Question 3 (b)
Value and overall cost of capital under the NOI approach
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 3 (b) · 8 marksTwo Companies are identical except that Kiran Ltd. has a debt of ₹12,00,000 at 9% whereas Mohan Ltd. has no debt in its capital structure. Kiran and Mohan have the same total assets, i.e. ₹24,00,000, on which each company earns 18% return. Using the net operating income (NOI) approach, find the value of each company and the overall cost of capital. The equity capitalisation rate for Mohan Ltd. is 12%. The tax rate is 25%.
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
- findFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
A tax rate is given, but the paper does not say whether the NOI value is struck before or after tax; the answer states its reading.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 EBIT, interest and the overall rate from the unlevered company 2 marks 4 min
- 2 Value of each company and of Kiran's equity 3 marks 5 min
- 3 Cost of equity and overall cost of capital of each company 2 marks 4 min
- 4 Conclusion 1 mark 1 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 4's one-line conclusion, whatever happens: never leave the figures without it.
Try it first. About 16 minutes for 8 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.
Approach. The net operating income (NOI) approach holds that the market capitalises the firm as a whole. Its overall cost of capital (ko) stays fixed whatever the proportions of debt and equity, which leaves the firm's value independent of its financing; the cost of equity climbs with debt by just enough to cancel the saving on cheaper debt. The value of the firm is the operating income divided by ko, equity is the firm's value less the debt, and the cost of equity is the equity earnings over that equity value; for an all-equity firm ke equals ko.
Inputs. Operating income (EBIT) of each company = 18% × ₹24,00,000 = ₹4,32,000. Mohan Ltd. has no debt, so its 12% equity capitalisation rate is the overall rate: ko = 12% for both companies. Interest of Kiran Ltd. = 9% × ₹12,00,000 = ₹1,08,000.
Our reading of the tax (paper note). The 25% tax is applied: the operating income after tax, EBIT × (1 − 0.25) = ₹3,24,000, is the income capitalised at 12%. This is the reading under which Mohan's own 12% rate, applied to its after-tax equity earnings, gives the same value as the NOI formula.
Value of each company (NOI approach)
| Particulars (₹) | Kiran Ltd. | Mohan Ltd. |
|---|---|---|
| EBIT (18% of 24,00,000) | 4,32,000 | 4,32,000 |
| Operating income after tax at 25% | 3,24,000 | 3,24,000 |
| Overall capitalisation rate (ko) | 12% | 12% |
| Value of the company (3,24,000 ÷ 0.12) | 27,00,000 | 27,00,000 |
| Less: debt | 12,00,000 | Nil |
| Value of equity | 15,00,000 | 27,00,000 |
Cost of equity and overall cost of capital
| Particulars (₹) | Kiran Ltd. | Mohan Ltd. |
|---|---|---|
| EBIT | 4,32,000 | 4,32,000 |
| Less: interest at 9% | 1,08,000 | Nil |
| Profit before tax | 3,24,000 | 4,32,000 |
| Less: tax at 25% | 81,000 | 1,08,000 |
| Earnings for equity | 2,43,000 | 3,24,000 |
| Cost of equity (earnings ÷ value of equity) | 16.2% | 12% |
Overall cost of capital of Kiran Ltd., weighted by the values above (cost of debt after tax = 9% × 0.75 = 6.75%):
| Source | Value (₹) | Weight | Cost | Weighted cost |
|---|---|---|---|---|
| Debt | 12,00,000 | 12/27 | 6.75% | 3% |
| Equity | 15,00,000 | 15/27 | 16.2% | 9% |
| Total | 27,00,000 | 12% |
Mohan Ltd., all equity: ko = ke = 12%.
Conclusion. Under the NOI approach both companies are worth ₹27,00,000 and both have an overall cost of capital of 12%. Kiran's debt does not raise its value: the benefit of the cheaper 9% debt is cancelled by the rise in its cost of equity from 12% to 16.2%.
The other reading (NOI value struck before tax). If the tax is ignored and EBIT itself is capitalised at 12%:
| Particulars | Kiran Ltd. | Mohan Ltd. |
|---|---|---|
| Value of the company (4,32,000 ÷ 0.12), ₹ | 36,00,000 | 36,00,000 |
| Value of equity, ₹ | 24,00,000 | 36,00,000 |
| Cost of equity [(4,32,000 − 1,08,000) ÷ 24,00,000] | 13.5% | 12% |
| Overall cost of capital | 12% | 12% |
The conclusion is the same: equal values and the same 12% overall cost. (A model that lets the tax saving on interest add value, as Modigliani and Miller's 1963 model with taxes does, would instead put Kiran above Mohan by 25% × ₹12,00,000 = ₹3,00,000; the question asks for the NOI approach, which does not.)
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | EBIT, interest and the overall rate from the unlevered company | 2 |
| 2 | Value of each company and of Kiran's equity | 3 |
| 3 | Cost of equity and overall cost of capital of each company | 2 |
| 4 | Conclusion | 1 |
| Total | 8 |
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