# Introduction to present value | Interest and debt | Finance & Capital Markets | Khan Academy (2023)

## Introduction

A choice between money now and money later. Created by Sal Khan.

Missed the previous lesson? Watch here: www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial/present-value/v/time-value-of-money

Finance and capital markets on Khan Academy: If you gladly pay for a hamburger on Tuesday for a hamburger today, is it equivalent to paying for it today? A reasonable argument can be made that most everything in finance really boils down to "present value". So pay attention to this tutorial.

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## Video

We'll now learn about what is arguably the most useful concept in finance, and that's called the present value.

And.

If you know the present value, then it's very easy to understand the net present value and the discounted cash flow and the internal rate of return.

And, we'll eventually learn all of those things.

But.

The present value.

What does that mean? Present value.

So, let's do a little exercise.

I could pay you \$100, today.

So, let's say today, I could pay you \$100.

Or, and it's up to you, in one year, I will pay you-- I, don't know-- let's say in a year, I agree to pay.

You \$110.

And my question to you-- and this is a fundamental question of finance.

Everything will build upon.

This-- is which one would you prefer? And? This is guaranteed.

I guarantee you.

I'm, either going to pay you \$100 today, and there's no risk.

Even if I get hit by a truck or whatever.

This is going to happen.

The U.S.

government.

If the earth exists, we will pay you \$110 in one year.

It is guaranteed.

So, there's no risk here.

So.

It's just the notion of you're definitely going to get \$100 today in your hand, or you're, definitely going to get \$110 one year from now.

So.

How do you compare the two? And? This is where present value comes in.

What.

If there were a way to say, well, what is \$110, a guaranteed \$110, in the future? What if there were a way to say,? How much is that worth? Today? How much is that worth in today's terms? So.

Let's do a little thought.

Experiment.

Let's say that you could put money in the bank.

And these days.

Banks are kind of risky.

But.

Let's say you could put it in the safest bank in the world.

Let's say you , although someone would debate, you put it in government.

Treasuries.

Which are considered risk-free, because the U.S.

government, the Treasury, can always indirectly print more money.

We'll one day do a whole thing on the money supply.

But at the end of the day, the U.S.

government has the rights on the printing press, et cetera., It's more complicated than that.

But for those purposes.

We assume that with the U.S.

Treasury, which essentially is you're lending money to the U.S.

government, that it's risk-free.

So, let's say today, I could give you \$100 and that you could invest it at 5%, risk-free.

And, then, in a year from now.

How much would that be worth, in a year? That would be worth \$105 in one year.

Actually.

Let me write the \$110 over here.

So.

This was a good way of thinking about it.

You're like, OK.

Instead of taking the money from Sal a year from now and getting \$110.

If I were to take \$100 today and put it in something risk-free, in a year, I would have \$105.

So, assuming I, don't have to spend the money today.

This is a better situation to be in.

Right? If I, take the money, today, and risk-free, invest it at 5%, I'm, going to end up with \$105 in a year.

If you just tell me, Sal, just give me the money in a year-- give me \$110-- you're, going to end up with more money in a year, right? You're, going to end up with \$110.

And.

That is actually the right way to think about it., And, remember, and I, keep saying it over and over again, everything I'm talking about.

It's critical that we're talking about risk-free.

Once you introduce risk, then we have to start introducing different interest rates and probabilities.

And, we'll get to that eventually.

But I want to just give the purest example right.

Now.

But.

We still don't know what the present value was.

So to some degree when you took this \$100- and you said well, if I lend it to the government, or, if I lend it to a risk-free bank at 5%, in a year.

They'll give me \$105.

This \$105 is a way of saying what is the one-year value of \$100 today? What is the one-year-out value of \$100 today? So? What if we wanted to go in the other direction? If? We have a certain amount of money and we want to figure out today's value.

