# Investment X offers to pay you $4,800 per year for 9 years, whereas Investment Y offers to pay...

## Question:

Investment X offers to pay you $4,800 per year for 9 years, whereas Investment Y offers to pay you $7,100 per year for 5 years.

a) If the discount rate is 6 per cent, what is the present value of these cash flows?

b) If the discount rate is 16 per cent, what is the present value of these cash flows?

## Time value of Money:

Time value of money means that the worth of a sum of money is different in different time periods. The future value of a present sum of money is calculated by the process of compounding, while the present value of a future sum of money is calculated by the process of discounting.

## Answer and Explanation: 1

**Answer a**

PRESENT VALUE OF INVESTMENT X:

- Investment X has a constant cash inflow (that is annuity) of $ 4,800 per year for 9 years.

The present value of an annuity is given by the following formula:

{eq}PVAn = A * PVIFAr,n {/eq}

Where *PVAn* is the present value of an annuity for n years

*A* is the amount of annuity, given as $4,800

*PVIFAr,n* is the present value interest factor for an annuiy of $1 at rate of interest*r* and number of years*n*.

- Using the above formula, we get

Present value = 4,800 * *PVIFA 6%,9years
*

*= 4,800 * 6.802
*

*= $32,650
*

*PRESENT VALUE OF INVESTMENT Y:
*

- Using the same formula. present value of investment Y can be calculated as follows:

Present value = 7,100 * PVIFA 6%,5years

= 7,100 * 4.212

= 29,905

**Answer b**

PRESENT VALUE OF INVESTMENT X:

- Here, the discount rate will be 16%. All other data would be same as the previous question.
- Present value = 4,800 * PVIFA 16%,9years

= 4,800 * 4.607

= $22,114

PRESENT VALUE OF INVESTMENT Y:

- Present value = 7,100 * PVIFA 16%,5years

= 7,100 * 3.274

= $23,245

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Chapter 11 / Lesson 2Study the time value of money formula. Learn the time value of money definition and practice how to calculate time value of money to understand the relation to purchasing power.

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