Question 4 (b)
MM with corporate tax: values and WACC of U and L
7 marks
- Time to write
- About 14 minutes
From an older CBCS paper
Question
Question 4 (b) · 7 marksCompanies U and L are alike in every respect, except that the former uses no debt in its capital structure, whereas the latter employs Rs. 7,20,000/- @ 15% debt. Assuming that (i) all the assumptions of the Modigliani-Miller (MM) approach are met, (ii) the rate of corporate tax is 30%, (iii) the EBIT is Rs. 2,40,000/-, and (iv) the unlevered firm's equity capitalization is 20%, what will be value of the two firms, U and L? Also determine, for each firm, the weighted average cost of capital.
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
- Are…?Determine…Two asks in one question: answer both.
- Assuming that (i) all the assumptions…The paper fixes this: use it as given, and say so in your answer.
- determineFormula 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 Value of U 1½ marks 3 min
- 2 Value of L with the tax shield 2 marks 3 min
- 3 Costs of equity 1½ marks 3 min
- 4 WACC of each firm 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 14 minutes for 7 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.
MM with corporate tax. Interest is tax-deductible, so a levered firm is worth more than an unlevered one by the present value of the tax shield on debt: VL = VU + tD, with VU = EBIT(1 − t) ÷ ke. Tax 30%; EBIT ₹2,40,000; U's equity capitalisation rate 20%; L's debt ₹7,20,000 at 15%.
Value of U = EBIT(1 − t) ÷ ke = 2,40,000 × 0.70 ÷ 0.20 = ₹8,40,000.
Value of L = VU + tD = 8,40,000 + 0.30 × 7,20,000 = 8,40,000 + 2,16,000 = ₹10,56,000.
Weighted average cost of capital
| Particulars (₹) | U | L |
|---|---|---|
| EBIT | 2,40,000 | 2,40,000 |
| Less: interest @ 15% | — | 1,08,000 |
| EBT | 2,40,000 | 1,32,000 |
| Less: tax @ 30% | 72,000 | 39,600 |
| Earnings for equity | 1,68,000 | 92,400 |
| Value of the firm | 8,40,000 | 10,56,000 |
| Value of debt | — | 7,20,000 |
| Value of equity | 8,40,000 | 3,36,000 |
| Cost of equity (earnings ÷ equity) | 20.00% | 27.50% |
- WACC of U = 20% (all equity).
- WACC of L = ke × S/V + kd(1 − t) × D/V = 27.50% × 3,36,000/10,56,000 + 10.50% × 7,20,000/10,56,000 = (92,400 + 75,600) ÷ 10,56,000 = 15.91%; equivalently EBIT(1 − t) ÷ VL = 1,68,000 ÷ 10,56,000.
With tax, debt lowers the WACC and raises the value of the firm, unlike MM without taxes.
Where the 7 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Value of U | 1.5 |
| 2 | Value of L with the tax shield | 2 |
| 3 | Costs of equity | 1.5 |
| 4 | WACC of each firm | 2 |
| Total | 7 |
Report a problemopens an email to admin@getkunji.com with the question ID318-Q4balready filled in.