What could we do? Well, to go from here to here,? What did we do? We essentially took \$100 and we multiplied by-? What did we multiply? By-- 1 plus 5%.

So, that's 1.05.

So to go the other way, to say how much money.

If I were to grow it by 5%, would end up being \$110? We'll just divide by 1.05.

And.

Then we will get the present value.

And.

The notation is PV.

We'll get the present value of \$110 a year from now.

So, the present value of \$110, let's say in 2009.

It's, currently, 2008.

I, don't know what year you're watching this video in.

Hopefully people will be watching this in the next millennia.

But, the present value of \$110 in 2009.

Assuming right now, it's 2008, a year from now, is equal to \$110, divided by 1.05.

And.

Let's take out this calculator, which is probably overkill for this problem.

Let me clear, everything.

OK, so I want to do.

110 divided by 1.05 is equal to-- let's just round-- so it equals \$104.76.

So the present value of \$110 a year from now.

If we assume that we could invest money risk-free at 5%, if we were to get it today, -- let me do it in a different color just to fight the monotony--.

The present value is equal to \$104.76.

Another way.

To kind of just talk about.

This is to get the present value of \$110 a year from now, we discounted the value by a discount rate.

And, the discount rate is this.

Right.

Here we grew the money by, you could say, our yield.

A 5% yield or our interest.

Here we're discounting the money, because we're going backwards in time.

We're, going from year-out to the present.

And.

So this is our yield.

To compound the amount of money we invest.

We multiply the amount we invest times, 1 plus the yield.

Then, to discount money in the future to the present, we divided by 1, plus the discount rate--.

So this is a 5% discount rate-- to get its present value.

So.

What does this tell? Us? This tells us if someone's willing to pay \$110, assuming this 5%-- remember.

This is a critical assumption.

This tells us that if I tell you I'm willing to pay you \$110 a year from now, and you could get 5%-- so you could kind of say that 5% is your discount rate risk-free-- that you should be willing to take today's money, if today I'm willing to give you more than the present value.

So.

If this comparison were-- let me clear all of this.

Let me just scroll down--.

So let's say that today, 1 year.

So.

We figured out that \$110 a year from now.

Its present value is equal to--.

So the present value of that \$110-- is equal to \$104.76.

And.

That's because I used a 5% discount rate, and that's a key assumption.

This is a dollar sign.

I know it's hard to read.

What.

This tells you is that.

If your choice was between \$110 a year from now and \$100 today, you should take the \$110 a year from now.

Why is that? Because.

Its present value is worth more than \$100.

However.

If I were to offer you \$110 a year from now or \$105, today.

This, the \$105 today, would be the better choice.

Because.

Its present value, , right, \$105 today,- you don't have to discount it .

It's, today.

Its present value is itself.

\$105 today is worth more than the present value of \$110, which is \$104.76.

Another way to think about it.

Is, I could take this \$105 to the bank--.

Let's assume I have a risk-free bank-- get 5% on it.

And, then I would have-- what would I end up.

With-- I'd end up with 105 times: 1.05.

Equal to \$110.25.

So a year from now, I'd, be better off by \$0.25.

And I'd have the joy of being able to touch my money for a year, which is hard to quantify, so we leave out of the equation.

Anyway, I'll, see you in the next video.

## FAQs

### What is the present value for dummies? ›

Present value is the concept that states an amount of money today is worth more than that same amount in the future. In other words, money received in the future is not worth as much as an equal amount received today. Receiving \$1,000 today is worth more than \$1,000 five years from now.

What is the present value of a payment of \$100 to be made one year from today? ›

Present value is the value today of an amount of money in the future. If the appropriate interest rate is 10 percent, then the present value of \$100 spent or earned one year from now is \$100 divided by 1.10, which is about \$91.

What is PV in accounting? ›

Present value is the current worth of cash to be received in the future with one or more payments, which has been discounted at a market rate of interest.

