Question 4 OR (b)
NI and NOI approaches: values, overall cost and equity rate
11 marks
- Time to write
- About 22 minutes
From an older CBCS paper
Question
Question 4 OR (b) · 11 marksCompany X and Company Y belong to the same risk class, and are alike in all respects, except that Y uses debt of ₹ 2,40,000 carrying an interest of 12%, while X is an all equity firm. Each company earns a return of 20% on its assets of ₹ 5,40,000.
Under the net income approach, taking the cost of equity as 15%, calculate the value of each of the two companies and their overall cost of capital.
Using the NOI approach, taking the overall cost of capital as 15%, calculate the value of each of the two companies and the equity capitalization rate.
Compare the results, and comment on the differences. 11
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
- CompareCompare in a table, basis by basis.
- and comment onThe comment carries marks too: say what the figures show, in two or three lines.
- 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 interest 1 mark 2 min
- 2 NI: values and overall cost of capital 4 marks 7 min
- 3 NOI: values and equity capitalisation rate 4 marks 7 min
- 4 Comparison 2 marks 4 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 22 minutes for 11 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.
EBIT of each company = 20% × 5,40,000 = ₹1,08,000. Y's interest = 12% × 2,40,000 = ₹28,800. No taxes are given.
(i) Net Income approach (ke = 15%). The costs of debt and equity stay constant, so debt, being cheaper, lowers the overall cost of capital and raises the value of the firm.
| Particulars (₹) | X | Y |
|---|---|---|
| EBIT | 1,08,000 | 1,08,000 |
| Less: interest | Nil | 28,800 |
| Earnings for equity | 1,08,000 | 79,200 |
| Value of equity (÷ 0.15) | 7,20,000 | 5,28,000 |
| Value of debt | Nil | 2,40,000 |
| Value of the company | 7,20,000 | 7,68,000 |
| Overall cost of capital (EBIT ÷ value) | 15.00% | 14.06% |
(ii) Net Operating Income approach (ko = 15%). The firm is valued as a whole at the overall rate, whatever its capital structure; the cost of equity rises with debt.
| Particulars (₹) | X | Y |
|---|---|---|
| EBIT | 1,08,000 | 1,08,000 |
| Value of the company (÷ 0.15) | 7,20,000 | 7,20,000 |
| Less: value of debt | Nil | 2,40,000 |
| Value of equity | 7,20,000 | 4,80,000 |
| Equity capitalisation rate (earnings for equity ÷ equity) | 15.00% | 16.50% |
(iii) Comparison. Under NI, debt raises Y's value to ₹7,68,000 and lowers its overall cost of capital to 14.06%, because ke stays at 15% while 12% debt replaces equity. Under NOI the two companies are worth the same ₹7,20,000 and the overall cost stays at 15%: Y's shareholders, bearing financial risk, demand 16.50%, which exactly offsets the cheaper debt. The difference lies entirely in the assumption about how ke responds to leverage.
Where the 11 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | EBIT and interest | 1 |
| 2 | NI: values and overall cost of capital | 4 |
| 3 | NOI: values and equity capitalisation rate | 4 |
| 4 | Comparison | 2 |
| Total | 11 |
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