Question

You anticipate a cash flow of $900 at the end of year 1, $600 at the end of year 2, and $500 at the end of year 4. What is the annual equivalent of the cash flow for years 1 through 4? In other words, what constant value “A” could you receive at the end of years 1-4 such that the two cash series of flows are economically equivalent? The interest rate is 6% annual compounded annually.​

Answer 1

Solution :- Present value of cash flows = 900 / (1.06)¹ + 600 / (1.06)² + 500 / (1.06)⁴

= 900 / 1.06 + 600 / 1.1236 + 500 / 1.26247696

= 849.06 + 534.00 + 396.05

= $ 1779.11 (approx).

Cumulative present value factors at the rate of 6 % = 1 / (1 + 0.06)¹ + 1 / (1 + 0.06)² + 1 / (1 + 0.06)⁴

= 1 / (1.06)¹ + 1 / (1.06)² + 1 / (1.06)⁴

= 1 / 1.06 + 1 / 1.1236 + 1 / 1.26247696

= 0.9434 + 0.890 + 0.7921

= 2.6255 (approx).

Annual equivalent value of cash flow = 1779.11 / Cumulative present value factors at the rate of 6 %.

= 1779.11 / 2.6255

= $ 677.63 (approx).

Conclusion :- Annual equivalent value of cash flow = $ 677.63 (approx).