What is the difference between present value and discounted cash flow? ›

The main difference between discounted cash flow vs. net present value is that net present value subtracts upfront year 0 costs (in actual dollars estimated) from the sum of the present value of the cash flows. The discounted cash flow method doesn't subtract these initial costs that include capital expenditures.

What is the easiest way to calculate present value? ›

The present value formula is PV=FV/(1+i)n, where you divide the future value FV by a factor of 1 + i for each period between present and future dates.

What is the rule of present value? ›

The net present value rule is the idea that company managers and investors should only invest in projects or engage in transactions that have a positive net present value (NPV). They should avoid investing in projects that have a negative net present value.

How much is \$100 dollars a month for 25 years? ›

You plan to invest \$100 per month for 25 years and expect a 10% return. In this case, you would contribute \$30,000 over your investment timeline. At the end of the term, your portfolio would be worth \$133,889. With that, your portfolio would earn around \$103,889 in returns during your 25 years of contributions.

How many years will it take \$100 to double in value at an annual interest rate of 10 percent? ›

For simple interest, you'd simply divide 1 by the interest rate expressed as a decimal. If you had \$100 with a 10 percent simple interest rate with no compounding, you'd divide 1 by 0.1, yielding a doubling rate of 10 years.

What is the value of \$1000 to be received in 5 years? ›

Summary: The present value of \$1,000 to be received in 5 years is \$548 if the discount rate is 12.78%.

What is an example of a present value problem? ›

For example, suppose you want to know the value today of receiving \$15,000 at the end of 5 years if a rate of return of 12% is earned. Another way of asking this question is: What amount would you need to invest today at 12% compounded annually in order to receive \$15,000 after 5 years?

### What is the present value in Excel? ›

Present value (PV) is the current value of an expected future stream of cash flow. Present value can be calculated relatively quickly using Microsoft Excel. The formula for calculating PV in Excel is =PV(rate, nper, pmt, [fv], [type]).

Is PV a financial function? ›

PV, one of the financial functions, calculates the present value of a loan or an investment, based on a constant interest rate. You can use PV with either periodic, constant payments (such as a mortgage or other loan), or a future value that's your investment goal.

What are the 3 discounted cash flow techniques? ›

Discounting cashflow methods
• Net present value (NPV) The NPV calculates the present value of all cashflow associated with an investment: the initial investment outflow and the future cashflow returns. ...
• Internal rate of return (IRR) ...
• Disadvantages of net present value and internal rate of return.

What is the math behind the DCF? ›

The discounted cash flow (DCF) formula is equal to the sum of the cash flow in each period divided by one plus the discount rate (WACC) raised to the power of the period number.

Why is present value important? ›

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.

What is the present value of \$100 to be deposited today into an account paying 8% compounded semiannually for 2 years? ›

How do we calculate the present value of the amount, assuming the interest rate is 8% per year compounded annually? The answer, \$85.73, tells us that receiving \$100 in two years is the same as receiving \$85.73 today, if the time value of money is 8% per year compounded annually.

How do you find the present value without a calculator? ›

PV = C / (1 + r) n
1. C = Future cash flow.
2. r = Discount rate.
3. n = Number of periods.

How do you manually calculate present value? ›

What is the formula for net present value?
1. NPV = Cash flow / (1 + i)^t – initial investment.
2. NPV = Today's value of the expected cash flows − Today's value of invested cash.
3. ROI = (Total benefits – total costs) / total costs.

What is 72 rule of present worth? ›

The Rule of 72 is a numerical concept that predicts how long an investment will require to double in worth. It is a simple formula that everyone can use. Multiply 72 by the annual interest generated on your savings to determine the amount of time it will require for your investments to increase by 100%.

What is the present value of 1000 due in 10 years? ›

Answer and Explanation: The calculated present value of \$1,000 due in 10 years is \$385.54.

