Suppose you were confronted with this scenario:
You have made an investment, and you are faced with two alternatives on how to pay back your loan:
1. You pay $135 00 one year after investment.
2. With the purchase of the investment, you pay $35 000, after two years you pay $50 000 and four years after purchase you pay the remaining $50 000 for the investments.
Which alternative would be the best from an economic standpoint, with an interest rate of 5%?
We will get to the answer shortly, but the key to realizing is a term in finance called Present Value. It would be described with the simple phrase “A dollar today is worth more than a dollar tomorrow.” (Were “worth more” implies that the dollar will be of greater value.) The dollar today will be worth more than the dollar tomorrow because it can be invested and accumulate to a value more than the dollar tomorrow. Thus, it is of greater benefit to receive money now than later and this principle is the underlying backbone of investments. Investors are willing to borrow their money if they expect a favorable return on their investment in the future.
The calculations of Present Value are extremely important in many financial calculations, not only with the example given above. The discount rate plays a crucial role, since the higher the rate, the higher the value for future money. For an investor to buy bonds, he or she must be certain that the interest rates will accumulate the investment to a higher value than the inflation will decrease the value of the investment.
So, back to our scenario. We will calculate the answer with help of the following formula:
FV = PV * (1+i)^n
Were PV is the value of the investment at time = 0 (present value). FV is the value in time n (future value) and i is the annual interest rate.
1. Since $135 000 is the future value after one year, we set up the equation:
135 000 = PV * (1+0.05)^1
PV = 128571.43
You are paying the value of $128 571 at the time of the investment. Let’s compare it with the second alternative:
2. With the formula above, we can calculate the present value with the equation below:
PV = 35 000 + 50000/(1.05^2) + 50000/(1.05^4)
PV = 121486.6
You are paying a present value of $121 486.
In conclusion, the second alternative is better and this hopefully gave you a clearer understanding of the underlying finance, when it comes to investments.