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Question

We are going to study an application of option theory to corporate finance. Consider a firm, XYZCorp, that has assets worth $500mm. In particular, XYZCorp has 10 million shares, and the price of a share is $50.

At time t = 0, XYZCorp decides to issue 5-year zero-coupon debt with $100mm face value. We are interested in understanding: (1) How much money will XYZCorp raise by doing this? (2) What interest rate will XYZCorp pay on its debt? (3) How will this affect the characteristics of XYZCorp's equity?

After XYZCorp issues debt we have:

total assets = equity + debt.

Moreover, assume that

If the firm's total assets are worth more than $100mm in 5 years, then the debt is fully repaid, and equity holders get the rest;

If the firm's assets are worth less than $100m, the bondholders get whatever remains of the firm's total assets and the equity holders get nothing.

1. Plot the value of equity against the value of assets in 5 years.
2. Based on your previous analysis, equity should look like a call option. Use the Black-Scholes formula to work out the value of equity after the issuance of debt. To this end, suppose that: (1) assets have a volatility= 40%; (2) the riskless interest rate,r, is 3%; (3) current total assets are $500mm; (4) amount owed to debt holders at timeTisN= $100mm; (5)T(the maturity of the option) is 5 years.
3. What is the value of the debt issued by the company?What would be the value of a risk-less debt with 5-year to maturity and a principal equal toN= $100mm. What is the credit spread on the company's debt?
4. In points (2) and (3) above you computed themarketvalue of equity and debt for afacevalue of debt equal toN= $100mm. Recompute the value of equity and debt for a face valueN= $200,400,600,800,1000 (mm). Plot themarketvalue l of debt against thefacevalue of debt. Does the market value of debt raise rises more slowly or faster than the face value? Why?
5. Plot the yield to maturity on the company's (risky) debt against thefacevalue of debt (e.g., assume in turnN= 100(the benchmark case),200,400,600,800,1000), under the benchmark case of= 40%. Repeat this exercise for a value of assets volatility= 20% and= 60%. Comment (e.g., what happens to the credit spread as the face value of debt raises? what happens to the credit spread as the volatility of the firm's assets increases?).
6. Conflicts between equity and debt - part A: XYZCorp is presented with a project that will decrease the value of its total assets by $5mm and will increase asset volatility to 60%. Should shareholders of XYZCorp undertake the project? (Recompute the value of equity using Black-Scholes formula. Continue to assume (1) a riskless interest rate,r= 3%; (2) and that the amount owed to debt holders at timeT= 5 years isN= $100mm).
7. Conflicts between equity and deb - part B: XYZCorp is presented with a project that will decrease the value of its total assets by $10mm and will increase asset volatility to 60%. Should shareholders of XYZCorp undertake the project? (Recompute the value of equity using Black-Scholes formula. Continue to assume (1) a riskless interest rate,r= 3%; (2) and that the amount owed to debt holders at timeT= 5 years isN= $100mm).
8. Conflicts between equity and deb - part C: Suppose the value of assets drops from $500mm to $120mm and bondholders are owed $100mm in five years. XYZCorp is presented with a project that will decrease further the value of its total assets by $15mm and will increase asset volatility to 60%. Should shareholders of XYZCorp undertake the project? (Recompute the value of equity using Black-Scholes formula. Continue to assume (1) a riskless interest rate,r= 3%; (2) and that the amount owed to debt holders at timeT= 5 years isN= $100mm).
9. Based on your answers in Q.7 and Q.8, if the company gets into trouble ( e.g.in Q.8 the value of assets drops from $500mm to $120mm) does the conflict between shareholders and bondholders gets worse (e.g. are shareholders more likely to accept a project that decrease the value of assets?)? Can you think of a possible solution to this problem?