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Previously, we talked about future value, where we saw that if you invest 100 dollars today, you

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will get more money in the future.

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Correspondingly, if someone promises to give you hundred dollars in the future, the present value

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of that is less than hundred dollars.

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In this lecture, we are going to discuss the concept behind present value.

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In this lecture and throughout this course will denote present value by Bebe.

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Now, I can say that Bibi is that initial sum of money, which, if I invest today at the best possible

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risk free investment rate, will then turn into hundred dollars.

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Let me highlight the important times in the last line I just said.

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BP is the initial investment.

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And I'm putting it in the risk free, risk free means that I am certain that I will get that return.

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I said best possible risk free, because there are several types of risk free opportunities, it could

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be saving the money as a deposit in a bank.

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It could be a fixed deposit or government bond and many more such opportunities.

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But we are choosing the one with the highest rate of return.

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So I suppose the best option available to you at the risk free rate is a fixed deposit, which is giving

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you eight percent return.

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Then the present value of this hundred dollar will be a hundred, divided by one plus zero point zero

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eight, which is for the interest rate.

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Then the present value comes to be ninety two point six.

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This means that having hundred dollars after one year is like having ninety two point six dollars today

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and making a fixed deposit out of it.

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Now, why are we calculating the present value, we calculate the present value to evaluate the investment

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opportunity.

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Generally, if the present value of the future cash flows is more then the investment you are doing

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today.

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Then the investment option is considered as a good option.

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And if you have two investment options with different amounts and periods of return.

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You can compare them also using the present value.

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For example, suppose you have these two investment options option and option B.

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And both of them, you are investing a thousand dollars in the beginning.

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And the first option, you are getting 250 dollars for the next five years.

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And in the second option, you're getting 600 dollars, but for the next two years only.

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The best possible interest rate that you can get is 10 percent.

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Now, which of these two options is the better option for investing your thousand dollars?

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For this, we will calculate the present value of the five future cash flows.

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For the first year, it is 250, divided by one plus zero point one race to the Power-One.

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Zero point one, because it is 10 percent interest and power, one because it is the first year.

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For the second year, the power will be to 438, the power will be three and so on.

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We add all these future cash flows and subtract the initial investment that we do in this investment

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opportunity, the initial investment is done at year zero.

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So there is no discounting of this money.

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When we calculate this, the present value comes out to be negative to two point three.

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This means that it is better to investors thousand dollars at 10 percent interest rate and the best

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risk free opportunity that you have.

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So whichever opportunity, for example, if it is a fixed deposit and it is giving you 10 percent interest

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rate, it is better to put your thousand dollars there than investing in this option A.

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Now, let us look at option B.

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The calculation is same.

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The only difference is that the payment is for two years and it is of six hundred dollars.

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We discounted using the present value formulas and subtract the initial investment out of it, so the

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net present value that we get is forty one point three.

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This is positive, which means that this investment opportunity is better than the best risk free opportunity

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that you have.

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So this option is a good investment opportunity.

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And out of option, and B, also, whichever option gives you a higher present value, that is the better

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option.

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Not that theoretically, there is no difference between present value or net present value.

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But often in software tools, the pre function and the NPV function handle different types of scenarios.

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So even though they are actually the same thing, softwares may use these terms differently.

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So in the letters, we will be using Bibi and Bibi interchangeably.

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NPV is a very important concept, and it is often used for the purpose of valuation, such as valuation

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of a company or valuation of a customer and many such things.

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So you must ensure that you understand the concept as well as learn its implementation in the software

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tool.

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I'll summarize the counterpart here.

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So NPB or Pewee is the amount of money that if you invest today at the best available risk free rate.

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Is equivalent to the expected future returns from the investment.

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If NBP is positive, it means that it makes more sense to invest the money in that opportunity instead

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of putting the money in the best available risk free option.

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When you have two or more investment options, whichever has positive and higher NPV is the better option

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available for investing.

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Now, let's check out the implementation and modeling of NPB in our software.