Simply Finance: The Time Value of Money

Simply Finance: the Time Value of Money

What is Value?

In its purest form, value can be defined as the monetary or material worth of a company. For example, one could say that the intrinsic value of a company is derived from the cashflows that it generates. After all, a company that can pay sizeable dividends to its stockholders is usually worth more. But cashflows are not static and do not arrive at the same time, which begs the question, how do we measure value? 

Throughout the last 25-50 years of finance, many different models, such as DCF (Discounted Cash Flow), established new ways of estimating value or worth of assets and companies. Nonetheless, all have one thing in common, the basilar and most fundamental concept in finance: the time value of money.

What is the Time Value of Money?

In finance, a dollar today is not the same thing as a dollar tomorrow. The reason is simple, if I give you a dollar today, you can invest that dollar, or put it in the bank and earn interest. The interest or return you gain on that dollar is the time value of money. The bottom line is: money now is better than the same amount of money later. If you do not have cash now, it means you can not earn interest or return on investment, and it is thus a lost opportunity.

How does the Time Value of Money work?

To put things in perspective, let’s consider a hypothetical example. Assume your boss offers to pay you one of two ways. They will either pay you 1,000 SGD today or 1,200 SGD in tomorrow. What do you do? Well, you pick the better option. But which one is it? As always, in finance and business, it depends. 

In this example, it depends on the rate of return you can gain on the $1,000 at present value. If you believe you can make more than 20% – $1,200 is 20% of $1,000, then you should probably take the $1,000. In that case, $1,000 today are worth more than $1,200 tomorrow. Otherwise, the converse is the better option. 

Future Value

Future value (FV) is the worth of an asset or investment at a defined future date assuming a set interest rate, or more commonly, rate of return. Future value calculations essentially move cashflows forward in time without chaining their “financial value.” FV answers the question, “what is the amount of money you will have in the future if you invest $X today?”

For example, assume you have $100, and your bank pays an annual interest rate of 3%. Then, in one year, the future value of your $100 will be $100 * (1 + 3%) = $103. If you reinvest the $103, then, after another year, you will have $103 * (1 + 3%) = $106.09. The key takeaway is: $100 today or $106.09 in two years are the same from a finance perspective. 

Future Value Formula

Present Value

Suppose you are promised an amount of money, say $100, at some future date. The present value (PV) of this future cash inflow is the amount that you would need to invest today to have $100 at that future point in time. In essence, present value calculations move cashflows backward in time without chaining their “financial value.”

For instance, let’s say you want to know how much you have to put into your retirement account today if you want $100,000 when you retire. Assume you are 35 years old, and you expect to retire when you turn 65, or in 30 years. Let’s also assume your retirement account has an expected return of 4% per year. Then, you would need

Present Value Formula

Valuing Multiple Cashflows

So far, we have analyzed how to transform Future and Present Value. You now know the difference between future and present cash, how to compare them, and how to decide which is better given an interest or return rate. But what if I were to give you this:

Simply Finance: the Time Value of Money Example 1

Which of these companies would you rather own? To answer this, we need to know how to value the entire stream of cashflows. 

One of the basic principles for calculating both PV and FV for multiple cash flows is value additivity. To calculate the PV or FV of the entire stream, you just need to add up the individual PV or FV of each cash flow. Of course, we need to first move all cashflows to the same point in time.

Simply Finance: the Time Value of Money Example 2
If you want to test yourself, download this Excel Template!
Bottom Line: to get the value of a stream of cashflows today, you cannot sum them up directly; you must sum the PV or FV of each respective cashflow. 

In a Nutshell

Simply Finance: the Time Value of Money

Test yourself!

Public companies usually publish their financial statments on a quarterly and annual basis. You can find  US-based public company’s balance sheets on the US Securities and Exchange Commission (SEC) website. Search for the 10-K, and you will be ready to go!

Written by

Cheryl Toh

Last updated on

September 12th 2019, 3:46 pm

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