Question 3 (b)
Net income approach: values and overall cost of capital
7 marks
- Time to write
- About 14 minutes
From an older CBCS paper
Question
Question 3 (b) · 7 marksX Ltd. and Y Ltd. belong to the same risk class, and are alike in all respects, except that company X Ltd uses debt and company Y Ltd doesn't use debt. X Ltd., the levered firm, has ₹10,80,000 Debentures carrying interest at a 10% rate. Both the firms earn a 20% operating profit on total assets amounting to ₹15 lakhs. The equity capitalization rate (ke) is 15%. Using the Net Income (NI) Approach, you are required to calculate the value of the firms X Ltd and Y Ltd. Also, calculate the overall cost of capital (ko) of each of X Ltd and Y Ltd.
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).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 EBIT and equity earnings 2 marks 3 min
- 2 Values of the two firms 3 marks 5 min
- 3 Overall cost of capital of each 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 14 minutes for 7 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.
NI approach. The cost of equity (15%) and the cost of debt (10%) stay constant whatever the leverage; the value of equity is the equity earnings capitalised at ke, and the value of the firm is equity plus debt. EBIT for each firm = 20% × ₹15,00,000 = ₹3,00,000.
| Particulars (₹) | X Ltd. (levered) | Y Ltd. (unlevered) |
|---|---|---|
| EBIT | 3,00,000 | 3,00,000 |
| Less: interest @ 10% on 10,80,000 | 1,08,000 | — |
| Earnings for equity | 1,92,000 | 3,00,000 |
| Equity capitalisation rate (ke) | 15% | 15% |
| Value of equity (S) | 12,80,000 | 20,00,000 |
| Value of debt (D) | 10,80,000 | — |
| Value of the firm (V) | 23,60,000 | 20,00,000 |
| Overall cost of capital (ko = EBIT ÷ V) | 12.71% | 15.00% |
Under the NI approach the levered firm X is worth ₹3,60,000 more and has the lower overall cost of capital, because cheaper debt replaces part of the equity while ke stays constant; the overall cost of capital is EBIT ÷ value of the firm.
Where the 7 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | EBIT and equity earnings | 2 |
| 2 | Values of the two firms | 3 |
| 3 | Overall cost of capital of each | 2 |
| Total | 7 |
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