Question

Donald Inc. has $2 million in assets, no debt, and no cash. It is listed with 100,000 shares outstanding. Assume there is no tax.

The company decides to take out a loan of $1 million at an interest rate of 10% in order to buy back shares.

1. How many shares can it buy back? How many shares are left after the buy-back?

2. If WACC was 15% before the buy-back, what is Darrian’s WACC after the buy-back? Why?

3. What is the required rate of return by equity holders after the buy-back? Why?

Answer 1

Current Total assets = $2 million = $2000000

As Donald Inc has no debt and cash, hence Current Total assets = Total Equity = $2000000

Price per share = Total Equity / No of shares = 2000000 / 100000 = $20

total equity to buy back or total equity repurchased = debt issued = $1 million = $1000000

No of shares to buy back or shares repurchased = Total equity to buy back / Price per share = 1000000 / 20 = 50000

Shares it can buy back = 50000 shares

Shares left after buyback = Total shares - Shares it can buy back = 100000 - 50000 = 50000 shares

Shares left after buyback = 50000 shares

If before buyback,WACC = 15%

According to Modigliani and Miller Proposition I without taxes, value of a company and its Weighted average cost of capital are independent of capital structure. Hence WACC remains unaffected by changes is capital structure and is constant.

WACC = R₀ = (D/V)(Cost of debt) + (E/V)(Cost of equity)

where R₀ = Cost of all equity firm

After buy back WACC = Before Buy back WACC = 15%

So After buy back WACC of Donald Inc = 15%

After buyback, Value of Equity = E = 1 million and value of debt = D = 1 million

D/E = 1/1 = 1

Cost of equity after buyback = R₀ + (R₀ - Cost of debt)(D/E) = 15% + (15%-10%)(1) = 15% + 5% = 20%

Hence Required rate of return on equity after buyback = 20%