Question

[2 points] Consider the following two options. You can receive $87,000 at the end of 4 years, or you could receive $P today. If you do not take the money now (i.e. today) you would deposit any money received (again received today) into a savings account that earns 7.25% interest per year. How much money would you have to receive today (i.e. what is the value of P) that would make you: a. [0.5 points] Prefer to take the option of accepting P dollars today b. [0.5 points] Prefer to take the option of accepting $87,000 at the end of 4 years c. [1 point] Indifferent in the option your choose

Answer 1

Answer:

If we are to receive an amount greater than $65,755 today , we should prefer to have the amount today.

If we are getting less than $65,755 today, we should rather wait to receive $87,000 four years later

If we are getting exactly $65,755 today, we should  be indifferent about getting $65,755 today or $87,000 four years later  

Explanation:

We need to find the present value of $87,000 that we have to receive four years after to make our choices. The discount rate to be used for the computation of the present value is given as 7.25%

Present value can be computed using the following formula

PV = FV/(1+i)^n

PV = 87,000/(1+0.0725)^4

PV = 87,000 / (1.0725)^4

PV = 87,000/ 1.3231 = 65,755

If we get more than 65,755, we can invest the amount today and we will have more than $87,000 four years later

If we get less than 65,755, and we reinvest the amount, the amount we will get four years later will be less than $87,000. In this case, we will be better off taking $87,000 four years later

Getting 65,755 today or $87,000 four years later provides the same benefit. If we get 65,755 today we can invest the amount to get 87,000 four years later. If we don't take 65,755 today, we will get $87,000 fouyr years later.