A forest stand yields a recurring timber harvest income of 1

A forest stand yields a recurring timber harvest income of $15,000 that occurs every 45 years

a. Using a 7% interest rate, find the present value of the perpetual harvest income stream assuming that the first income occurs 45 years from now

b. Suppose the stand is 20 years old at the present time. Using a 7% interest rate, find the present value of the perpetual harvest income stream assuming that the first income occurs 25 years from now and then continues occurring in cycles of 45 years

Solution

a. If present value is x then,

x(1+0.07)^45=15000

or, 21.002x=15000

or, x=714.21

b. Its value is 714.21(1.07)^20=$2762.95 and its value 25years from now==714.21(1.07)^45=$15000