As of June of 2016,Facebook (FB)had no debt.Suppose the firm's managers consider issuing zero-coupon debt with a face value of $231 billion due in January of 2018 (19 months)and using the proceeds to pay a special dividend.FB has 2.31 billion shares outstanding,with a market price (June,2016)of $116.62.The risk-free rate over this horizon is 0.25%. There is a call option trading on FB with a strike price of $100 and a price of $29.24.What is the implied credit spread of Facebook's proposed debt issue assuming perfect capital markets?
A)8.89%
B)8.64%
C)19.74%
D)Cannot be determined from information given.

Question

Quizplus · Accepted Answer

To calculate the implied credit spread, we need to use the formula:
Implied Spread = (Bond Price - Treasury Price) / Duration
Duration = time to maturity x (1 - present value of principal) / yield to maturity

Using the given information, we can calculate the duration:
Duration = (19/12) x (1 - 1/(1+0.0025)^19) / (0.2924 + 100/(1+0.0025)^19) = 1.1258

To calculate the bond price, we need to discount the face value by the yield to maturity:
Bond Price = 231/(1+y)^1.5833, where y is the yield to maturity
Using the market price and the call option, we can calculate the stock price volatility:
Volatility = (call price - intrinsic value) / (stock price x strike price x time to maturity)^0.5
Intrinsic value = max(0, stock price - strike price) = $16.62
Volatility = (29.24 - 16.62) / (116.62 x 100 x 19/12)^0.5 = 0.2914

Using the Black-Scholes formula, we can calculate the yield to maturity:
29.24 = (231/(1+y)^1.5833) x N(-d1) - 116.62 x N(-d2)
d1 = (ln(231/116.62) + (0.0025 + 0.5 x 0.2914^2) x 1.5833) / (0.2914 x 1.258)
d2 = d1 - 0.2914 x 1.258
y = 1.321%

Finally, we can calculate the implied spread:
Implied Spread = (231/(1+0.01321)^1.5833 - 231) / 1.1258 = 0.0864 = 8.64%

As of June of 2016,Facebook (FB)had No Debt