A company’s asset is worth 20 now, and will be worth 16 (in the bad state) or 24

Question

A company’s asset is worth 20 now, and will be worth 16 (in the bad state) or 24 (in the good state) with equal probabilities tomorrow. The riskfree interest rate is 10%. The company lives for only one period. It promises to repay 18 to the debtholders next period.

a).What is the value of debt?

b).What is the expected yield of the debt? How does it compare with the riskfree rate?

c).What is the value of equity?

d).Suppose the company receives a government loan guarantee. What is the loan guarantee worth? What is the value of the company after it receives the loan guarantee? Why is the company worth more?

Explanation / Answer

Solution-

a) As the present worth is 18, the amount to be paid in 1 year time would be 18(A/P,10%,1) = 16.36

Thus the value of Debt is 16.36.

b) What is the expected yield of the debt = 0.1 * 18 / 16.36 = 11%.

The expected yield of debt is more than the risk free rate

c) Value of equity = 20 - 16.36 = 3.64

d)Loan guarentee would be based on the amount of debt equity ratio which for this company is 16.36 / 3.64 = 4.6 approximately

So the loan would be around 22% of the asset that is roughly around 4

Company is worth more because the money given in loan could be used to create much more value in the 1 year.

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