Question 3
Is equity costless? NI approach for two firms with tax
18.75 marks
- Time to write
- About 38 minutes
From an older CBCS paper
Question
Question 3 · 18.75 marksQ3. All successful firms have equity as their predominant source of capital, and their market values are higher, always, than those of firms that use debt in the same line of business. Since debt has a cost while equity has no apparent cost, an increased amount of equity would reduce the cost of capital and so maximise the firm's value. Discuss: do you agree with these statements?
Two firms, X and Y, are implementing one and the same project, with debts of Rs. 600 lakhs and Rs 840 lakhs respectively. X's and Y's costs of debt are 12% and 15% respectively. The earnings before interest and taxes expected from these projects are Rs 360 Lakhs annually. Both firms are subject to income tax, levied at the rate of 35%.
For each firm, find the amount of earnings available to the shareholders.
On the basis of the NI approach, find out the value of equity, the value of the firm and the overall cost of capital of each of the two firms, when the costs of equity of firm X and firm Y are 22% and 24% respectively,
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
- do you agree…?A yes-or-no question: answer it in your first line, then explain why.
- findFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
No mark is printed for the question; the paper asks for any four of six, equal marks.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Discussion of the statements 7 marks 13 min
- 2 Earnings available to shareholders 4 marks 7 min
- 3 Values of equity and of the firms 4 marks 7 min
- 4 Overall cost of capital 3.8 marks 7 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 38 minutes for 18.75 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.
Part 1: I do not agree with the statements.
- Equity is not cost-free. The cost of equity is the minimum return the company must earn on the equity-financed part of its investments; it is not an out-of-pocket or legally binding payment, but equity is not cost-free capital. Because shareholders bear more risk than lenders, their required return is higher than the cost of debt.
- Debt is usually the cheaper source. Interest rates are lower than the returns equity investors require, and interest is tax-deductible; so, up to a point, replacing equity with debt lowers the overall cost of capital and raises the value of the firm. More equity therefore does not reduce the cost of capital.
- Successful firms are not always all-equity. Market value depends on earning power and risk. A firm that uses debt judiciously can be worth more than an unlevered one; the aim is an optimal mix at which the overall cost of capital is lowest and the value highest. Too much debt raises financial risk and the costs of both debt and equity, which is why many strong firms keep equity dominant; but that is a choice of risk, not a sign that equity is free.
Part 2: X and Y (₹ lakh), EBIT 360, tax 35%.
1. Earnings available to shareholders
| Particulars | Firm X | Firm Y |
|---|---|---|
| EBIT | 360.00 | 360.00 |
| Less: interest (12% × 600; 15% × 840) | 72.00 | 126.00 |
| EBT | 288.00 | 234.00 |
| Less: tax @ 35% | 100.80 | 81.90 |
| Earnings available to shareholders | 187.20 | 152.10 |
2. NI approach. The equity earnings are capitalised at the given cost of equity, and debt is added at its value.
| Particulars | Firm X | Firm Y |
|---|---|---|
| Cost of equity | 22% | 24% |
| Value of equity (earnings ÷ ke) | 850.91 | 633.75 |
| Value of debt | 600.00 | 840.00 |
| Value of the firm | 1,450.91 | 1,473.75 |
| Overall cost of capital, EBIT(1 − t) ÷ value | 16.13% | 15.88% |
The overall cost of capital is the after-tax weighted average: for X, (600 × 12% × 0.65 + 850.91 × 22%) ÷ 1,450.91 = 234 ÷ 1,450.91 = 16.13%, which equals EBIT(1 − t) ÷ value. (On EBIT before tax, EBIT ÷ value is 24.81% for X and 24.43% for Y.) Y, with more debt, has the higher value and the lower overall cost of capital, as the NI approach predicts.
Where the 18.75 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Discussion of the statements | 7 |
| 2 | Earnings available to shareholders | 4 |
| 3 | Values of equity and of the firms | 4 |
| 4 | Overall cost of capital | 3.75 |
| Total | 18.75 |
Report a problemopens an email to admin@getkunji.com with the question IDFMH21-Q3already filled in.