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3. Risky Debt Analysis: Merton-type Model
ABCD is a firm with $100 million in assets (market value). The estimated return standard deviation of ABCD’s assets is 20% per year, and the risk-free rate is 5% per year (not continuously compounded). ABCD has outstanding debt, including:
1. $40 million face value of Senior 2-year, zero-coupon debt
2. $50 million face value of Junior 2-year, zero-coupon debt

In the event of default, the senior debt will have first priority to have its principal amounts paid before junior debt receives anything. ABCD is prohibited by covenant from either issuing any more debt or making any distributions to its shareholders until all outstanding debt is paid. Use the Black-Scholes option price calculator to answer the following questions.
(a) Plot the payoff diagram associated with the senior debt, the junior debt, and the equity, with the firm’s asset value at the end of two years on the horizontal axis.
(b) What is the current dollar value and yield to maturity (YTM) of the senior debt?
(c) What is the current dollar value and yield to maturity (YTM) of the junior debt?
(d) What is the current dollar value of the equity?
(e) In class we created synthetic debt using puts, calls, risk- free bonds and equity shares. If the assets of ABCD were $100 million of Microsoft, describe how you could create a static portfolio composed of these securities that would
i) replicate the payoff to the junior debt of ABCD
ii) replicate the senior debt of ABCD
iii) replicate the equity of ABCD.

4. Capital Structure Analysis: Merton-type Model
QRST is a firm with the same asset and debt structure and facing the same market conditions as firm ABCD in Question 3. However, in addition to its 1,000,000 shares of outstanding common stock, QRST also has 250,000 2-year warrants outstanding with an exercise price of $20/share
Use the Black-Scholes option price calculator to answer the following questions.

(a) Plot the payoff diagram associated with the senior debt, the junior debt, the warrants, and the equity, with the firm’s asset value at the end of two years on the horizontal axis.
(b) What is the current dollar value and yield to maturity (YTM) of the senior debt?
(c) What is the current dollar value and yield to maturity (YTM) of the junior debt?
(d) What is the current dollar value of the warrants?
(e) What is the current dollar value of the equity?
(f) Consider the creation of synthetic debt using puts, calls, risk- free bonds and equity shares. If the assets of QRST were $100 million of Microsoft, describe how you could create a static portfolio composed of these securities that would
i) replicate the payoff to the junior debt of QRST
ii) replicate the senior debt of QRST
iii) replicate the warrants of QRST
iii) replicate the equity of QRST

5. Credit Derivatives
      CDR is a credit derivative that covers (replicates) the actual loss incurred by junior creditors of firm ABCD in Question 3, in the event that a default occurs.
a. Plot the diagram associated with credit derivative CDR, letting firm ABCD’s asset value at end of two years be on the horizontal axis.
b. What is the price of credit derivative contract CDR at Time 0?
c. If the assets of ABCD are $100 million of Microsoft stock, what portfolio of option positions in Microsoft stock would provide the same protection as CDR?

6. (Optional) Asset/Liability Management for Defined-Benefit Pension Plan
Suppose a firm’s pension fund is permitted to invest in the firm’s own stock (not allowed under current US ERISA laws). How does the funding of the pension change if the pension invested all of its assets into the firm’s stock?

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