Produce a graph comparing a call's intrinsic value [defined as max(S-X,0)] and its Black-Scholes price. Stock prices to produce respective intrinsic values should start at 36 and end at 68 (units of 2). From this graph, provide an explanation of why it is never optimal to exercise early on a call priced by the Black-Scholes. Use the inputs below:

S	50
X	50
r	10.00%
T	0.5
Sigma	25%

\fStock Price Intrinsic V Black-Scholes Price Explanation 36 0.179581 This worksheet compares the intrinsic 38 0.363892 value and Black-Scholes price of a call 40 0.6663 option for a range of stock prices. The 42 1.11982 Intrinsic Value is calculated as MAX(S- 44 1.750285 X,0), where S is the stock price and X is 46 2.572536 48 3.589079 50 4.791118 52 6.161241 54 7.676806 Intrinsic Value vs Black-Scholes Price 56 9.313178 25 58 11.04632 60 12.85451 20 62 14.71926 15 64 16.62554 Option Value 66 18.56164 10 Intrinsic Value 68 20.51869 Black-Scholes Price in 0 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 Stock Price (S)