### What is \$570 next year worth now at an interest rate of 10%? ›

Net Present Value (NPV)

Use an Interest Rate of 10% to work out the NPV. Money In: \$570 next year: PV = \$570 / (1+0.15)1 = \$570 / 1.15. PV = \$495.65 (to nearest cent).

How much will \$10 000 be worth in 30 years? ›

Over the years, that money can really add up: If you kept that money in a retirement account over 30 years and earned that average 6% return, for example, your \$10,000 would grow to more than \$57,000.

What will \$5,000 be worth in 20 years? ›

Answer and Explanation: The calculated present worth of \$5,000 due in 20 years is \$1,884.45.

How much to save a month to be a millionaire in 20 years? ›

Given an average 10% rate of return on the S&P 500, you need to save about \$1,400 per month in order to save up \$1 million over 20 years.

What is 5% interest on \$5000? ›

If you have \$5,000 in a savings account that pays five percent interest, you will earn \$250 in interest each year.

What is \$5000 invested for 10 years at 10 percent compounded annually? ›

The future value of the investment is \$12,968.71. It is the accumulated value of investing \$5,000 for 10 years at a rate of 10% compound interest.

How much interest will I earn on \$1 million dollars? ›

Bank Savings Accounts

As noted above, the average rate on savings accounts as of February 3rd 2021, is 0.05% APY. A million-dollar deposit with that APY would generate \$500 of interest after one year (\$1,000,000 X 0.0005 = \$500). If left to compound monthly for 10 years, it would generate \$5,011.27.

What is the future value of \$700 saved for 10 years at 8 percent? ›

700 ( ( 1 + 8 % ) 10 − 1 ) 8 % = 10 , 140.59.

What is the future value of \$1,500 after 5 years? ›

In this question, the initial investment is 1500, quarterly interest rate is 6%/4 = 1.5%, and there are 20 quarters in 5 years. Applying the formula, the future value is: 1500 ∗ ( 1 + 1.5 % ) 20 = 2 , 020.28.

What is the future value of \$1000 a year for five years at a 6% rate of interest? ›

Example 1: Calculate Future Value Using Simple Annual Interest. What is the future value of \$1,000 invested today in 5 years assuming 6% simple annual interest rate? The future value will be calculated using the future value formula using simple interest rate and will equal: \$1,000 * (1+(0.06*5)), or \$1,300.

### What are the disadvantages of present value? ›

The biggest disadvantage to the net present value method is that it requires some guesswork about the firm's cost of capital. Assuming a cost of capital that is too low will result in making suboptimal investments. Assuming a cost of capital that is too high will result in forgoing too many good investments.

How much would you have to deposit today to have \$10000 in five years at 6% interest discounted quarterly? ›

What is the future value of \$10,000 on deposit for 5 years at 6% simple interest? Hence the required future value is \$13,000.

What is the present value of \$84523 to be received or paid in 5 years discounted at 11% by table and factor formula? ›

The PV is calculated by discounting \$84,253 at 11% for 5 years, as shown below: Formula Snip: Thus, the PV is \$50,000.

Why is present value negative? ›

A negative net present value indicates an investment is earning less than the discount rate, but may be earning a positive rate. For example, if the cash flows are discounted by 12%, a slightly negative NPV could mean that the investment is earning 11%.

What is the difference between NPV and PV? ›

Net Present Value: An Overview. Present value (PV) is the current value of a future sum of money or stream of cash flow given a specified rate of return. Meanwhile, net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

How to use VLOOKUP in Excel? ›

1. In the Formula Bar, type =VLOOKUP().
2. In the parentheses, enter your lookup value, followed by a comma. ...
3. Enter your table array or lookup table, the range of data you want to search, and a comma: (H2,B3:F25,
4. Enter column index number. ...
5. Enter the range lookup value, either TRUE or FALSE.

What is the PV of a cashflow? ›

Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows.

