Question 3 (a)
MM with tax: value and WACC of firms U and L
9 marks
- Time to write
- About 18 minutes
Question
Question 3 (a) · 9 marksCompanies U & L are alike in every respect, except that the former uses no debt in its capital structure, while the later employees ₹12,00,000 of 8% debt. Assuming that all the assumptions of the Modigliani Miller approach are met, the corporate tax rate is 30%, EBIT is ₹4,80,000, and the equity capitalization rate of the unlevered firm is 20%. What will the value of the firms, U & L, be? Also determine the weighted average cost of capital of both firms?
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
- What…?Determine…?Two asks in one question: answer both.
- Assuming that all the assumptions of…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).
What the paper leaves open
"The later employees" is read as "the latter employs".
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Value of U 3 marks 5 min
- 2 Value of L 3 marks 5 min
- 3 WACC of both firms 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: VL = Vu + tD, where the unlevered firm is valued at EBIT(1 − t) ÷ ke(u).
Value of U (unlevered): Vu = 4,80,000 × (1 − 0.30) ÷ 0.20 = 3,36,000 ÷ 0.20 = ₹16,80,000.
| ₹ | |
|---|---|
| Value of the unlevered firm (Vu) | 16,80,000 |
| Add: tax advantage of debt (30% × 12,00,000) | 3,60,000 |
| Value of L | 20,40,000 |
| Less: debt | 12,00,000 |
| Value of L's equity | 8,40,000 |
Weighted average cost of capital
- U: all-equity, so WACC = ke(u) = 20%.
- L: earnings for equity = (4,80,000 − 96,000) × 0.70 = ₹2,68,800, so ke = 2,68,800 ÷ 8,40,000 = 32%. WACC = 8% × (1 − 0.30) × 12,00,000 ÷ 20,40,000 + 32% × 8,40,000 ÷ 20,40,000 = 3.29% + 13.18% = 16.47%. Check by MM's formula for a levered firm: ke(u) × (1 − t × D ÷ V) = 20% × (1 − 0.30 × 12,00,000 ÷ 20,40,000) = 16.47%.
L is worth ₹3,60,000 more than U, the present value of its tax shield, and its WACC is lower (16.47% against 20%).
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Value of U | 3 |
| 2 | Value of L | 3 |
| 3 | WACC of both firms | 3 |
| Total | 9 |
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