Question 4 (a)

MM approach with corporate tax: value and cost of equity

5 marks

Time to write
About 10 minutes

From an older CBCS paper

Question

Question 4 (a) · 5 marks

Companies U and L are alike in every respect, except that U is an unlevered firm, while L has Rs. 12,00,000 of 8% debt. Both firms' EBIT is Rs. 7,20,000 and the tax rate is 35%. U's equity capitalisation rate is 10%. According to the MM approach, calculate each firm's cost of equity and value.

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

10 minfor 5 marks

Read from the question

  • calculateFormula first, then the working, then the answer with its unit (₹, %, units).

Write it in this order

  1. Read the data; note exactly what is asked 1 min
  2. 1 Value and cost of equity of U 1½ marks 2 min
  3. 2 Value of L VU + tD 1½ marks 2 min
  4. 3 Value and cost of equity of L, with check 2 marks 3 min
  5. Check: arithmetic, units (₹, %), final answer underlined 2 min

Try it first. About 10 minutes for 5 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 debt adds value: the value of the unlevered firm is EBIT(1 − t) ÷ its capitalisation rate, and the value of the levered firm is VL = VU + tD. The levered firm is worth more than the unlevered one by the amount of debt multiplied by the corporate tax rate.

Firm U (unlevered)

  • Value VU = 7,20,000 × (1 − 0.35) ÷ 0.10 = 4,68,000 ÷ 0.10 = ₹46,80,000.
  • Cost of equity = its capitalisation rate = 10%.

Firm L (levered)

Particulars₹
Value of U (VU)46,80,000
Add: tax advantage of debt (tD = 0.35 × 12,00,000)4,20,000
Value of L (VL)51,00,000
Particulars₹
Value of L's equity (VL − D)39,00,000
Debt12,00,000
Value of L51,00,000

Cost of equity of L = (EBIT − interest)(1 − t) ÷ value of equity = (7,20,000 − 96,000) × 0.65 ÷ 39,00,000 = 4,05,600 ÷ 39,00,000 = 10.40%.

Check (MM proposition on the cost of equity): keL = keU + (keU − kd)(1 − t) × D/S = 10% + (10% − 8%) × 0.65 × 12/39 = 10% + 0.40% = 10.40%.

Where the 5 marks sit

#ComponentMarks
1Value and cost of equity of U1.5
2Value of L (VU + tD)1.5
3Value and cost of equity of L, with check2
Total5
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