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### Course: Finance and capital markets>Unit 1

Lesson 5: 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?

• 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.
• 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.
• 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.
• Thank you! This is what I'm stuck on and reviewing the comments for some clarification. PV, as I've learned in my textbook, asks "how much do I need to pay today to get \$X in the future?" so the lower the PV in this case, the better! It has been years since Sal made this video; hoping either he or someone in his team can respond to this!
• 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?
• I have a question. I used the 'Future Value' method for calculating the amounts in scenario 3. Following is what I arrived at.
For the \$100 now, after 2 years at 5% interest rate annually (5% since we are depositing the money for 2 years), we would have \$110.25 at the end of 2 years.
For the \$110 after 2 years, we don't have to do any calculations since the amount is already at the end of 2 years.
For the \$20 now, \$50 after 1 year, \$35 after 2 years, we have, \$20 at the end of 2 years = \$22.05 (5% interest rate annually for 2 years), \$50 at the end of 1 year = \$50.5 (1% interest rate annually since we are depositing the \$50 for only 1 year) and \$35 at the end of 2 years, which gives us a total of \$107.55.
This would suggest that the first option is the best one in this scenario.
Where did I go wrong in my approach to the problem?
• What is the different between Interest rate and Discount rate?
• discount rate is the interest rate that you assume reflects the return you could get on an alternative investment whose risk is similar to the cash flows whose PV you are trying to calculate
(1 vote)
• I am confused on FV of option 1 in scenario 3:

my understanding is it's given 2 different rate 1% year 1 and 5% year 2 so the calculation of FV should be 100*(1.01) for year 1 = 101 then 101*(1.05) for year 2 = 106.05 instead of taking 100*(1.05)^2 = 110.25

• Just want to point out if the video is inaccurate, Sal should make a correction to avoid people learning in mistake. For option 1 in scenario 3, the FV2 at the end of Year 2 should be using the formula below:

FV1 = PV0(1 + i) which i = 1%, PV0 = 100 here
FV2 = FV1(1 + i) which I = 5%, PV1 = 101 here
• I am working on a present value problem on excel and find myself confused with the answer. The problem statement is: What will be the present value of \$500 payments on a loan if you pay each month for 5 years at a 1.0% rate each month. I have used the built in PV function and come out with the answer of \$22,702.3 which i believe is the correct answer. I presume that my question is 'what does this value represent?'

Is this saying that \$30,000 (\$500*(12 months *5 years)) will be worth \$22,702.3 in 5 years due to the time value of money?

I have also done a future value calculation with the same numbers and got \$41,243.2.
• Can you please let me know the next video if available. The one that talks about PV with the different kind of risks
• present value given an interest rate and a growth rate