Question

You are considering entering the watch business. You believe there's a narrow window for entering this market. Because of holiday demand, the time is right today, and you believe that exactly a year from now would also be a good opportunity. Other than these two windows, you do not think another opportunity will exist to break into this business. It will cost you $35 million to enter the market. Because other watch manufacturers exist and are public companies, you can construct a perfectly comparable company. Hence, you want to use the Black-Scholes formula to decide when and if you should enter the watch business. Your analysis implies that the current value of your watch company would be $40 million, and that the volatility is 25% per year. Of the $40 million current value, $6 million is coming from the free cash flows expected in the first year. The risk-free rate is 4%. What is the value of the investment opportunity if you choose to wait? (Hint: think of the investment as a call option)

A) $10.29 million

B) $1.03 million

C) $5.72 million

D) $3.54 million

Answer 1

The correct answer is the last option i.e. option D) $3.54 million

Value of call = S N (d1) - Kert Nd2) where di = od d2 = d1 - 0 Vt

Of the $40 million current value, $6 million is coming from the free cash flows expected in the first year. Hence, the value of the company if we enter a year later = 40 - 6 = 34 million.

Please see the table below. Please be guided by the last column to understand the mathematics. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.

11 K 12 7 Inputs 8s 34.00 1.00 1 year = 2 six months period 25.00% 35 Strike price of call option 4.00% 13 Output Values Formula Used 14 d1 0.169049853=(LN(C8/C11)+(C12+C10^2/2)*(9)/(C10*SQRT(09)) 15 d2 -0.080950147 =C14-C10*SQRT(09) 16 N(d1)= 0.567121285 =NORMSDIST(C14) 17 N(D2) 0.467740799 =NORMSDIST(C15) 18 Value of the call option, c. 3.553109 =C8*C16-C11*EXP(-C12*09)*C17