Present value – the key word in finance theory

### Parents’ promise to their child Let’s assume that parents promise their child Moshe 20,000 NIS in 3 years, when he is discharged from the IDF. The theory of finance will ask us to calculate what amount of money must be deposited in the bank today so that it will grow to 20,000 NIS within 3 years. The answer depends on the interest rate that the bank gives. Let’s assume it is 8% per year. Until you learn to calculate the amount, we will do it for you, and the answer is 15,877 NIS. That is: an amount of 15,877 NIS, deposited in the bank today at an interest rate of 8% per year, will grow to 20,000 NIS in 3 years. The amount of money we specified in the answer has a nickname: **”present value equivalent”** or for short, “present value”. Using it in a full sentence would be: 15,877 NIS is the **present value** of 20,000 NIS that are due in 3 years. ### Indifference The word **indifference** in economics describes a situation in which, from an economic perspective, you have no justification for preferring one alternative over another. Since each of the alternatives gives you the same return. In this situation, you are indifferent between the alternatives. **Example:** Let’s return to Moshe from the previous example. Let’s assume that his parents improve their financial offer and offer him to receive money in 2 alternatives: – Alternative 1 – 15,877 NIS today.
– Alternative 2 – 20,000 NIS in 3 years. Moshe calls the bank and asks the teller how much he will accumulate in 3 years if he deposits 15,877 NIS today (alternative 1), and the answer is 20,000 NIS. In this situation, Moshe is indifferent to the choice between receiving 15,877 NIS from his parents today and receiving 20,000 NIS in 3 years (alternative 2). This is because through each of the two alternatives, he will have 20,000 NIS in his hands in 3 years (and this is assuming that he does not need the money during the 3 years). **Let’s return to the term present value** We offer you to receive an amount of 20,000 NIS in 3 years. **The present value** of 20,000 NIS to be received in 3 years is the amount you would demand to receive today as an alternative, in order to be indifferent to the choice between the two alternatives. In this example, the present value of 20,000 NIS that will be received in 3 years is 15,877 NIS. ### Preference versus indifference If our Moshe could receive more than 15,877 NIS today, even 15,878 NIS (1 shekel more), he would prefer this to receiving 20,000 NIS in 3 years. And the explanation: If Moshe deposits 15,878 NIS today, he will have more than 20,000 NIS in 3 years. And the opposite: If Moshe could receive more than 20,000 NIS in 3 years (even 20,001 NIS) in 3 years, he would prefer this to receiving 15,877 NIS today. And the explanation: If he deposits 15,877 NIS today, in 3 years he will only have 20,000 NIS. ### Present value in free translation: “How much is it worth to us today?” Let’s say a rich uncle offers to give you money in 2 alternatives: – Alternative 1: 100k NIS today (date Sunday)
– Alternative 2: 140k NIS in 3 years (Date B). What will you choose? The answer depends on your financial situation or, in other words, on the interest rate that applies to you. We will consider two situations represented by two people: **”Thrifty”** and **”Debtor”**. 1. **Thrifty**. He has no debts and all his money is invested in savings plans that yield 10% interest per year.
2. **Debtor**. Purchased an apartment using a loan at an interest rate of 20% per year. #### The thrifty person would prefer alternative 2 and the explanation: If he chooses alternative 1 and receives 100k NIS today, it will grow in the bank only to 133k NIS in 3 years, less than 140k NIS. But if in alternative 1 they were offered 105,184 NIS, the thrifty person would be indifferent to the choice between the alternatives, since 105,184 NIS will grow to 140k NIS in 3 years. If in alternative 1 they were offered more than 105,184 NIS, he would prefer alternative 1.

#### Debtor The debtor will prefer alternative 1 – receiving 100k NIS today. And the explanation: By paying off a debt of 100k NIS today (Date A), he resigns from a debt that will grow to 173k NIS in 3 years (Date B), or in other words, by paying off 100k NIS today, he reduces the scope of his debts in 3 years by 173k NIS. If **the debtor** chooses alternative 2 (receiving 140k NIS in 3 years), he will be able to reduce the scope of his debts in 3 years (Date B) by only 140k NIS. If in alternative 2 they were to offer him 173k NIS, he would be indifferent to the choice between the 2 alternatives, since in the 2 alternatives the scope of his debts in date B would be reduced by 173k NIS. If in alternative 2 they were to offer **To owe** more than 173k NIS, he would prefer to choose it. As we see, a “thrifty” and a “debtor” have a different indifference threshold, given the different interest rate that each of them takes into account. In other words, the **present value** is affected by your financial situation.