Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,270,000. Over the past five years, the price of land in the area has increased 7 percent per year, with an annual standard deviation of 33 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,420,000. The risk-free rate of interest is 5 percent per year, compounded continuously.

How much should you charge for the option? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

   

Call price

$

Answer 1

Step 1: Calculate d1 and d2

The value of d1 and d2 is arrived as follows:

d1 = (IN(S/X) + (r+σ^(2))*t)/(σ^(2)*t)^(1/2) where

S = $1,270,000, X = $1,420,000, r = 5%, σ = 33% and  t = 12/12

Subsituting these values in the above formula for d1, we get,

d1 = (IN(1,270,000/1,420,000) + (5%+33%^(2)/2)*12/12)/(33%^(2)*12/12)^1/2

Solving further, we get,

d1 = (IN(0.894366197183099) + 0.10445)/.33

d1 = (-0.11163997114 + 0.10445)/.33 = -0.0218 [-0.11163997114 is arrived with the use of log table by taking e as the base. e indicates exponential value]

Now, we can arrive at the value of d2 as follows:

d2 = d1 - (σ^(2)*t)^(1/2) = -0.0218 -.33 = -0.3518

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Step 2: Calculate Nd1 and Nd2

The value of Nd1 and Nd2 is calculated with the normsdist function of EXCEL as follows:

Nd1 = normsdist(-0.0218) = 0.4913

Nd2 = normsdist(-0.3518) = 0.3625

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Step 3: Calculate Call Price

The call price of the option is determined as below:

Call Price = 1,270,000*0.4913 - 1,420,000*e^(-5%*12/12)*0.3625

Solving further by taking value of e = 2.718 (exponential value), we get,

Call Price = 1,270,000*0.4913 - 1,420,000*2.718^(-5%*12/12)*0.3625 = $134,318.34 (answer)

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Notes:

There can be a slight difference in final answer on account of rounding off values.