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Time Value of Money (Discounting Cash Flows) article

Have you heard the phrase Time Value of Money and wondered what that is? If you want to invest in anything that takes multiple years to complete (like a Bank CD, Bonds, or Commercial Real Estate) then the Time Value of Money should be something you want to know about. The concept of the Time Value of Money, in its simplest form, is that receiving the same amount of money now is better than receiving that same amount of money later. It gets more complicated when the amounts aren't the same when comparing two or more investments. The Time Value of Money measurement tools (NPV and IRR) help us when it gets complicated. The video and article look at the idea of the Time Value of Money in depth.

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Discounted Cash Flow Theory

While there are many measures which have been developed over time, virtually all of them are based on the answers to the three simple questions which, in a financial sense, are the most important things an investor is concerned with.

1. How much money must I invest?
2. How much money will I make?
3. When do these 'cash flows' happen?

The first two of these questions are the most commonly asked, but the last question is typically the most important. Consider an investment of $1,000 which returns $1,100 in one year. Most people would say that this investment has a 10% 'rate of return'. However, if the time period is expanded from one to ten years, that 10% rate of return vanishes, and we are left with a rate of return under one percent. In other words, while the answers to the first two questions are the same in this case, the answer to the third question makes all the difference. For this reason, financial analysts and sophisticated investors have come to rely on investment measures known in the literature of the field as the 'Net Present Value' the 'Internal Rate of Return', and the 'Modified Internal Rate of Return'. These measures are based, in turn, on a technique known as 'Discounted Cash Flow Analysis'.

Time Value of Money

The basic premise of Discounted Cash Flow Analysis is that the value of money is related to time. That is, a dollar in hand today is worth more than a dollar which is received one year from now. For instance, the investor could take the dollar he has today and put it in a savings account at six percent interest. One year from now he would have $1.06 in the bank. In other words, a dollar today is worth $1.06 one year from now. Expressing this another way, the 'Present Value' of a dollar one year from now is $.9434 discounted at 6%, since an investor placing $.9434 in the bank at 6% would have a dollar in the bank at the endfyf a year. (The 0.9434, or 1 divided by 1.06, is known as the 'Present Value Discount Factor'.)

Present Value

This concept of Present Value is most useful, since it enables us to express the value of money received in the future in terms of today’s dollars. For example, in the investment returning $1,100 one year from now, the Present Value of $1,100 discounted at 6% is $1,100 divided by 1.06, or $1,038. Since this is greater than the $1,000 investment, the investor would be better off by making the investment than by taking the alternative of putting his money in the bank at 6%.

Net Present Value (NPV)

This leads to the concept of Net Present Value. If we subtract the $1,000 investment from the $1,038 Present Value of the future cash flow, the difference, or Net Present Value, is $38. Since this difference is positive, we know that receiving $1,100 a year from now is better than investing the $1,000 in the bank at 6%. Another way to interpret the Net Present Value is as follows: the investor could afford to pay $38 more than the $1,000 for this investment and still make 6% interest on his money. All the Present Values shown in planEASe analyses are actually Net Present Values. For this reason, a positive Net Present Value in the analysis means that the particular stream of cash flows is attractive, as compared with other investments which earn interest at the discount rate.

A major difficulty with using Net Present Values in order to make investment decisions is determining what discount rate to use in the calculations. Theoretically, the proper discount rate is the rate at which alternative investments may be made. Thus, if a savings account is the investor’s alternative, the six percent discount rate may be appropriate. Other investors may feel that they have different alternatives, however. For this reason, the individual investor’s discount rate is an assumption in the analysis so that it may be varied for each investor. This difficulty in determining the proper discount rate is eliminated, however, when the investor uses the Internal Rate of Return to evaluate the investment.

Internal Rate of Return (IRR)

It is a small step from Net Present Values to the Internal Rate of Return for an investment. In the $1,000 investment example, we used a 6% discount rate to obtain the $1,038 Present Value of the future cash receipts. If we had used an 8% discount rate, the corresponding Present Value would have been $1,019, and the Net Present Value would have been a positive $19. At a 10% discount rate, the Present Value of $1,100 is exactly $1,000, so the Net Present Value of the investment is exactly zero.

The particular discount rate which gives us a Net Present Value of zero is called the 'Internal Rate of Return.' The meaning of this number may be expressed in many ways, but the most useful definition for our purposes is as an effective interest rate. For example, if you had placed $1,000 in a savings account and removed $1,100 from the account a year later and the account had no more money in it, then the bank would have paid you 10% interest compounded annually on your money. A calculation quite similar to this is used to compute the Annual Percentage Rate (APR) for loans, the yield to maturity for bonds, and the annual yield for savings certificates. This is what makes the Rate of Return so useful as an investment measure: it may easily be compared to alternative investments because the rates of return for those investments are typically expressed in the same terms.

Example

You win a prize of $100,000, but you can not receive the prize for four years. If you wanted to sell your prize to someone else, how much should you ask for? If a person put $100,000 in a bank for four years, how much would the $100,000 dollars be worth at the end of the four years? Most likely more than $100,000, because the bank pays interest on the money while it is in the bank. So it is very unlikely that you will find someone who is willing to give you $100,000 today and have to wait four years to get the $100,000. So really the question is what is the Present Value of $100,000 to be received four years from now? Let's break it down into components.

How much money will be received at the future date? $100,000

How long is the time between now and the future date? 4 years (48 months) (1461 days, considering the leap year)

What is the monetary value during that time? This is called the Present Value Discount Rate which we will assume for this example is 10%. The 10% is equivalent to the APY rate on a bank account or the yield on a bond of equal time.

Now lets run the Present Value calculation also known as the Net Present Value calculation. (The only difference between a PV and a NPV is that the PV starts with zero dollars, so in this case they're both really a NPV).

Date	Years	Cash Flow	Present Value Discount Factor	Present Value at 10.0000%
1 Jan 2010	0.00	0	1.0000000	0
31 Dec 13	4.00	100,000.00	0.6830135	$68,301.35
TOTALS		$100,000.00		$68,301.35

So this means if you invest $68,301.35 in the bank with a 10% Annual Percentage Yield (APY) then you should have $100,000 at the end of four years.

Year	Beginning of Year Amount	Add 10% Interest	End of Year Amount
Year 0 - 1	$68,301.35	$6,830.14	$75,131.49
Year 1 - 2	$75,131.49	$7,513.15	$82,644.64
Year 2 - 3	$82,644.64	$8,264.46	$90,909.10
Year 3 - 4	$90,909.10	$9,090.10	$100,000.01

Now the problem is that there are a few things that can change with some of the questions on a lot of investments, such as: How much money will be received at the future date?, How long is the time between now and the future date?, What is the monetary value during that time?, and many more when it comes to commercial real estate. This is why planEASe has been updating it's software every year for the past 25 years, to reveal the assumptions that an investment is sensitive to, and how sensitive is the NPV and/or the IRR to those assumptions.

Where is the Time Value of Money on the report?

Usually when someone asks what the Rate of Return is on an investment they mean the Internal Rate of Return (IRR) and in general expect a 'Time Value of Money' measure to be the answer. These are all 'Time Value of Money' measures:

• Net Present Value (NPV) (Discounted Cash Flow Measure)
• Internal Rate of Return (IRR) (Discounted Cash Flow Measure)
• Modified Internal Rate of Return (MIRR) (Discounted Cash Flow Measure)
• Lender Yield (Discounted Cash Flow Measure)

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Written by
Michael Feakins, CCIM
of planEASe Software