Question

LG2 4-12 Present value concept Answer each of the following questions. a. What single investment made today, earning 12% annual interest, will be worth $6,000 at the end of 6 years? b. What is the present value of $6,000 to be received at the end of 6 years if the discount rate is 12%? c. What is the most you would pay today for a promise to repay you $6,000 at the end of 6 years if your opportunity cost is 12%? d. Compare, contrast, and discuss your findings in parts a through c.

Answer 1

(a) Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $6000, PV = Present value, r = rate of interest = 12%, n= time period = 6

now, putting theses values in the above equation, we get,

$6000 = PV * (1 + 12%)⁶

$6000 = PV * (1 + 0.12)⁶

$6000 = PV * (1.12)⁶

$6000 = PV * 1.97382268518

PV = $6000 / 1.97382268518

PV = $3039.79

So, $3039.79 should be the size of investment today.

(b) Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $6000, PV = Present value, r = rate of interest = 12%, n= time period = 6

now, putting theses values in the above equation, we get,

Since the values are same as in previous question, so the answer will also be same.

PV = $3039.79

(c) Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $6000, PV = Present value, r = rate of interest = 12%, n= time period = 6

now, putting theses values in the above equation, we get,

Since the values are same as in previous question, so the answer will also be same.

PV = $3039.79

(d) In all the questions given above, since the future value, interest rate and time period are same, so the present value will also be the same. The only difference is how we take the question. Like in point (a), we look forwards. The rate of interest will be called as interest rate as the money will be invested and it will earn the given 12% interest rate and returns a future value of $6000.

In point (b), when look backwards. The rate of interest will be called as discount rate because we have future money that has been accumulated by earning interest. We need to find out its present value. So we should discount its future value to remove interest element from it, to arrive at present value.

In point (c) the rate of interest will be called as opportunity cost, as the funds here can be invested to other uses / investments. We can earn an income equal to the opportunity cost of capital, if we do not make such alternative use of capital.