Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1.5 million. Over the past five years, the price of land in the area has increased 9 percent per year, with an annual standard deviation of 20 percent. A buyer has recently approached you about buying the land in the next 10 months for $1,620,000. The risk-free rate of interest is 6 percent per year, compounded continuously. You want the option to sell the land to the buyer in one year. What is the price of the transaction today? Multiple Choice Ο $132,290.15 Ο $86,506.00 Ο $138,904.66 Ο $96,914.05 Ο $91,298.49

Answer 1

A 1 Today price 2 Option exercise price 3 Number of periods in year 1500000 1620000 =10/12 4 Risk free rate 0,06 5 Standard deviation 0.2 6 | B2*EXP(-B4*B3) Present value of exercise price 7 8 Standard deviation*Number of period 0.5 B5*B3^0.5 9 d1 =(LN(B1/B2)+(B4+B5*B5/2)*B3)/(B5*B3^0.5) 10 d2 -B9-B8 11 N(d1) 12 N(d2) 13 Call price =NORMDIST(B9,0,1,TRUE) =NORMDIST(B10,0,1,TRUE) B7 B11*B1-B12

The resultant values for above table are given below

A В 1 Today price Option exercise price Number of periods in year 4 Risk free rate 5 Standard deviation $1,500,000.00 $1,620,000.00 0.833 3333 0.06 0.2 6 7 Present value of exercise price 8 Standard deviation*Number of period^0.5 9 d1 1540991.668 0.182574186 0.056384611 10 d2 -0.238958797 11 N(d1) 12 N(d2) 13 Call price 0.477517708 624978.0895 $ 91,298.49

The price of transaction today is $91,298.49.

Thus, the correct option is e.