Question 3
Book versus market value weights; WACC both ways
18.75 marks
- Time to write
- About 38 minutes
From an older CBCS paper
Question
Question 3 · 18.75 marksQ3. In measuring the cost of capital, how do book value weights differ from market value weights?
LMN Ltd.'s capital structure is as follows:
| Particulars | Amount (Rs.) |
|---|---|
| Equity Share Capital (Rs.10 per share face value) | 24,00,000 |
| 10% Preference Share Capital (Rs.100 per share face value) | 4,80,000 |
| 12% Debentures (Rs.100 per debenture face value) | 19,20,000 |
| Total | 48,00,000 |
Each of these securities is traded in the capital market, at these recent prices: Debentures, Rs.108 a debenture; Preference share, Rs.125 a share; Equity shares, Rs.50 a share. A year-end dividend of Rs. 5 per share is expected to be paid by the company, and to grow at 8% p.a. It pays income tax @ 35%. Using book value weights and market value weights, calculate the company's cost pf 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
- differSet the differences out in a table, basis by basis, not as two separate essays.
- calculateFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
No mark is printed for the question; the paper asks for any four of six, equal marks. "Cost pf capital" is kept as printed. The debentures and preference shares have no redemption terms and are treated as irredeemable.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Book versus market weights 6 marks 11 min
- 2 Specific costs 4 marks 7 min
- 3 WACC at book value weights 4 marks 7 min
- 4 WACC at market value weights 4.8 marks 9 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 38 minutes for 18.75 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.
Book value weights versus market value weights
The WACC weights each specific cost by the source's share of total funds; the weights may be book values or market values, and the WACC differs if they differ.
| Point | Book value weights | Market value weights |
|---|---|---|
| Basis | Amounts in the balance sheet (historical) | Current market prices of the securities |
| Equity | Share capital plus reserves and retained earnings | Market value of the shares, which already includes retained earnings |
| Reflects | The past; not current values or prospects | Current conditions and the investors' true value |
| Availability | Readily available, stable | Hard to determine; prices fluctuate |
| Consistency | Matches target capital structures set in book terms | Matches specific costs computed from market prices |
| Effect | Usually a lower weight for equity | Usually a higher weight for equity, hence a higher WACC |
Cost of capital of LMN Ltd.
Specific costs. No redemption terms are given, so the debentures and preference shares are treated as irredeemable (paper note); costs are measured on current market prices.
- Equity: Ke = D1 ÷ P0 + g = 5 ÷ 50 + 8% = 18%.
- 10% preference shares: Kp = D ÷ P = 10 ÷ 125 = 8%.
- 12% debentures: Kd = I(1 − t) ÷ P = 12 × 0.65 ÷ 108 = 7.22%.
| Source | Book value (₹) | Cost | Weighted cost (₹) |
|---|---|---|---|
| Equity share capital | 24,00,000 | 18.00% | 4,32,000 |
| 10% Preference shares | 4,80,000 | 8.00% | 38,400 |
| 12% Debentures | 19,20,000 | 7.22% | 1,38,666.67 |
| Total | 48,00,000 | 6,09,066.67 |
WACC (book) = 6,09,066.67 ÷ 48,00,000 = 12.69%.
(ii) Market value weights. Equity 2,40,000 shares × ₹50; preference 4,800 shares × ₹125; debentures 19,200 × ₹108.
| Source | Market value (₹) | Cost | Weighted cost (₹) |
|---|---|---|---|
| Equity share capital | 1,20,00,000 | 18.00% | 21,60,000 |
| 10% Preference shares | 6,00,000 | 8.00% | 48,000 |
| 12% Debentures | 20,73,600 | 7.22% | 1,49,760 |
| Total | 1,46,73,600 | 23,57,760 |
WACC (market) = 23,57,760 ÷ 1,46,73,600 = 16.07%.
The market-weighted cost is much higher because the equity, the costliest source, is worth five times its book value.
Where the 18.75 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Book versus market weights | 6 |
| 2 | Specific costs | 4 |
| 3 | WACC at book value weights | 4 |
| 4 | WACC at market value weights | 4.75 |
| Total | 18.75 |
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