Question

Calculate the value of T which makes the two cash flow diagrams economically equivalent (i.c. have the same present value) at an effective annual interest rate of 8%. $1,000 $1,000 2T 5500 $500 EOY EOY 3T

Answer 1

Calculating the Present Value of cash flow I -

PV = $1,000 + $500(P/F, 8%, 2) + $1,000(P/F, 8%, 4) + $500(P/F, 8%, 6)

PV = $1,000 + ($500 * 0.8573) + ($1,000 * 0.7350) + ($500 * 0.6302)

PV = $1,000 + $428.65 + $735 + $315.10

PV = $2,478.75

The Present Value of cash flow I is $2,478.75

Calculating the present value of cash flow II -

PV = T(P/F, 8%, 1) + 2T(P/F, 8%, 3) - 3T(P/F, 8%, 6)

PV = (T * 0.9259) + (2T * 0.7938) - (3T * 0.6302)

PV = 0.9259T + 1.5876T - 1.8906T

PV = 2.5135T - 1.8906T

PV = 0.6229T

The Present Value of cash flow II is 0.6229T

Equating the two present values -

0.6229T = 2478.75

T = 2478.75/0.6229

T = 3,979.37

The value of T that would make the two cash flow diagrams economically equivalent is $3,979.37