# Calculating Annuity Cash Flows. If you put up $20,000 today in exchange for a 8 percent, 12-year...

## Question:

Calculating Annuity Cash Flows.

If you put up $20,000 today in exchange for a 8 percent, 12-year annuity, What will the annual cash flow be?

Calculating Annuity Values.

Your company will generate $50,000 in cash flow each year for the next nine years from a new information database. The computer system needed to set up the database costs $300,000. If you can borrow the money to buy the computer system at 8 percent annual interest, can you afford the new system?

## Present Value of an Annuity:

An annuity consists of payments of equal amount over a finite period of time. The present value of an annuity is proportional to the periodic payment, and the proportionality depends on the interest rate and the duration of the annuity.

## Answer and Explanation:

**Question 1**

The annual cash flow is such that the present value of the cash flow is equal to 20,000 today. The annual cash flow is given by:

- {eq}\displaystyle \frac{20,000*8\%}{1 - (1 + 8\%)^{-12}} = 2653.90 {/eq}

**Question 2**

You can afford the system if the discounted present value of the cash flows generated from the database is higher than the cost of the system. We can use the following formula to compute the present value of an annuity with periodic payment {eq}M {/eq} for {eq}T{/eq} periods, given periodic return {eq}r{/eq}:

- {eq}\displaystyle \frac{M(1 - (1 + r)^{-T})}{r} {/eq}

Applying the formula, the present value of the cash flows is:

- {eq}\displaystyle \frac{50,000(1 - (1 + 8\%)^{-9})}{8\%} = 312,344.40 {/eq}

Since the present value of the cash inflows is higher than the cost of $300,000, therefore you can afford the system.

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from Business 110: Business Math

Chapter 8 / Lesson 3