# What is the difference between the net present value and the internal rate of return?

## How to calculate present value with discount rate in Excel

Net Present Value (NPV)To understand Net Present value (NPV), one need to understand the concept of Present value (PV).

n n In simplest of terms Present value (PV) is inverse of future value.

We all have at some point or other calculated the future value.

Remember asking yourself this question u201cIf I invest \$100 today for 2 years with interest rate of 10% what amount I will get after 2 years.

u201d That is future value of \$100 after 2 years.

n n\$100 would become \$121 after 2 years at 10%n nSo the future value (2 years) of \$100 is \$121n nNow how about asking this question u201c How much I need to invest today to get \$121 after two years with an interest rate of 10%.

Off course we know the answer, which is \$100.

This is Present value (PV).

n nSo the present value of \$121 for two years is \$100.

n nThe mathematical formula for PV isn nPV= Ct / (1+r)^t Where C is cash flow, r is interest rate and t is the time period.

n nNow if you invest \$100 each year for 3 years, and after 3 years you get \$330, will you consider the investment to be profitable.

It looks profitable as you have invested \$300 to get \$330.

n nTo compare the cash inflow and cash outflow, both need to be at same time.

Lets bring both your investments and your cash inflow after 3 years on same time that is today.

n nSo the present value of your investment will ben nPV = 100/(1+0.

1) + 100/(1+0.

1)^2 + 100/(1+0.

1)^3n = 90.

9 + 82.

6 + 75.

1 = \$248.

6n nSo in todays time, you want to get more than \$248.

6 to have a profitable investment.

Lets see if \$330 what you got after 3 years is worth more than your investment todayn nPV= \$330/(1+0.

1)^3 = \$247.

9n nSo when brought to same time, which is today, you are investing \$248.

6 to get \$247.

9.

The difference is called NPV.

In this case it is negative and sure this is not a profitable investment.

n nClearly more the NPV for an investment, more profitable the investment.

If the NPV is negative, the investment will lead to a loss.

,,Table above shows, how a NPV is calculated.

In the above table NPV of \$3549 shows that project will be profitable & can be taken.

n nInternal Rate of Return (IRR)n nIn the table above we have mentioned, the assumed discount rate as 10%.

So at assumed rate of discount of 10%, NPV is \$3549.

Now the IRR is the discount rate at which the NPV will be equal to zero.

n nThere are number of methods to calculate IRR.

First is to keep on changing the value of discount rate until you get NPV as zero.

Second is to use the IRR function in the excel sheet.

Third is to get NPV for 3 to 4 values of discount rate and plot it on the graph & then join (or extrapolate) the dots to read out the discount rate at which NPV is zero.

n nSignificance of IRR: In the above example (in the table), if you calculate, the IRR is 19%.

That is at 19% discount rate the NPV is zero.

The significance of IRR is that if the opportunity cost of the project is lesser than IRR, the project should be accepted.

n nThe Difference in NPV & IRRNow look at both the statementsn n1) If NPV is positive, project should be acceptedn2) If Opportunity cost is lower than IRR, project should be accepted.

,Arenu2019t we saying the same thing as if opportunity cost is lesser than IRR, NPV will be positive and hence the same thing as the first statement.

n nWell yes, both are same things but both NPV and IRR conveys different message to the investors.

,To understand this see, Look at below table,,nIf you have to accept one project, Which project will you accept.

If you follow IRR, you will choose Project A and get 108% return on your investments but will end up making \$10727 when you can make \$12000 with project B.

,So now you think you should prefer NPV over IRR, when hold your thoughts to see another example below.

,,So which project will you choose? If you consider only the NPV, you would tend to choose project B with larger NPV of \$1066 compared to \$728 for project A.

But do you think that is a wiser decision? You are choosing to invest \$100,000 to have a profit of \$1066 over investing just \$1000 to get profit of \$728 over same period.

Actually here the wiser decision would be to choose IRR for making a decision.

,Although both NPV & IRR are capital budgeting techniques, both have advantages and disadvantages.

Relying solely on one can make you take wrong decisions.

NPV & IRR are not to be used in isolation but together to make a decision about capital budgeting.

## Discount rate formula

You go for buying a shirt and you see two prices written ,1.

MRP 1000n2.

