Time Value of Money

An important strategic factor in planning and presenting projects, time value of money is a concept you should understand and use to your advantage.

Would you loan me $5 for lunch? I'll pay you back tomorrow.

No big deal, right? I've borrowed from you in the past and always paid you back.

Better still, how about if I repay you in a week? I promise I won't forget.

Interested? I didn't think so. Assuming the guy remembers to pay you back, next year's $5 repayment won't buy as much as $5 today.

That's the time value of money at work. To be an effective IT manager, you must take the time value of your precious budget dollars into account. This is especially important in large systems computing, where project time is measured in months and years, not days and weeks, and costs can run into the millions. Time value of money can become an important strategic factor in planning and presenting project proposals. Let's first examine the fundamentals of this concept.

One Proposal, Four Perspectives
Let's suppose you have $1,000 in unused project funds lying around that your company has asked you to manage for the coming year. You have two smart options to make your boss happy: Invest it (in a certificate of deposit or the stock market) or loan it to me and I'll pay you $1,040 a year from now.

Of course, you could do nothing—the equivalent of putting money under your mattress. If you choose this option, inflation will leave you with less buying power a year from now—not a good way to curry favor with the boss.

There are four ways to evaluate your two smart options. You can consider:

  • the amount of money you'll have a year from now

  • the interest rate you'll earn

  • the value today of the money you'll have next year

  • how much more (or less) you'll make by making the loan.

It's important to understand that though all four perspectives lead to the same conclusion (loaning me the $1,000 is a better investment), each has a different focus.

Why learn four different perspectives? Because you never know which one will be used to evaluate your IT project. Different managers (and companies) prefer to use different perspectives. Perhaps your manager is comfortable looking at the amount of money your project will bring in next year. Your CFO, however, is probably trained to look only at the value today of next year's payments, consider investment alternatives, and examine interest rates and rate forecasts.

Knowing which perspective is important to your approving authority will help you to tailor your project proposal to the appropriate audience. That, in turn, improves its chances of getting the green light.

Before we look at each of these ways of evaluating your options, a word of warning. The first two perspectives are straightforward. They're probably the way you've been used to thinking about investment strategies. The last two ask you to think backward—a more challenging perspective.

#1: How Much Money Will You Have in a Year?
In the first perspective, you focus on how much cash you'll have one year from today if you choose either of the "smart" options.

This is the easy part. If you'll give me that $1,000, I'm offering to pay you $1,040 exactly one year from now. I've always paid back loans to you on time, so there's probably little risk in loaning me the money.

Banks will probably pay you 3 percent interest on a $1,000 certificate of deposit (CD). So if you invest that $1,000 in a bank, you'll wind up with $10 less than I'm proposing for my loan. Of course, CDs are virtually risk-free.

But by looking at the amount you'll receive a year from now, it's clear that I'm offering you a better deal with my loan ($1,040) than you'll get with a CD ($1,030).

#2: What Rate of Return is Offered by Each Option?
This time, instead of looking at the amount of money you'll have after one year with each option, you'll look at the interest rate each investment will earn.

Again, this is a pretty common method for evaluating investment options, and you probably do this all the time without realizing it. If Bank A offers a CD for 3 percent and Bank B offers 3.1 percent for the same $1,000 CD investment, then it's obvious that Bank B is the way to go. The rate each investment provides is called the Internal Rate of Return (IRR).

In this perspective on the time value of money, you simply ask, what return does each investment offer?

I've made the math for this example very simple. In fact, you can probably just look at the numbers and the answers will pop out at you. But let's go through the exercise anyway, because investments in the real world will never be quite this tidy.

We know that a 3 percent CD offers a 3 percent return, so we know that its IRR is 3 percent. We need to compare this with the rate earned by a $1,040 loan repayment made in a year on a $1,000 investment.

To calculate the IRR, you must find the (interest) rate that solves this equation:

Investment = Future payment / (1 + rate)

Thus, we need to know what rate makes this equation true:

1000 = 1040 / (1 + rate)

You can use trial and error to compute the rate, look up the value in an IRR table (in many accounting books), or use Excel's IRR function (see "Calculating IRR in Excel").

In any case, the answer is 4 percent:

1000 = 1040 / (1.04)

So your choices from this perspective are: Do you take an investment with an IRR of 3 percent (the CD) or my proposed loan with an IRR of 4 percent? Obviously in this case, my offer wins.

That 3 percent rate is commonly called the discount rate—the rate you know you can reasonably achieve. When you're managing money for your company, you'll soon learn that any investment that beats the discount rate should be seriously considered. Any investment with an IRR below the discount rate should be ignored.

Calculating IRR in Excel

If you haven't got an Internal Rate of Return (IRR) table handy, you'll find Excel's IRR function easy to use.

