Question 3 (b)
Net operating income approach: value and cost of equity
9 marks
- Time to write
- About 18 minutes
Question
Question 3 (b) · 9 marksA company's expected annual net operating income is ₹6,00,000. It has ₹36,00,000 of 10% debentures. The overall, cost of capital is 12.5%. According to the NOI approach, calculate the value of the firm and the cost of equity.
If the company raises its debt from ₹36,00,000 to ₹42,00,000, calculate the value of firm and cost of equity. Also comment, as per NOI approach, on the value of the firm and cost of equity.
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).
What the paper leaves open
"The overall, cost of capital" is printed with a stray comma and kept.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Value and cost of equity lakh debt 3 marks 5 min
- 2 Value and cost of equity lakh debt 3 marks 5 min
- 3 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.
Under the NOI approach the market capitalises the firm's operating income as a whole at a constant overall rate (ko), so V = NOI ÷ ko whatever the debt; equity is the residual, E = V − D, and ke = (NOI − interest) ÷ E.
| ₹ | Debt ₹36,00,000 | Debt ₹42,00,000 |
|---|---|---|
| Net operating income | 6,00,000 | 6,00,000 |
| Overall cost of capital (ko) | 12.5% | 12.5% |
| Value of the firm (NOI ÷ ko) | 48,00,000 | 48,00,000 |
| Less: debt | 36,00,000 | 42,00,000 |
| Value of equity | 12,00,000 | 6,00,000 |
| Interest @ 10% | 3,60,000 | 4,20,000 |
| Earnings for equity (NOI − interest) | 2,40,000 | 1,80,000 |
| Cost of equity (ke) | 20% | 30% |
Comment. Raising debt from ₹36 lakh to ₹42 lakh leaves the value of the firm unchanged at ₹48,00,000 and ko at 12.5%, but raises the cost of equity from 20% to 30%. The extra financial risk borne by shareholders raises ke by exactly enough to offset the advantage of the cheaper debt, so, under the NOI approach, capital structure does not affect the value of the firm and there is no optimum structure.
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Value and cost of equity at ₹36 lakh debt | 3 |
| 2 | Value and cost of equity at ₹42 lakh debt | 3 |
| 3 | Comment | 3 |
| Total | 9 |
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