Question

1. Consider cash flow diagrams A and B below. Determine the value of X so that both cash flow diagrams are equivalent at 10%/yr. Show your calculations. The diagrams are not drawn to scale, Your calculations for cash flow diagram A must include at least one uniform series factor. Your calculations for cash flow diagram B must include at least one gradient series factor

Answer 1

The equation for equivalence of both the cash flows can be written as

- 200 + 60 $\times$ ( P/A, 10% , 4 years ) = - 400 + 5x $\times$ ( P/A, 10% , 4 years ) - x ( P/G, 10% , 4 years )

Where  ( P/A, 10% , 4 years ) = Uniform series present worth factor

( P/G, 10% , 4 years ) = Gradient series factor

- 200 + 60 $\times$ 3.170 = - 400 + 5x $\times$ 3.170 - x $\times$ 4.378

- 200 + 190.2 = - 400 + 11.472 x

11.472 x = -200 + 400 + 190.2

11.472 x = 390.2

x = 390.2 $\div$ 11.472

x = 34.01 $\approx$ 34

The value of x so that both cash flow diagrams are equivalent = 34