Question 5 (a)
Weighted average cost of capital at market-value weights
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 5 (a) · 10 marksFrom the following information provided by MNP ltd., calculate the weighted average cost of capital with market value weights. The present capital structure of MNP ltd, at book value, is:
| Debentures (₹ 100 per debenture) | 12,50,000 |
| Preference Shares (₹ 100 per share) | 6,40,000 |
| Equity Shares (₹ 10 per share) | 24,80,000 |
| Retained Earnings | 6,40,000 |
All these securities are traded in capital markets. Recent prices are: debentures @ ₹105, preference shares @ ₹125 and equity shares @ ₹30. The external financing opportunities anticipated are:
₹100 per debentures redeemable at par: 25 year maturity, 9% coupon rate, 3% floating costs, selling price ₹100.
₹100 preference shares redeemable at par: 12-year maturity, 11% dividend rate, 6% floating costs, selling price ₹100.
Equity shares: ₹3 per share floating costs, sale price ₹30.
In addition, the equity shares are expected to pay a dividend of ₹3 per share at the end of the year, the anticipated growth rate in dividends is 6%, and the company has the practice of distributing all its earnings as dividends. The corporate tax rate is 35%.
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
- calculateFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
Retained earnings have no market price of their own, so the market value of the equity shares is taken to include them (the cost of retained earnings is the cost of equity). The weights use the recent market prices; the costs use the anticipated financing terms. "Floating costs" is read as flotation costs.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 After-tax cost of the redeemable debentures 2½ marks 4 min
- 2 Cost of the redeemable preference shares 2 marks 4 min
- 3 Cost of new equity with flotation cost and growth 2 marks 4 min
- 4 Market-value weights, with the treatment of retained earnings 2 marks 3 min
- 5 WACC 1½ marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 20 minutes for 10 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.
Specific costs (on the anticipated financing terms, paper note). Net proceeds are the selling price less the flotation cost.
- 9% debentures, redeemable at par after 25 years. Net proceeds (NP) = 100 − 3% of 100 = ₹97; redemption value (RV) = ₹100. Before-tax cost Kdb = [I + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2], and the after-tax cost is Kdb (1 − t). Kdb = [9 + (100 − 97) ÷ 25] ÷ [(100 + 97) ÷ 2] = 9.12 ÷ 98.5 = 9.2589%; Kd = 9.2589% × (1 − 0.35) = 6.0183%.
- 11% preference shares, redeemable at par after 12 years. NP = 100 − 6% of 100 = ₹94. Kp = [D + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2], and no tax adjustment is made, since a preference dividend is not deductible for tax. Kp = [11 + (100 − 94) ÷ 12] ÷ [(100 + 94) ÷ 2] = 11.5 ÷ 97 = 11.8557%.
- Equity shares (new issue, constant growth). Ke = D1 ÷ (P0 − F) + g, where F is the flotation cost per share. Ke = 3 ÷ (30 − 3) + 0.06 = 0.1111 + 0.06 = 17.1111%. The company distributes all its earnings, so further equity comes from a fresh issue, which bears the flotation cost.
Weights. Market values are the number of securities at their recent prices: 12,50,000 ÷ 100 = 12,500 debentures, 6,40,000 ÷ 100 = 6,400 preference shares and 24,80,000 ÷ 10 = 2,48,000 equity shares. Retained earnings have no market value of their own: the shares' market value already reflects the retained earnings as well as the paid-up capital, so the equity weight is the shares' market value, and the retained earnings take the cost of equity (paper note). Splitting that value between share capital and retained earnings in proportion to their book values (24,80,000: 6,40,000) would not change the result here, because both parts carry the same 17.1111%.
Weighted average cost of capital (market-value weights)
| Source | Market value (₹) | Weight | Cost after tax | Market value × cost (₹) |
|---|---|---|---|---|
| 9% Debentures (12,500 × ₹105) | 13,12,500 | 0.1374 | 6.0183% | 78,990.19 |
| 11% Preference shares (6,400 × ₹125) | 8,00,000 | 0.0837 | 11.8557% | 94,845.60 |
| Equity shares incl. retained earnings (2,48,000 × ₹30) | 74,40,000 | 0.7789 | 17.1111% | 12,73,065.84 |
| Total | 95,52,500 | 1.0000 | 14,46,901.63 |
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | After-tax cost of the redeemable debentures | 2.5 |
| 2 | Cost of the redeemable preference shares | 2 |
| 3 | Cost of new equity with flotation cost and growth | 2 |
| 4 | Market-value weights, with the treatment of retained earnings | 2 |
| 5 | WACC | 1.5 |
| Total | 10 |
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