We’ve already discussed what the time value of money (TVM) concept is and why it’s important. You may recall that it accounts for the different purchasing power of a dollar between two periods. As such, it allows you to translate multi-year cash flows into a standard denomination. Remember, on the surface it may seem fine to add cash flows generated over multiple years. In reality, you will be overestimating your income though. Knowing this, you must discount your cash flows accordingly so they can be compared in a common year’s dollar value.
Applying TVM to annuities and perpetuities.
It’s important to ensure that your cash flow projections are accurate. The TVM concept is especially relevant when it comes to dealing with annuities and perpetuities. In these cases, we are dealing with a stream of payments at some period(s) into the future. By incorporating the TVM concept, you will avoid overstating the value of these future payments. This is because TVM allows you to discount its value to today’s dollars and understand its true value in terms of today’s purchasing power.
Now we will show you how to apply it beyond just discounting back to present value or determine future values. Today we will apply it to annuities and perpetuities. In other words, the former case deals with a finite number of future cash flows, while the latter deals with an infinite number of payments into the future.
Conditions that must be met to use TVM here.
Just like our previous TVM applications, there are certain conditions that must be met here. They are almost identical to the future and present value techniques. These include:
Comparing payments over multiple periods: Multiple time periods must be involved that each present a transaction relevant to the calculation.
This implies that present and future cash flows are involved: We must be dealing with future and present cash flows since we are translating them into common dollars.
Relevant interest and inflation rates: These rates are necessary as they are what affect the true purchasing power of a dollar today versus at some point in the future.
A discussion of annuities.
Annuities represent a finite number of payments into the future at a given value. With annuities, you are essentially discounting each future payment. However, with each payment that’s further into the future (i.e. ahead several time periods) you must discount it back based on the corresponding amount. For example, if it’s one year into the future, you discount it one year. If it’s two years, then you discount it by two years. The same goes for three years and so on. Technically you can apply the present value formula for TVM as discussed in our
previous article to each payment period (discounting each by the appropriate factor) and then summing them. The alternative is this formula that we have for you. It will make it easier than the previous method we’ve just suggested. Here it is: FVA = PMT [(1+i) n- 1/i] FVA: Future Value of the Annuity PMT: Payment per Period i: Interest Rate n: Number of Periods
However, it should be noted that this formula assumes a constant discount rate year over year. Thus, if you want to use different discount rates for each year, then you will need to use the lengthier process previously described.
A discussion of perpetuities.
Perpetuities represent an infinite number of payments into the future of a given value. The logic here is very similar to that of an annuity, except that in this case, the stream of payments never end. Again, you can discount each year’s payment by the appropriate factor and then sum them. Or, we have a simplified formula that you can use which is even easier than the annuity one. However, keep in mind again that this assumes a constant discount rate year over year. Here it is:
Present Value of a Perpetuity = Payment / Interest Rate
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