Question

The future worth in year 10 of an arithmetic gradient cash flow series for years 1 through 10 is $675,000. If the gradient increase each year, G, is $1500, determine the cash flow in year 1 at an interest rate of 10% per year.

The cash flow in year 1 is $

Answer 1

The present value of future worth.

The present value of the future worth of the arithmetic gradient cash flow is calculated below:

P = F( P / F,i,n)

675000 (P / F ,0.1,10)

=675000 / (1 + 0.1)¹⁰

= 260,241.72.

The present value equates the sum of cash flow per year and the gradient:

P = A(P / A,i,n) + G (P / G,i,n)

260,241.72 = A (P / A,i,n) + 1500 (P / G 0.1,10)

260,241.72 = (A * 6.14456) + (1500 * 22.8913)

260241.72 = (A * 6.14456) + 34336.95

260241.72 - 34336.95 = (A * 6.14456)

A = (225904.77 / 6.14456)

A = 36,765

Therefore, the cash flow in the year 1 is 36,765