Time Value Money Example Problems
Real World Example Of Value
How Is Time Value Of Money Used
Real World Examples Of Time Value For Money Analysis

Being completely comfortable with the time value of money is critical when working in the field of finance and commercial real estate. The time value of money is impossible to ignore when dealing with loans, investment analysis, capital budgeting, and many other financial decisions. It’s a fundamental building block that the entire field of finance is built upon. And yet, many finance and commercial real estate professionals still lack a solid working knowledge of time value of money concepts and they consistently make the same common mistakes. In this article we take a deep dive into the time value of money, discuss the intuition behind the calculations, and we’ll also clear up several misconceptions along the way.

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Chapter 4: Time Value of Money The concept of Time Value of Money: An amount of money received today is worth more than the same dollar value received a year from now. Do you prefer a $100 today or a $100 one year from now? -Consumption forgone has value -Investment lost has opportunity cost. Quick real estate schemes here, but you will gain a better understanding of one of the most important principles of finance—that the value of money is time dependent, and that a dollar in your hands today is worth more than the promise of a dollar tomorrow. Money has a present valueand a future value. Most of the time, if you.

Why Money Has Time Value

First of all, why does money have time value? Time value of money is the economic principal that a dollar received today has greater value than a dollar received in the future. The intuition behind this concept is easy to see with a simple example. Suppose you were given the choice between receiving $100,000 today or $100,000 in 100 years. Which option would you rather take? Clearly the first option is more valuable for the following reasons:

No Risk – There is no risk of getting money back that you already have today.

Higher Purchasing Power – Because of inflation, $100,000 can be exchanged for more goods and services today than $100,000 in 100 years. Put another way, just think back to what $100,000 could buy you 100 years ago. $100,000 in 1914 would be the equivalent of roughly $2,300,000 today.

Opportunity cost – a dollar received today can be invested now to earn interest, resulting in a higher value in the future. In contrast, a dollar received in the future can not begin earning interest until it is received. This lost opportunity to earn interest is the opportunity cost.

For these reasons we can boil down time value of money into two fundamental principals:

More is better than less.
Sooner is better than later.

With this fundamental intuition out of the way, let’s jump right in to the two basic techniques used in all time value of money calculations: compounding and discounting.

Compounding and Discounting: The Foundation For All Time Value of Money Problems

All time value of money problems involve two fundamental techniques: compounding and discounting. Compounding and discounting is a process used to compare dollars in our pocket today versus dollars we have to wait to receive at some time in the future. Before we dive into specific time value of money examples, let’s first review these basic building blocks.

Compounding is about moving money forwards in time. It’s the process of determining the future value of an investment made today and/or the future value of a series of equal payments made over time (periodic payments).

What’s the intuition behind compounding? Most people immediately understand the concept of compound growth. If you invest $100,000 today and earn 10% annually, then your initial investment will grow to some figure larger than the original amount invested. For example, in the illustration above $100,000 is invested at time 0 and grows at a 10% rate to $121,000 at time 2. We’ll go over the details of this calculation later, but for now just focus on the intuition. The initial investment compounds because it earns interest on the principal amount invested, plus it also earns interest on the interest.

Discounting is about moving money backwards in time. It’s the process of determining the present value of money to be received in the future (as a lump sum and/or as periodic payments). Present value is determined by applying a discount rate (opportunity cost) to the sums of money to be received in the future.

What’s the intuition behind discounting? When solving for the future value of money set aside today, we compound our investment at a particular rate of interest. When solving for the present value of future cash flows, the problem is one of discounting, rather than growing, and the required expected return acts as the discount rate. In other words, discounting is merely the inverse of growing.

The 5 Components of All Time Value of Money Problems

So now that we have some basic intuition about compounding and discounting, let’s take a look at the 5 components of all time value of money problems. Why is it important to understand this? Because in every single time value of money problem you’ll know four out of these five variables and will be able to easily solve for the fifth unknown variable. The 5 components of all time value of money problems are as follows:

Periods (n). The total number of compounding or discounting periods in the holding period.

Rate (i). The periodic interest rate or discount rate used in the analysis, usually expressed as an annual percentage.

Present Value (PV). Represents a single sum of money today.

Payment (PMT). Represents equal periodic payments received or paid each period. When payments are received they are positive, when payments are made they are negative.

Future Value (FV). A one-time single sum of money to be received or paid in the future.

The Key to Solving Any Time Value of Money Problem

Every single time value of money problem includes the above 5 components. Understanding this is critical because of one simple fact: if you can identify any 4 of the 5 components then you can easily solve for the 5th. The key is to simply learn to identify the 4 known variables in a time value of money problem. Let’s revisit the example above to illustrate how this works.

Suppose you invest $100,000 today at 10% compounded annually. What will this investment be worth in 2 years?

First of all we know that our present value (PV) is $100,000 since this is what we are investing today. Next the rate (i) is given to us as 10%. Third, the number of periods (n) in this problem is 2 years. So that leaves 2 remaining variables out of the five: payment (PMT) and future value (FV). Which one out of the two do we know? While it wasn’t explicitly given to us, we do know that the payment (PMT) in this problem is zero. Whenever payment isn’t explicitly given to us, it’s implied that there is no payment. So, all that leaves us with is the future value (FV) component, which we can now easily solve. For now don’t worry about actually doing the ca

Real World Examples Of Time Value For Money