Question 24.3: Equity as a Call Option Swenson Software has a pure discount...
Equity as a Call Option
Swenson Software has a pure discount debt issue with a face value of $100. The issue is due in one year. At that time, the assets of the firm will be worth either $55 or $160, depending on the sales success of Swenson’s latest product. The assets of the firm are currently worth $110. If the risk-free rate is 10 percent, what is the value of the equity in Swenson? The value of the debt? The interest rate on the debt?
To replicate the value of the assets of the firm, we first need to invest the present value of $55 in the risk-free asset. This costs $55/1.10 = $50. If the assets turn out to be worth $160, then the option is worth $160 − 100 = $60. Our risk-free asset will be worth $55, so we need ($160 − 55)/$60 = 1.75 call options. Because the firm is currently worth $110, we have:
$110 = 1.75 × C_{0} + $50
C_{0} = $34.29
The equity is worth $34.29; the debt is worth $110 − 34.29 = $75.71. The interest rate on the debt is about ($100/$75.71) − 1 = .321, or 32.1%.