interest-ratesI’m looking at this page, which explains the valuation of equity as a call option. I can calculate the value of the call and the value of the outstanding debt using the black and Scholes formula. I don’t understand the formula to calculate the Interest rate on debt.
It says:
($ 80 / $24.06)1/10 -1 = 12.77%
but I do not see how this formula gets to 12.77%
This is in the source:
The parameters of equity as a call option are as follows:
Value of the underlying asset = S = Value of the firm = $ 100 million
Exercise price = K = Face Value of outstanding debt = $ 80 million
Life of the option = t = Life of zero-coupon debt = 10 years
Variance in the value of the underlying asset = s2 = Variance in firm value = 0.16
Riskless rate = r = Treasury bond rate corresponding to option life = 10% Valuing Equity as a Call Option
Based upon these inputs, the Black-Scholes model provides the following value for the call:
d1 = 1.5994 N(d1) = 0.9451
d2 = 0.3345 N(d2) = 0.6310 Value of the call = 100 (0.9451) - 80 exp(-0.10)(10) (0.6310) = $75.94 million
Value of the outstanding debt = $100 - $75.94 = $24.06 million
Interest rate on debt = ($ 80 / $24.06)1/10 -1 = 12.77%
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