The syntax of the IRR formula is:

IRR(money flow, guess)

By money flow, I mean the money out (investments, expressed as negative numbers since it's an outflow) and back in (paybacks, expressed in positive numbers). Guess is an optional parameter; your guess as to the IRR gives Excel a starting point, making the calculation slightly faster. It's completely optional.

For the money flow parameter, you can include the investments and paybacks directly, or use an Excel range. I prefer using a range, because I usually enter income and outgo in a table.

For the loan in our example, enter

A1: -1000
A2: 1040

And in cell A3 enter the formula:


The result: 4 percent.

If you prefer to enter the money flow directly, the formula would be:


Should you enter a guess, you might start by using the discount rate:

=IRR("-1000,1040", 3%)

The result will still be the same: 4 percent. Your guess simply helps reduce the number of iterations Excel must make to calculate the IRR.

Calculating PV in Excel
To calculate PV of a future loan payment, use the PV function. The syntax is:

PV(rate, number of periods, payment amount)

This assumes your loan will be paid in equal amounts over the period of the loan. In our example, the formula is:

PV(.03, 1, 1040)

The discount rate is 3 percent (represented as .03) per period, there is one period, and you'll receive $1,040 one period later. In this case, a period is one year. But the result (-1009.71) is negative! Excel's PV function is interpreted as the money you'd pay out to receive $1,040 one period later. Therefore, to find the value of $1,040 in the future, just take the negative of the function's value:

-PV(.03, 1, 1040)

To calculate the net present value, simply subtract the original cost:

-PV(.03, 1, 10401) - 1000

The result ($1,009.71 - $1,000.00) is $9.71.



#3: What's the Value Today of Each Option?
Instead of looking at the amount of money you'll have in a year as in Perspective #1, look at the money from today's point of view. This forces us to think in an unfamiliar way: The value today of each investment's future payment. This is more commonly called Present Value (PV for short). We'll compare how much $1,030 (the amount of the CD will pay you in a year) to how much my loan repayment ($1,040) is worth … today.

The PV computation requires two pieces of information: The future payment amount and the discount rate we discussed earlier (the minimum rate you'd need to earn in order to make some other investment than a CD).

To compute the present value, we "discount" the dollars received a year from now by the discount rate. (Aha! That's why it's called the discount rate!) The formula for a single-period (in our example, a one-year investment) is:

Future $ / (1 + discount rate)

Let's look at the PV of each investment option. If you invest in the CD, the present value of your investment is:

$1,030 / (1 + .03) = $1,030 / 1.03 = $1,000

This may seem kind of silly. After all, if you have $1,000 to invest in a CD, the value of your $1,000 today is $1,000. I'll grant you that.

Using the same formula, we calculate the present value of my loan payment to you:

$1,040 / (1 + .03) = $1,040 / 1.03 = $1,009.71

This also makes sense when you think of it this way: If you invest $1,009.71 (the present value) at 3 percent (the discount rate), you'll have $1,040 (the future payment) a year from now. Thus, the present value of my $1,040 payment is $1,009.71. That's how much my loan repayment is worth to you today.

PV answers the question: How much would I have to invest at the discount rate in order to earn the future payment? In this case, you would have to invest $1,009.71 at 3 percent to get $1,040.

You'll often hear the present value amount described as being in "today's dollars." Thus, my loan payment is worth (has a present value of) $1,009.71 in today's dollars.

So now that you have these two present values, what do you do with them? Just answer one easy (whew!) question: Which would you rather have today: $1,000 or $1,009.71? You don't care what the interest rate is, or how much you'll have a year from now. The question is simply this: Looking at the investment using today's dollars, which investment offers you the most money today? Because $1,009.71 (the present value of my loan) is more than $1,000 (the present value of a CD), you'll still be inclined to loan me the money.

Here's yet one more way to think of the choice: In order to get the same amount ($1,040) a year from now, you'd have to invest $1,009.71. But you only have $1,000. Therefore, I'm offering you the payback that you'd need $1,009.71 to get. You invest $1,000 but get the benefit as though it were $1,009.71 invested in a CD. Thus, you'll be ahead of the game if you make me the loan.

#4: The Net Present Value
Net present value (NPV) is a variation of the present value, so if you understand PV, NPV is pretty simple. To calculate the NPV, calculate the present value of future payments, then subtract investments. If the result is positive, the investment should be considered. If it's negative, you'll want to pass.

In our case, there's just one future payment (when I pay off the loan), and the investment is the $1,000 that you loan me.

The NPV of the loan is the present value of my payment less your initial investment:

PV($1,040) - $1,000
$1,009.71 - $1,000.00 = $9.71

Because the loan has a positive NPV, the investment is worth your consideration. You'll make $9.71 more from my loan (measured in today's dollars) than you'd make from investing in a CD.

Bottom Line
PV and NPV are the financial standards, and are especially preferred when calculating the costs and benefits of multi-year projects. In fact, PV and NPV are critical when investments (project expenses) occur during various times along a project's course, and paybacks (benefits) may be spread over several years.

Must Read Articles