# 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 interestr and number of yearsn.

• 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