table | 4 |
| 2 | WACC on book-value weights: 8.75% | 1 |
| 3 | Market values: debentures at 94%, preference at par, equity at ₹13 apportioned to retained earnings | 3 |
| 4 | Market-value weights table and WACC 8.64% | 3 |
| 5 | Comment on the difference | 1 |
| Total | 12 |
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