# An investment offers the following year end cash flows: Using a 15% interest rate, convert this...

## Question:

An investment offers the following year-end cash flows:

End of Year 1 2 3
Cash Flow $20,000$30,000 $15,000 Using a 15% interest rate, convert this series of irregular cash flows to an equivalent (in present value terms) 3 year annuity. ## Equivalent Annual Cash Flow: The equivalent annual cash flow is an annuity that has the same present value as a irregular cash flow. In capital budgeting, converting an irregular cash flow to a uniform series is convenient for project evaluation. ## Answer and Explanation: We first compute the present of the original cash flow: • {eq}\dfrac{20,000}{(1 + 15\%)} + \dfrac{30,000}{(1 + 15\%)^2} + \dfrac{15,000}{(1 + 15\%)^3} =$49,938.36 {/eq}

The equivalent annual cash flow of a given present value {eq}P{/eq}, periodic discount rate {eq}r{/eq}, and duration {eq}T{/eq} is:

• {eq}\dfrac{P*r}{1 - (1 + r)^{-T}} {/eq}

Applying the formula, the equivalent annual cash flow is:

• {eq}\dfrac{49,938.36*15\%}{1 - (1 +15\%)^{-3}} = \$21,871.85 {/eq} 