Question 4 (b)
Net Income and Net Operating Income approaches: value of two firms
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 4 (b) · 10 marksL Ltd. and U Ltd. are alike in all respects, except that Ltd has issued 10% debentures of ₹10,80,000, whereas U Ltd.'s capital structure has only equity shares. Both firms have an operating profit of ₹3,60,000. Assume that the capitalization rate for all equity firms is 15%.
Using the Net Income Approach, compute the value of the two firms.
Using the Net Operating Income Approach, compute the value of the two firms.
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
- Assume that the capitalization rate for…The paper fixes this: use it as given, and say so in your answer.
- computeFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
- "Ltd has issued" is read as L Ltd.
- Under the Net Income approach the 15% equity capitalisation rate is applied to both firms' equity earnings; under the Net Operating Income approach 15% is the overall capitalisation rate for both firms.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 NI approach: equity earnings, value of equity and of each firm 5 marks 9 min
- 2 NOI approach: value of each firm, value and cost of equity 4 marks 8 min
- 3 Conclusion 1 mark 1 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 3's one-line conclusion, whatever happens: never leave the figures without it.
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.
Interest of L Ltd. = 10% of 10,80,000 = ₹1,08,000. No taxes. "Ltd has issued" is read as L Ltd. (paper note).
(i) Net Income approach. The costs of debt and equity stay constant whatever the leverage, so more (cheaper) debt lowers the overall cost of capital and raises the value of the firm. The equity earnings are capitalised at 15% and debt is added at its value.
| Particulars (₹) | L Ltd. | U Ltd. |
|---|---|---|
| Operating profit (EBIT) | 3,60,000 | 3,60,000 |
| Less: interest | 1,08,000 | Nil |
| Earnings for equity shareholders | 2,52,000 | 3,60,000 |
| Equity capitalisation rate | 15% | 15% |
| Market value of equity (earnings ÷ 0.15) | 16,80,000 | 24,00,000 |
| Market value of debt | 10,80,000 | Nil |
| Value of the firm | 27,60,000 | 24,00,000 |
| Overall cost of capital (EBIT ÷ value) | 13.04% | 15% |
(ii) Net Operating Income approach. The market capitalises the firm as a whole: the overall cost of capital stays constant whatever the debt–equity mix, so the value of the firm does not change with leverage. The cheaper debt is exactly offset by a higher cost of equity. EBIT is capitalised at the 15% overall rate.
| Particulars (₹) | L Ltd. | U Ltd. |
|---|---|---|
| Operating profit (EBIT) | 3,60,000 | 3,60,000 |
| Overall capitalisation rate | 15% | 15% |
| Value of the firm (EBIT ÷ 0.15) | 24,00,000 | 24,00,000 |
| Less: market value of debt | 10,80,000 | Nil |
| Market value of equity | 13,20,000 | 24,00,000 |
| Implied cost of equity [(EBIT − interest) ÷ equity] | 19.09% | 15% |
Conclusion. Under the NI approach the levered firm is worth more (₹27,60,000 against ₹24,00,000). Under the NOI approach both firms are worth ₹24,00,000, and L Ltd.'s cost of equity rises to 19.09%, which keeps its overall cost of capital at 15%.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | NI approach: equity earnings, value of equity and of each firm | 5 |
| 2 | NOI approach: value of each firm, value and cost of equity | 4 |
| 3 | Conclusion | 1 |
| Total | 10 |
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