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:

- 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?
- What is the current value of riskless debt with the same face value and maturity as Kirk Limited’s debt? (1 mark)
- 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**

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