Question

The firm Kappa has just decided to undertake a major new project. As a result, the value of the firm in one year’s time will be either $120 million (probability 0.25), $250 million (probability 0.5) or $360 million (probability 0.25). The firm is financed entirely by equity and has 10 million shares. All investors are risk-neutral, the risk-free rate is 4% and there are no taxes or other market imperfections.

Kappa decides to issue debt with face value $146 million due in one year and use the proceeds to repurchase shares now. Assume now that bankruptcy costs will be 15% of the value of the firm’s assets in the event of default on debt repayment.

(c) What is the expected value of the firm and the price per share? How many shares will be repurchased?

(d) Assume Kappa decides instead to issue debt with face value $100 million due in one year and repurchase shares with the proceeds. What is the firm’s value now? Why? What is its share price?

(e) Explain how the presence of corporate taxes would influence Kappa’s restructuring decision. (100 words)

Answer 1

(c)
Kappa – Firm
Description	Amount (in Mn $)
Present Value of Debt (146 × (1÷(1+4%)))	140.3846154
Present Value of Equity (245* × (1÷(1+4%)))	235.5769231
∴ Total Value of the Firm (PV of Debt + PV of Equity)	375.9615385
Price Per Share (235.5769231 ÷ 10)	23.55769231
No. of Shares Repurchased (140.3846154 ÷ 23.55769231)	5.959183674 = 5.96 (approx.)
Note: *Value of Equity = (120 × 0.25) + (250 × 0.50) + (360 × 0.25) = $245 Mn

(d)
Kappa – Firm
Description	Amount (in Mn $)
Present Value of Debt (100 × (1÷(1+4%)))	96.15384615
Present Value of Equity (245* × (1÷(1+4%)))	235.5769231
∴ Total Value of the Firm (PV of Debt + PV of Equity)	331.7307693
Price Per Share (235.5769231 ÷ 10)	23.55769231
No. of Shares Repurchased (96.15384615 ÷ 23.55769231)	4.081632652 = 4.08 (approx.)
Note: *Value of Equity = (120 × 0.25) + (250 × 0.50) + (360 × 0.25) = $245 Mn

(e)

Kappa – Firm

The presence of corporate taxes in this layout would efficiently increase the leverage positions of the firm and will provide various tax deductions and incentives. Due to this, the debt value of the firm will increase and eventually the value of the firm will tend to appreciate. Thus, Kappa firm should restructure the its decision-making process, in adding more of debt capital instead of repurchasing share with the existing proceeds.

DO UPVOTE! In case of any doubt, feel free to write in the comment section below.