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.

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

(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

Following data follows below

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)Calculating 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.

alue 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)Calculating  value of the debt now and yield

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)Calculating- expected value of the firm and the price per share

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) Kappa decides instead to issue debt with face value $100 million due in one year and repurchase shares with the proceeds

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)the presence of corporate taxes would influence Kappa’s restructuring decision

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.   Any doubt comment below i will explain or resolve until you got....
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