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.

(a) What is the value of the company and its share price?

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.

2. (b) What is the value of the debt now? What is its yield?

3. (c) What is the expected value of the firm and the price per share? How many

   shares will be repurchased?

4. (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?

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

Answer 1

a	Particulars	Amount ($) million	Probability	Amount ($) million
	Value of the firm	120	0.25	30
		250	0.5	125
		360	0.25	90
	Value of the firm after 1 year			245
	Rate of interest			4%
	Present value factor at 4% for 1 year (1/1.04)			0.96
	Present value of firm value (245*Present value factor)			235.58
	Value of the firm today			235.58
	As it has only equity, the value of equity = value of the firm = 235.57
b	Value of debt after one year	146
	Present value factor at 4% for 1 year (1/1.04)	0.96
	Value of debt today	140.38
	Yield = (146-140.38)/140.38	4.00%
c	Value of debt today	140.38
	Value of equity	235.58
	Value of firm (Value of equity+Value of debt)	375.96
	Price per share (235.58/10)	23.558
	Number of shares repurchased (140.38/23.558)	6 million
d	Value of debt after one year	100
	Present value factor at 4% for 1 year (1/1.04)	0.96
	Value of debt today	96.15
	Yield = (146-140.38)/140.38	4.00%
	Value of debt today	96.15
	Value of equity	235.58
	Value of firm (Value of equity+Value of debt)	331.73
	Price per share (235.58/10)	23.558
	Number of shares repurchased (96.15/23.558)	4 million
e	If there are corporate taxes, the value of debt would be higher due to the tax saving allowed on interest paid. As the value would be higher, higher number of shares can be repurchased. The higher value of debt will also increase the value of firm.

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