0 0

### 1 Formula You Need for any Financial Decisions

29 Jul 2016
SOURCE: Big Fat Purse

Would you choose S\$1,000 today or S\$1,000 in three years?

You would instinctively go for S\$1,000 today rather than receiving the same amount of cash three years later. But, is there any argument for why you would prefer to receive the cash today other than because you want to beat inflation?

This concept is called the time value of money.

The idea is that the money available today is worth more than the same amount of money at a later date due to the earning power of the money today. This concept is applicable not just for calculating loans but can be used in a wide spectrum of financial decisions such as insurance plans, investments, etc. Back to the S\$1,000 example. When you deposit the money into a savings account, you earn interest on your deposit. By the time three years has passed, you would have earned three years' worth of year-on-year interest on your initial deposit.

So, how much would S\$1,000 in three years be worth today?

Let's say you want to know how much you have to invest today in a savings account to have exactly S\$1,000 in three years given a certain interest rate. For the ones not wanting to do the math, there is a table below that illustrates this, given different interest rates. Calculating what a future value is worth today is called discounting in financial lingo.

 Interest rate Initial deposit amount (rounded) Final value 1 % S\$ 971 S\$ 1,000 3 % S\$ 915 S\$ 1,000 5 % S\$ 864 S\$ 1,000 7 % S\$ 816 S\$ 1,000 10 % S\$ 751 S\$ 1,000 12 % S\$ 712 S\$ 1,000

From the table, you can see that if the interest rate on a savings account is 3 percent, we need to deposit S\$915 today in order to have S\$1,000 in three years. So if you were asked to choose between receiving S\$1,000 in three years or S\$915 today, you could pick either one as they would be equivalent, considering the time value of money.

Got it! But can the concepts of time value of money and discounting only be used for calculating the present value of a deposit in a savings account?

No, not really! The two concepts can be used for calculating a broad array of financial decisions including choosing between different types of housing or loans, buying furniture and paying monthly installments, etc.

In fact, for all financial decisions that involve a fixed interest rate and a monthly payment, you can use the discounting procedure.

You can also use the concept of discounting to calculate how much you need to save every year to reach your retirement goal.

The example with the savings account was pretty straightforward. Can you give me an example of how to compare two car loans?

Let's imagine that you're trying to make a decision between two cars that have two different car loans.

We assume that you are indifferent between buying car A and car B, and want to buy the car that is cheaper in terms of the present value. We also assume that you can borrow the exact amount of the price of the car.

Normally, you would get to know the loan amount, annual interest rate, and number of months that the loan should be paid back in.

The structure of the loans can be seen in the table below.

 Car A (Loan A) Car B (Loan B) Car price (loan amount) S\$ 14,800 S\$ 15,500 Term of loan 4 years 4 years Annual Interest rate 2 % 2 % Up-front payment S\$ 100 S\$ 100 On-going fee(s) 0 0 Second hand value (in 4 yrs) S\$ 8,000 S\$ 8,700

Just by looking at the table and doing a few quick calculations, there is no apparent way of deciding which is the best car and car loan to choose from. The term of the loans, the annual interest rate, and the fee structure are the same for the both car loans.

While the cost of Car A is lesser than Car B, the secondhand value of Car B is higher than Car A. Yet, the difference between the car prices and their secondhand value is exactly the same – S\$6,800.

How do we decide which car loan is better, and how do we go about?

Well, in this case, we simply just calculate the present value of the cost of the car, and whichever car has the lowest present value must be the cheaper one.

We discount the second hand value to get a present value. (0.03 represents the 3 percent interest rate that you might get from a savings account. Replace the number with the interest rate of your own savings account when doing your own financial calculations) It turns out that Car A is the cheapest car to buy, since the present value of the cost of the car is lower than for Car B. Notice that you did not have to care for the annual interest rate or the fees, as they are the same for the two loans.

Also notice that we are interested in the lowest present value in this case, since we are discounting the cost.

However, when we go about making pure investment decisions such as buying bonds, we are interested in the option that generates the highest present value for us.

Great! I think I understand the powers of using the time value of money approach for making financial decisions. Anything more I should think about?

You often hear people say that time is money. This could not be a more a valid statement, as time literally is money. Being able to compare investments with different time horizons or taking loans with different repayment periods is crucial to making well-informed decisions.

Using discounting essentially enables us to compare apples with apples by knowing the present values of future values, whether or not we are comparing investments or loans.

​​​​​​​​​​​​​​​​​​​​​​​​ ​​​​