Question

Consider an EOY geometric gradient, which lasts for eight years, whose initial value at EOY one is $5500 and g = 6% per year thereafter. For equivalent cash flow, find the equivalent uniform gradient amount, G over the same period if the initial value of the cash flows at the end of year one is $(4500). The interest rate is 10% per year.

Write the complete equations used (e.g. P=A(P/A, 12%, 5)+ F(P/F,12%,5)) and substitute the values of the factors to find the final answer.

Draw the cash flow diagram when applicable.

Answer 1

Present worth of geometric cash flow = A*[1 - (1+g)^n /(1+i)^n]/(i-g)

Present worth of cash flow = 5500*[1 - (1+0.06)^8 /(1+0.1)^8]/(0.1-0.06)

= 5500*[1 - (1.06)^8 /(1.1)^8]/(0.04)

= 5500 *6.41145276

= 35262.99

Let Gradient amount in second series be G then

PW of gradient series = 4500*(P/A,10%,8) + G*(P/G,10%,8)

= 4500*5.334926 + G*16.028672

As per given condition

4500*5.334926 + G*16.028672 = 35262.99

G = (35262.99 - 4500*5.334926)/ 16.028672 = 702.23

CFD 1

CFD 2