# Investment X offers to pay you $6,900 per year for 9 years, whereas Investment Y offers to pay...

## Question:

Investment X offers to pay you $6,900 per year for 9 years, whereas Investment Y offers to pay you $9,300 per year for 5 years.

Requirement:

If the discount rate is 21 percent, what is the present value of these cash flows? (Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

## Present Value of Annuity:

The annuity is a fixed sum of cash flow that occurs at a regular interval for a definite period of time. The formula to calculate present value of annuity is

{eq}Present\ value\ of\ annuity\ = P\left [ \dfrac{1 - (1+r)^{-n}}{r} \right ] {/eq}

## Answer and Explanation: 1

**Present value of the investment X**

From the question the values are-

- Periodic cash flow (P) = $6900 /Year
- Interest rate (r) = 21% /Year
- Time (n) = 9 Year

Lets put all the values in the formula to calculate present value of the cash flow:

{eq}Present\ value\ of\ annuity\ = \$6900\left [ \dfrac{1 - (1 + 0.21)^{-9}}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$6900\left [ \dfrac{1 - (1.21)^{-9}}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$6900\left [ \dfrac{1 - 0.1798587899}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$6900\left [ \dfrac{0.8201412101}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$6900* 3.9054 {/eq}

{eq}Present\ value\ of\ annuity\ = \$26947.26 {/eq}

So the present value of the cash flow will be $26947.26

**Present value of the investment Y**

From the question the values are-

- Periodic cash flow (P) = $9300 /Year
- Interest rate (r) = 21% /Year
- Time (n) = 5 Year

Lets put all the values in the formula to calculate present value of the cash flow:

{eq}Present\ value\ of\ annuity\ = \$9300\left [ \dfrac{1 - (1 + 0.21)^{-5}}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$9300\left [ \dfrac{1 - (1.21)^{-5}}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$9300\left [ \dfrac{1 - 0.3855432894}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$9300\left [ \dfrac{0.6144567106}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$9300* 2.926 {/eq}

{eq}Present\ value\ of\ annuity\ = \$27211.8 {/eq}

So the present value of the cash flow will be $27211.8

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Chapter 8 / Lesson 3Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.

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