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

Lesson 5: Present value

# Introduction to present value

The video explains the concept of present value in finance. Present value helps compare money received today to money received in the future. To find present value, we discount future money using a discount rate (like 5%). This helps decide which option is better: getting money now or later. Created by Sal Khan.

## Want to join the conversation?

• Can someone help me to understand how can sal suddenly came up with 1.05? I know 5% is 0.05 but where is 1 number came from? It tried to understand all of this but stuck just because i cannot figure it out where 1 come from.. Thanks for the help!
• What Dhananjay said. It's like if you add the tip in a restaurant, the tip amount is, say 20%, but what happens to the bill when tip is added in is that the bill is now 120% of what it was. In Sal's example, the Present Value is the bill, and a tip gets added on so you multiply by a number greater than one (1+ 20%) to get the future value.
• How did you get that interest rate of 5%? What about the inflation value?
• Here, we do not need to consider the inflation value, since we are comparing the future value of both sum.
It would be interesting to have the inflation values, but they would be useless.
• what is the meaning of "discount rate"? is that different from the meaning of yield?
• The discount rate is the rate at which you could otherwise invest your money if you took the \$100 today instead of \$110 in a year. So if you can only get 5% yield on your money investing in a risk free asset such as gov't bonds, you would need to invest \$104.76 now to get \$110 in a year, which means it is a better deal to take the \$110 in a year, rather than the \$100 now. If they offered even a penny more than \$104.76 to you today, you should take it because investing at 5% yield will give you slightly more than \$110 in a year.
• What is the risk of lending money to a risky bank?
• The risk is not getting it back!
• I just don't grapple this PV concept. 104.76 is not the present value in my mind because it will only become that after one year.
• After the year, the value of the money will be \$110. Think of 104.76 as the amount you would have to invest at 5% interest to get to \$110 a year from now.
• In the case of comparing a present value with future value, should Present Value always be determined excluding other variables or is it important to take into account inflation, etc. when calculating present value. If so, what other factors besides inflation should be considered?
• To calculate present value you need a forecast of the future cash flows, and you need to choose an appropriate interest rate. A lot of things can go into both of those.
• Are we also assuming that the interest rate will be fixed too? If the interest rate fluctuates this will change the present value won't it?
• yes, it will. We do not need to assume a fixed rate, although it often makes sense to do that, since the various risk free rates are fixed over specific terms. In other words, if you have a 30 year project, you can evaluate it today against the 30 year fixed treasury rate. But you don't have to. You could use the 10 yr rate for the first 10 yrs of cash flows and then a different rate for the last 20. Probably won't make much difference. PV seems really precise and scientific, and on paper it is, but in practice there's a lot of guesswork and estimation involved. There are large uncertainties in both the future cash flows and the future discount rate.
• I am assuming that he chose the 5% interest rate at random, my question is, what is a reasonable interest rate to expect from a bank in the present day (2012)?
• I think I understand your question as - 'Why is it that the rate of interest is always lower when we invest compared to when we borrow?".
My take is that obviously, the other party (Bank in general) needs to make a profit by giving comparatively lower interests to investors, and collecting comparatively higher interest from borrowers, which helps them make the profit.

But, reading through the comments makes me believe there are higher interest returns on investments as well, but the risk involved gets higher as the interest rate increases.
(1 vote)
• I don't understand where the 5% rate comes from. Is there anyone could explain it for me?
(1 vote)
• The particular value of 5% was just chosen as an example. It could have been any number. Historically, "safe" returns of 5% were fairly typical (or a bit optimistic), so Sal used it in his calculations.
• Is the discount rate, for the most part, the standard bank interest rate?
• No, it's the rate that you would expect to get on an equally risky alternative investment.