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Present value

# Present value 4 (and discounted cash flow)

Discounted cash flows are a way of valuing a future stream of cash flows using a discount rate. In this video, we explore what is meant by a discount rate and how to calculated a discounted cash flow by expanding our analysis of present value. Created by Sal Khan.

## Want to join the conversation?

• Khan claims that with the last discount rate (5% for 2y, 1% for 1y) you would be best off going with the 3rd option because the PV of the 3rd option =\$101.25 where PV of the 1st option =\$100. We can apply all the same variables and find that the two year future value (FV) of the 3rd option =\$20*1.05^2+\$50*1.01+\$35=\$107.55, but the FV of the 1st option =\$110.25. If we look at PV then the 3rd option is better but if we look at the FV then the 1st option is better. Shouldn't we decide based off the FV? •   HankyUSA, this is a great question, but your (and the rest of the responders') logic is slightly off. Think about what you are really saying in your example:

I will invest \$20 at a 5% interest rate STARTING NOW
I will invest \$50 at a 1% interest rate STARTING NOW
I will invest \$35 at a 0% interest rate STARTING NOW

Do you see the error? You are assuming a timeline that starts all of your investments at the current time. But of course that isn't true. You won't have access to the \$50 for a whole year and the \$35 for a whole two years. Therefore you can't use addition to simply sum \$20, \$50*1.01, and \$35*(1.02^2) because \$50 isn't the present value it's the FUTURE VALUE in one year's time. Similarly, \$35 is what the value WILL BE in 2 years time. This conundrum is the entire reason for using the discounting method.

The correct logic is to ask the question: How much money would I need today to have \$50 in a year at a 1% interest rate. That is exactly the formula Sal gave (\$50/1.01). And the same goes for \$35 in two years at 2%.

Another way to think about it is that the present value as Sal calculated is \$101.25. Using the FV interest calculation given in a previous video we have (1.05)^2 multiplied by \$101.25 (the present value of the investment) which gives us \$111.63. Clearly more than the \$110.25 in option 1. Hope this helps.
• Why was inflation not included in the discount rate? •  Sal is going to address inflation in a later video, I think. Presently he is not dealing with inflation because it would complicate the topic that he is trying to teach.
• Why does Sal do compound interest? When do you use compound interest? • Towards the end where Sal says that Option 3 would be the best ( the one where he works out discount rate in 1st yr=1% and 2nd yr=5%) and says if you understand why this is actually better than Choice 2 you understand this very well......i can see that Choice 3 is better but don't understand why that choice is better :S can someone help me understand this? • To understand why, it is helpful to also understand why option 2 is worse. You are offered \$110 after 2 years, but the discount rate for 2 years is much bigger (5%) than it is for 1 year. The full amount has to be discounted at the higher rate, and you have to do it twice, to get the present value of \$99.77. That 5% discount rate really eats away at the \$110.

In the third option, the PV is split three ways, Unlike in option 2, you are discounting only \$35 at the higher rate, a fraction of the full amount. Then, you are discounting a much higher fraction of the total -- \$50 -- at a much lower discount rate of 1%, so you "lose" less money from the \$50 by discounting.
• Is inflation and the value of money reflected in the exercise? • Inflation basically is the value of money, domestically at least. The exercise does NOT include those figures, sort of. If by value of money, you mean value of liquid assets, no. In some cases in life, it is more worth while to have \$150 dollars today than \$20,000 in 10 years. That sort of emotional/societal value is not included.

Now what I think you're really trying to get at is inflation and the physical value of money. While it is not directly involved, it can easily be understood and inferred.

Let's assume that in Country A, inflation is always rising by a steady 2%. All you have to do is adjust your discount rate (the gross interest rate). If you were going to make 5% a year on the deal, you will now be making 3%. This is the REAL interest rate (Gross adjusted for inflation, gives you the real buying power of the currency).

Lets apply this to Sal's example:
Instead of offering 1% the bank offered you 2%. But there was 1% inflation that year. You would use the 1.01 discount rate in the denominator. Although the bank advertises 2%, and you will receive 2%! Your money will be able to only purchase 1% more, because the average prices will rise as well.
In CD number 2, the bank offered you 8%. But the was 1% inflation in year one and 2% inflation in year two! Your REAL interest rate is 5% that is the 8% adjusted for inflation.

You really will go from having \$100 to \$108. But in year two because of inflation \$108 dollars will only buy as much \$105 dollars bought when you made the investment.

I know this is actually complex. So I'll check back in a few days to see if I need to re explain anything.
• Why would you get a higher interest rate if you locked up your money longer? Is this beneficial for the banks or beneficial for the customers? This concept doesn't make sense to me.
(1 vote) • When a lending institution is planning its cash flows putting the flexibility in their control as opposed to yours is beneficial to them so they offer you a benefit (higher interest rate) to entice you to give them that flexibility. Leave behind Sals Govt. Bonds storyboard for a second and think of a bank. A bank may wish to improve its balance sheet by increasing the volume of car loans it offers. This will require the bank to make loans with terms of 3 -5 years. One of the ways they might raise the money needed to make these loans is to sell CD’s. CD’s are similar to bonds in that they are a way consumers and institutions can lend banks money. If the bank issues a bunch of 1 year CD’s it’s not in a very good position to make those auto loans. However if it issues a bunch of 5 year CD’s and keeps selling those year after year they can increase the number of auto loans they are able to sell. So it makes sense for them to offer you an incentive to keep that in the bank longer. For another answer to your question watch the video on Fractional Reserve Banking.
• Can I just clarify that if you agree to 'lock in' your money for two years you get 5% interest for both years 1 and 2? Not just 1% in the first year then 5% in the second? Why is this? What would happen if you just choose to lend it to the government for 1 year? Would you only receive \$101 and not receive anything in year 2 or would it be 1% over the two years? • Hello Sal, in this video when you are calculating PV backwards from the FV you always choose the highest PV as the best option. This is seen in the summary given at the 6-minute mark. However, if you are calculating the PV backwards from the highest FV wouldn't you want your PV to be the lowest possible so that you have to invest the lowest amount possible and yet have high returns? Meaning you want to have the widest gap between the PV and FV since that would indicate a greater return. • What is the different between Interest rate and Discount rate?  