Question 1 (c)
MM with corporate tax: value of the two firms
9 marks
- Time to write
- About 18 minutes
Question
Question 1 (c) · 9 marksFirms X and Y are identical in every aspect apart from their levels of leverage. Firm X has 9% debentures totalling ₹24,00,000, an operating profit of ₹7,20,000, and a tax rate of 30%. The overall cost of capital of Firm Y is 10%. Using the Modigliani-Miller (MM) approach, calculate the value of each firm. Also determine, for Firm X, the equity capitalization rate and the overall 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
- 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 Value of the unlevered firm Y 3 marks 5 min
- 2 Value of the levered firm X Vu + tD 3 marks 5 min
- 3 Equity capitalisation rate and overall cost of capital of X 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.
With corporate tax, MM hold that debt adds value because interest is deductible for tax. The value of a levered firm is the value of an unlevered firm plus the tax benefit of debt, VL = Vu + tD, where the unlevered firm is valued at NOI(1 − t) ÷ ke.
1. Value of Firm Y (unlevered)
Vu = 7,20,000 × (1 − 0.30) ÷ 0.10 = 5,04,000 ÷ 0.10 = ₹50,40,000.
| ₹ | |
|---|---|
| Value of the unlevered firm (Vu) | 50,40,000 |
| Add: tax advantage of debt (tD = 30% × 24,00,000) | 7,20,000 |
| Value of Firm X (VL) | 57,60,000 |
| Less: value of debt | 24,00,000 |
| Value of X's equity (E) | 33,60,000 |
3. Equity capitalisation rate and overall cost of capital of Firm X
| ₹ | |
|---|---|
| EBIT | 7,20,000 |
| Less: interest (9% × 24,00,000) | 2,16,000 |
| Profit before tax | 5,04,000 |
| Less: tax @ 30% | 1,51,200 |
| Earnings for equity | 3,52,800 |
- Equity capitalisation rate, ke = 3,52,800 ÷ 33,60,000 = 10.50%.
- Overall cost of capital, ko = EBIT(1 − t) ÷ V = 5,04,000 ÷ 57,60,000 = 8.75%. This agrees with MM's formula for a levered firm, ko = keu(1 − tL) with L = D ÷ V: 10% × (1 − 0.30 × 24,00,000 ÷ 57,60,000) = 10% × 0.875 = 8.75%; and with the weighted average 9% × (1 − 0.30) × 24,00,000 ÷ 57,60,000 + 10.50% × 33,60,000 ÷ 57,60,000 = 2.625% + 6.125% = 8.75%.
Firm X, using debt, is worth ₹7,20,000 more than Y and has a lower overall cost of capital (8.75% against 10%), because of the tax saved on interest.
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Value of the unlevered firm Y | 3 |
| 2 | Value of the levered firm X (Vu + tD) | 3 |
| 3 | Equity capitalisation rate and overall cost of capital of X | 3 |
| Total | 9 |
Report a problemopens an email to admin@getkunji.com with the question ID7357-Q1calready filled in.