Present Value (PV)

In the previous section of the Present Value (Basic), I explained how to derive a present value. Here, let me go a little deeper on it and tell you what those numbers actually mean.

In short, the difference between the amount you receive in future and the present value represents the sum of interests you have forgone by not receiving cash today. So, in case of Case 2, the difference is $13.7 ($100 in Year 5 - $86.3 present value). Keep this number in mind.

Now, for Case 1, because you are receiving $100 today and depositing it in a bank with 3% interest for 5 years, you can enjoy total of $15.9 interests as shown below and not forgoing any interest:

On the other hand, in Case 2, you are receiving $100 in Year 5, not today, so you are not able to enjoy that $15.9 interest. In other words, at the end of Year 5, you are saying “damn…I have forgone the $15.9 worth of compound interest because I received cash later…”.

Now, with the present value formula I posted in the previous section, you can also find out the present value of the “forgone interest” by discounting that $15.9 (because $15.9 is the amount you are looking at Year 5). And, the present value of that forgone $15.9 interest is…..$13.7.

Doesn’t this number ring any bell? Yes! This is the same as the difference between the $100 in Year 5 and $86.3 present value.

So, what’s happening here is that, if you receive $100 in Year 5, you now know that you are going to miss $13.7 worth of interest on which you could also gain compound interest. Hence, by subtracting that $13.7 from $100, you get $86.3, which is the present value of $100 receiving in Year 5.

Well. Do you remember there was another quote that I mentioned in the earlier present value session:

“It’s better to pay out later than earlier”

Given what you’ve learned up to here, you can validate it with the same exercise: convert them into present values and compare. But this time, because we are now talking about payment (cash outflow), unlike the sections so far on cash receipts (cash inflow), you need to use negative signs.

For simplicity, let me reuse the Case 1 and Case 2, but this time with negative signs.

Case 1 (cash outflow ver.)

What’s happening here is that all the figures (cash flow) are the same as the previous exercise, but this time all in negatives. In Case 1, you are “paying out” $100 today, and in Case 2, you are paying out $100 in Year 5.

You might wonder “if you are paying out today, why is there an ending balance in Year 5 with even larger number?”. Well, this does not mean that you pay $100 and you also pay additional $15.9 through the course of 5 years. Rather, this $15.9 can be interpreted as “an amount you could have earned from compound interest through 5 years IF you did not payout $100 today”. In other words, because you are paying out cash earlier, you have forgone an opportunity to get benefits of compound interest.

To support that idea, let’s take a look at Case 2. You are paying out $100 in Year 5, you have not forgone any opportunity for compound interest. Hence, the ending balance remains the same, $100.

Then, how much benefit have you forgone in Case 1? Let the present value work it out for you.

While in the cash receipt (cash inflow) exercise, the PV of Case 1 was higher than Case 2 ($100 v. $86.3). However, here, in the cash payment (cash outflow) exercise, the PV of Case 1 is lower than Case 2 (-$100 v. -$86.3).

As I mentioned, the payment is earlier in Case 1 (today) compared to that of Case 2 (Year 5). Therefore, under Case 1, you are forgoing a benefit of compound interest because you don’t have any balance in your bank account from Year 0 on which you could have earned compound interest, whereas you are retaining that $100 in your account until Year 5, so are able to benefit from the compound interest. And the difference of $13.7 is, yes, that benefit you have forgone.

Let me summarize here. Because of the time value of money concept, cash is more valuable when received earlier and paid out later. Why? Because if you receive cash earlier, you have longer duration to enjoy compound interest. If you pay out earlier, you have less balance in the account on which you could have enjoyed compound interest.

I hope you understand the point.