Question

Your project has an estimated cost for land reclamation to be realized at the end of 20 years from today for $70,000,000. If current bond long-term interest rates are 7% compounded annually, what would you need to invest in zero-coupon bonds today to cover the estimated cost after 20 years. (We will learn about zero-coupon bonds later. For now, just calculate the present value (P) at time zero for a future value (F) of $70,0000,000 20 years from today at an interest rate of 7% compounded annually.) What uniform series of payments (A) at the end of periods 1 through 20 would also cover the year 20 cost? (Use 7% interest.)

Answer 1

FV = 70,000,000,

i= 7% = 0.07,

t = 20yrs

To find present value we use formula P= FV/(1+i)^t

P = 70000000/(1+.07)^20

= 70000000/3.86968 = 18,089,330.2

Using the present value calculated above and using factor (A/P,i%,t)

we calculate uniform series payment A = 18089330.2* (A/P, 7%, 20yrs)

A= 18089330.2*0.0943929 = 1,707,504.8