Digital Organics has 11.4 million outstanding shares trading at $39 per share. I
ID: 2640031 • Letter: D
Question
Digital Organics has 11.4 million outstanding shares trading at $39 per share. It also has a large amount of debt outstanding, all coming due in one year. The debt pays interest at 6%. It has a par (face) value of $336 million, but is trading at a market value of only $294 million. The one-year risk-free interest rate is 4%.
Complete the put
Digital Organics has 11.4 million outstanding shares trading at $39 per share. It also has a large amount of debt outstanding, all coming due in one year. The debt pays interest at 6%. It has a par (face) value of $336 million, but is trading at a market value of only $294 million. The one-year risk-free interest rate is 4%.
Explanation / Answer
No of shares=11.4mn
Market value of Equity=11.4*39=$444.6mn
Market Value of debt=$294mn
Value of Firm= Market value of Equity+ Market Value of debt
Value of Firm=444.6+294=$738.6mn
For Option pricing valuation
Value of the underlying asset = S = Value of the firm = $738.6mn
Exercise price = K = Face Value of outstanding debt =336mn
Life of the option = t = Life of zero-coupon debt = 1 years
Payoff to equity on liquidation
= V - D if V > D = 0
where, V = Value of the firm D = Face Value of the outstanding debt and other external claims
Put Call Parity
C+K*exp(-r*t)= P+S
Value of call +Face value of debt*exp(-r*t)=Value of Put+ Value of firm
Value of call +336 *exp(-0.04*1)mn= Value of Put+ $738.6mn
Value of Call +$322.83mn= Value of Put+$738.6mn
At expiry, the debt matures and the debt holder gets the face value or if the firm defaults on its debt, the bondholders take ownership of the firm, and the stockholders are left with nothing:
The value to debt holder=Face value of Debt(K)-Max(K-V,0)
Market value of Debt=Face value of Debt-Value of Default Put
Value of Default Put= Face value of Debt- Market value of Debt
Value of Default Put=336mn-$294mn=$42
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