Question 1 OR (c)
Net income and net operating income approaches
9 marks
- Time to write
- About 18 minutes
Question
Question 1 OR (c) · 9 marksCompany X and Company Y fall in the same risk class and are identical in every respect except that Y uses debt of ₹7,20,000 carrying interest at 15%, whereas X is an all-equity firm. Each company earns a return of 20% on its assets of ₹12,00,000.
Taking the cost of equity as 18%, calculate the value of both companies and their overall cost of capital according to the net income approach.
Calculate the value of both companies and the equity capitalization rate using the Net Operating Income approach, with the overall cost of capital taken as 18%.
Compare the results and comment on how they differ.
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
- Calculate…Compare…Two asks in one question: answer both.
- 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 (i) NI approach: values and overall cost of capital 3 marks 5 min
- 2 (ii) NOI approach: values and equity capitalisation rates 3 marks 5 min
- 3 (iii) Comparison and comment 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 18 minutes for 9 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% × ₹12,00,000 = ₹2,40,000. Interest of Y = 15% × ₹7,20,000 = ₹1,08,000. No taxes are given, so none are taken.
(i) Net income (NI) approach (ke = 18% and kd = 15% stay constant whatever the debt, so the cheaper debt lowers the overall cost of capital)
| ₹ | X | Y |
|---|---|---|
| EBIT | 2,40,000 | 2,40,000 |
| Less: interest | — | 1,08,000 |
| Net income for equity (NI) | 2,40,000 | 1,32,000 |
| Equity capitalisation rate (ke) | 18% | 18% |
| Value of equity (E = NI ÷ ke) | 13,33,333.33 | 7,33,333.33 |
| Value of debt (D) | — | 7,20,000 |
| Value of the firm (V = E + D) | 13,33,333.33 | 14,53,333.33 |
| Overall cost of capital (ko = EBIT ÷ V) | 18.00% | 16.51% |
(ii) Net operating income (NOI) approach (the market capitalises EBIT at a constant ko of 18%; equity is the residual)
| ₹ | X | Y |
|---|---|---|
| EBIT | 2,40,000 | 2,40,000 |
| Overall capitalisation rate (ko) | 18% | 18% |
| Value of the firm (V = EBIT ÷ ko) | 13,33,333.33 | 13,33,333.33 |
| Less: value of debt | — | 7,20,000 |
| Value of equity (E) | 13,33,333.33 | 6,13,333.33 |
| Net income for equity | 2,40,000 | 1,32,000 |
| Equity capitalisation rate (ke = NI ÷ E) | 18.00% | 21.52% |
- Under NI, the levered firm Y is worth more (₹14,53,333.33 against ₹13,33,333.33) and has the lower overall cost of capital (16.51% against 18%). Debt, being cheaper than equity, lowers ko and raises value, because ke is assumed not to rise with leverage.
- Under NOI, both firms are worth the same ₹13,33,333.33 and ko is 18% for both: capital structure is irrelevant. The advantage of cheaper debt is exactly offset by the rise in Y's cost of equity, from 18% to 21.52%, as its shareholders bear more financial risk.
- The difference lies wholly in the assumption about ke: constant under NI, rising with debt under NOI.
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | (i) NI approach: values and overall cost of capital | 3 |
| 2 | (ii) NOI approach: values and equity capitalisation rates | 3 |
| 3 | (iii) Comparison and comment | 3 |
| Total | 9 |
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