Question

3. Suppose that the current value of a company's operating assets is $100 million. company has 10-year zero-coupon debt outstanding the only debt it has with a prin- cipal amount at maturity of $155 million. Its debt has a yield to maturity of 10%. (a) Draw a payoff diagram of the company's debt at maturity, as a function of the value of its assets then. Be sure to label all relevant payoffs and axes. (b) Suppose that the government announces that the company is "too big to fail”, so it will fully and unconditionally guarantee the debt of the subsidiary, meaning that the government will ensure that its bonds always pay off the full amount that they owe. Draw the payoff diagram of the company's debt with the guarantee included. (c) What is the value of the guarantee? You can assume a risk-free rate of 5%. (Hint: Calculate the value of the debt in part a, and the value of the combined debt and guarantee in part b. You can then infer the value of the guarantee based on those.)

Can't even figure out how to start this problem. Thanks!

Answer 1

Current value of company's operating asset is $ 100 million

The company has 10 year old zero coupon bond as debt which has a maturity value of 155 million $

Yield to maturity of the bond is 10%

Present Value of the company's debt is = PV(.1,10,0,-155) = 59.76 million $

Company's debt at maturity is fixed however the company's obligation to service the debt at maturity depends on the rate it can realize from its operating asset. If the operating asset grows at a good rate then it can service the debt else it will default at maturity. So the pay off diagram of the debt as a function of asset at different rates of return can be plotted

$300.00 $250.00 $200.00 - Value of Asset at Maturity Debt Obligation $150.00 - $100.00 — Return on Asset (%) $50.00 $0.00 + 1 2 3 4 5

If the Govt provides guarantee for the bond then the Govt will provide any shortfall that the company can not provides from its operating asset. Hence the value of the guarantee would be the difference between the bond value and the asset value and this can be plotted as below

$300.00 $250.00 $200.00 $150.00 Value of Asset at Maturity Debt Obligation $100.00 $50.00 Govt Gurantee $0.00 - Return on Asset (%) 5 ($50.00) ($100.00) ($150.00)