Question

Kirk Limited, an automobile company financed by both debt and equity, is undertaking a new project. If the project is successful, the value of the firm in one year will be $100,000, but if the project is a failure, the firm will be worth only $20,000. The current value of Kirk is $50,000, a figure that includes the prospects for the new project. Kirk has outstanding zero coupon bonds due in one year with a face value of $40,000. Treasury bills that mature in one year yield a 5 percent Effective Annual Rate (EAR). Kirk pays no dividends. (Please note that no marks will be awarded if there are no workings provided in your answer.)

Required:

1. Use risk-neutral valuation approach to find the current value of Kirk Limited's debt and equity: what is the risk-neutral probability of the up state (i.e., the risk-neutral probability of an increase in the asset value)? What is the value of Kirk Limited’s equity? What is the value of Kirk Limited’s debt?
2. What is the current value of riskless debt with the same face value and maturity as Kirk Limited’s debt? (1 mark)
3. If Kirk Limited seeks a loan guarantee from its parent firm (Kirk Group holding), how much does this loan guarantee cost the parent firm? (1 mark)

Answer 1

If the project is successful, the firm's value will be $100000 , debt value will be $40000 and equity value will be $60000

If the project is successful, the firm's value will be $20000 , debt value will be $20000 and equity value will be $0

So, u= 100000/50000 = 2

d= 20000/50000 = 0.4

So, risk neutral probability p= (1.05-0.4)/(2-0.4) =0.40625

So, Value of debt = (40000 *0.40625+ 20000*(1-0.40625))/1.05 = $26785.71

Value of Equity = (60000*0.40625+0*(1-0.40625))/1.05 = $23214.29

Current value of Riskless Debt = $40000/1.05 =$38095.24

If Kirk Limited seeks a loan guarantee from its parent firm (Kirk Group holding), the cost of this loan guarantee

= value of Riskless Debt - Value of Debt of the firm

=38095.24-26785.71

= $11309.52