How can you use the PV function to help with an investment? ›

PV, one of the financial functions, calculates the present value of a loan or an investment, based on a constant interest rate. You can use PV with either periodic, constant payments (such as a mortgage or other loan), or a future value that's your investment goal.

What is the present value of a loan? ›

The present value is the total amount that a series of future payments is worth now. For example, when you borrow money, the loan amount is the present value to the lender.

What is the 4 techniques for capital budgeting? ›

Payback Period, Net Present Value Method, Internal Rate of Return, and Profitability Index are the methods to carry out capital budgeting.

### What are the three 3 major types of cash flow? ›

There are three cash flow types that companies should track and analyze to determine the liquidity and solvency of the business: cash flow from operating activities, cash flow from investing activities and cash flow from financing activities. All three are included on a company's cash flow statement.

What are the two types of DCF? ›

The most common variations of the DCF model are the dividend discount model (DDM) and the free cash flow (FCF) model, which, in turn, has two forms: free cash flow to equity (FCFE) and free cash flow to firm (FCFF) models.

What are the 4 steps of DCF? ›

Steps in the DCF Analysis

Choose a discount rate. Calculate the TV. Calculate the enterprise value (EV) by discounting the projected UFCFs and TV to net present value. Calculate the equity value by subtracting net debt from EV.

What are the formulas used in DCF? ›

DCF Formula =CFt /( 1 +r)t

CFt = cash flow. It proves to be a prerequisite for analyzing the business's strength, profitability, & scope for betterment. read more in period t. R = Appropriate discount rate that has given the riskiness of the cash flows.

What is the difference between NPV and DCF? ›

The difference between discounted cash flow and net present value is that net present value (NPV) subtracts the initial cash investment, but DCF doesn't. Discounted cash flow models may produce incorrect valuation results if forecast cash flows or the risk rate are inaccurate.

What is present value vs future value for dummies? ›

Present value is the sum of money that must be invested in order to achieve a specific future goal. Future value is the dollar amount that will accrue over time when that sum is invested. The present value is the amount you must invest in order to realize the future value.

What is present value quizlet? ›

The present value is the value today of one or more future cash flows discounted to today at an appropriate interest rate.

What is present value vs value? ›

Present value is defined as the current worth of the future cash flow, whereas Future value is the value of the future cash flow after a certain time period in the future. While calculating present value, inflation is taken into account, but while calculating future value, inflation is not considered.

Should I use present value or future value? ›

Present value can take inflation into account, while future value typically does not. Present value can be useful to know if you're considering buying an annuity or selling one that you already own. Future value, meanwhile, can be a helpful tool for retirement planning.

Why is the present value important? ›

Importance Of Present Value

Present value allows a solid basis where you can assess the level of fairness of any financial liabilities or benefits at a future date. So for example, a future cash rebate discounted to present value could or could outweigh the downsides of having a higher potential purchase price.

### What does the rule of 72 have to do with the calculation of future values? ›

The Rule of 72 is a calculation that estimates the number of years it takes to double your money at a specified rate of return. If, for example, your account earns 4 percent, divide 72 by 4 to get the number of years it will take for your money to double. In this case, 18 years.

Is present value positive or negative? ›

A positive NPV indicates that the projected earnings generated by a project or investment—discounted for their present value—exceed the anticipated costs, also in today's dollars. It is assumed that an investment with a positive NPV will be profitable. An investment with a negative NPV will result in a net loss.

What are the types of present value? ›

9 Present Value Models
• net present value (NPV),
• internal rate of return (IRR),
• maximum (minimum) bid (sell),
• annuity equivalent (AE),
• loan formula,
• optimal term,
• replacement,
• incremental,

What is present value also known as? ›

In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation.

What is present value in Excel? ›

Present value (PV) is the current value of an expected future stream of cash flow. Present value can be calculated relatively quickly using Microsoft Excel. The formula for calculating PV in Excel is =PV(rate, nper, pmt, [fv], [type]).

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