An investor has asked for your help with the following time value of money appli

Question

An investor has asked for your help with the following time value of money applications. Table 6-4. (Use appropriate factor(s) from the tables provided. Round the PV factors to 4 decimals.)  

Required:

a. What is the present value of $54,000 to be received in six years using a discount rate of 12%? (Round your answer to 1 decimal place.)

b. How much should be invested today at a return on investment of 12% compounded annually to have $54,000 in six years? (Round your answer to 1 decimal place.)

c. If the return on investment was greater than 12% compounded annually, would the amount to be invested today to have $54,000 in six years be more or less than the answer to part b?

Explanation / Answer

Answer a We can use present value of sum formula to calculate the present value. PV = FV * [1/(1+r)^n] PV = Present value = ? FV = Future value = $54000 r = discount rate per year = 12% n = no.of years = 6 PV = 54000 *[1/(1+0.12)^6] PV = 54000 * 0.5066 Present value = $27,358.1 Answer b The answer is same as calculated in Part a. Amount to be invested today = $27,358.1 Answer c Let us assume return on investment be 13% (i.e.more than 12%) PV = FV * [1/(1+r)^n] PV = Present value = ? FV = Future value = $54000 r = return on investment per year = 13% n = no.of years = 6 PV = 54000 *[1/(1+0.13)^6] PV = 54000 * 0.4803 Present value = 25937.2 Amount to be invested today at 13% = $25,937.2 The amount is less than the answer to Part b.

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