Answer to Question #123580 in Financial Math for Moses

Question

a. Esther, Vida, and Clair were asked to consider two different cash flows: GH¢1000 that they could receive today and GH¢3000 that would be received 3 years from today. Esther wanted the GH¢1000 today, Vida chose to collect GH¢3000 in 3 years, and Clair was indifferent between these two options. Which of the three women made the right choice? Explain.

Answer 1

Assuming the discount market rate is currently 10%

The Future Value of GH¢3000 after 3 years will be given by:

Year 1

Interest Factor (IF) = (I+r)^-t

IF = (1+0.1)^-1

IF = 1.1^-1

IF = 0.909090909

Year 2

IF = (1+0.1)^-2

IF = 1.1^-2

IF = 0.826446281

Year 3

IF = (1+0.1)^-2

IF = 1.1^-3

IF = 0.751314801

Amount = 3,000 * 0.751314801 = 2,253.944403

If Esther invests the money at the market rate of 10%, she will receive the following

Year 0 = 1,000

Year 1 = 1,000 *0.909090909 = 909.090909

Year 2 = 1,000 * 0.826446281 = 826.446281

Year 3 = 1,000 * 0.751314801 = 751.314801

Total                                                     2,486.852

After 3 years, Esther would receive an amount equal to 2,486.852 at 10 percent interest rate while Vida’s amount would be equal to 2,253.94 which is less than the investment gain of Esther’s amount. It I hence advisable to take the money and invest the same rather than wait to receive 3,000 after 3 years because from the above assumption, it is can be seen that the value will decline and it is actually Vida who will get less than GH 3,000 currency.

Inference

As evidence in the above scenarios where interest rate was assumed to be 1%, 8%, 10% and 20%, it is advisable to take the money and invest the same rather than wait to receive 3,000 after 3 years because from the above assumption, it is can be seen that the value will decline and it is actually Vida who will get less than GH 3,000 currency.  Thus, in all situations, as long as the investment period is 3 years and beyond, it is better to invest the GH1,000. If the investment period is 2 years and below, it is better to wait for to receive the money at the end of the 1 or 2 years.