Finance

Present Value Means “How Much is it Worth to Us Today?”

Assume that a rich uncle offers to give you money in either of two  ways:  

  • Alternative 1: $100k today (date A). 
  • Alternative 2: $140k three years from now (date B).

Which will you choose?

The answer depends upon your financial situation, or, in other words, the rate of interest that applies to you. We will refer to two situations represented by two people, saver and debtor:  

  • Saver has no debts, and all his money is invested in savings plans that yield 10% annual interest.
  • Debtor has purchased an apartment with a loan at 20% annual interest.

Saver:

The saver will prefer Alternative 2, for the following reason:  If he chooses Alternative 1, and receives $100k today, it will grow to only $133k in three years, which is less than $140k.   

If he is offered $105,184 under Alternative 1, however, the saver will be indifferent to the choice between the alternatives, since $105,184 will grow to $140k in three years. If he is offered more than $105,184 under Alternative 1, he will prefer Alternative 1.

Debtor:

The debtor will prefer Alternative 1 - receiving $100k today, for the following reason: By paying a debt of $100k today (date A), he gets rid of a debt that will grow to $173k within three years. In other words, by paying back $100k, he reduces his debt three years from now by $173k.

If the debtor chooses Alternative 2 (receiving $140k three years from now), he can reduce his debt three years from now (date B) by only 140k. 

If he is offered $173k under Alternative 2, he will be indifferent to the choice between the two alternatives, since under both alternatives his debts at date B will be reduced by 173k. If he is offered more than 173k under Alternative 2, he will choose this alternative. As we can see, the saver and the debtor have different indifference thresholds, due to the various interest rates that they use in their calculations. In other words, the present value is influenced by your financial situation.

Present Value Means “How Much is it Worth to Us Today?”544Present Value Means “How Much is it Worth to Us Today?”