Discounted price 800,So u figure out Discount is 200 ,Discount %= (Discount/MRP)*100,= (200/1000)*100,= 20 %,Thanks for A2A

## Discount rate formula Excel

Net Present Value (NPV)To understand Net Present value (NPV), one need to understand the concept of Present value (PV).

n n In simplest of terms Present value (PV) is inverse of future value.

We all have at some point or other calculated the future value.

Remember asking yourself this question u201cIf I invest \$100 today for 2 years with interest rate of 10% what amount I will get after 2 years.

u201d That is future value of \$100 after 2 years.

n n\$100 would become \$121 after 2 years at 10%n nSo the future value (2 years) of \$100 is \$121n nNow how about asking this question u201c How much I need to invest today to get \$121 after two years with an interest rate of 10%.

Off course we know the answer, which is \$100.

This is Present value (PV).

n nSo the present value of \$121 for two years is \$100.

n nThe mathematical formula for PV isn nPV= Ct / (1+r)^t Where C is cash flow, r is interest rate and t is the time period.

n nNow if you invest \$100 each year for 3 years, and after 3 years you get \$330, will you consider the investment to be profitable.

It looks profitable as you have invested \$300 to get \$330.

n nTo compare the cash inflow and cash outflow, both need to be at same time.

Lets bring both your investments and your cash inflow after 3 years on same time that is today.

n nSo the present value of your investment will ben nPV = 100/(1+0.

1) + 100/(1+0.

1)^2 + 100/(1+0.

1)^3n = 90.

9 + 82.

6 + 75.

1 = \$248.

6n nSo in todays time, you want to get more than \$248.

6 to have a profitable investment.

Lets see if \$330 what you got after 3 years is worth more than your investment todayn nPV= \$330/(1+0.

1)^3 = \$247.

9n nSo when brought to same time, which is today, you are investing \$248.

6 to get \$247.

9.

The difference is called NPV.

In this case it is negative and sure this is not a profitable investment.

n nClearly more the NPV for an investment, more profitable the investment.

If the NPV is negative, the investment will lead to a loss.

,,Table above shows, how a NPV is calculated.

In the above table NPV of \$3549 shows that project will be profitable & can be taken.

n nInternal Rate of Return (IRR)n nIn the table above we have mentioned, the assumed discount rate as 10%.

So at assumed rate of discount of 10%, NPV is \$3549.

Now the IRR is the discount rate at which the NPV will be equal to zero.

n nThere are number of methods to calculate IRR.

First is to keep on changing the value of discount rate until you get NPV as zero.

Second is to use the IRR function in the excel sheet.

Third is to get NPV for 3 to 4 values of discount rate and plot it on the graph & then join (or extrapolate) the dots to read out the discount rate at which NPV is zero.

n nSignificance of IRR: In the above example (in the table), if you calculate, the IRR is 19%.

That is at 19% discount rate the NPV is zero.

The significance of IRR is that if the opportunity cost of the project is lesser than IRR, the project should be accepted.

n nThe Difference in NPV & IRRNow look at both the statementsn n1) If NPV is positive, project should be acceptedn2) If Opportunity cost is lower than IRR, project should be accepted.

,Arenu2019t we saying the same thing as if opportunity cost is lesser than IRR, NPV will be positive and hence the same thing as the first statement.

n nWell yes, both are same things but both NPV and IRR conveys different message to the investors.

,To understand this see, Look at below table,,nIf you have to accept one project, Which project will you accept.

If you follow IRR, you will choose Project A and get 108% return on your investments but will end up making \$10727 when you can make \$12000 with project B.

,So now you think you should prefer NPV over IRR, when hold your thoughts to see another example below.

,,So which project will you choose? If you consider only the NPV, you would tend to choose project B with larger NPV of \$1066 compared to \$728 for project A.

But do you think that is a wiser decision? You are choosing to invest \$100,000 to have a profit of \$1066 over investing just \$1000 to get profit of \$728 over same period.

Actually here the wiser decision would be to choose IRR for making a decision.

,Although both NPV & IRR are capital budgeting techniques, both have advantages and disadvantages.

Relying solely on one can make you take wrong decisions.

NPV & IRR are not to be used in isolation but together to make a decision about capital budgeting.

## Net present value PDF

Quantitative finance is the use of mathematical techniques to determine actions and predicted outcomes related to trading stocks, bonds and other instrumentsu2014-options, swaps, etc.

,Mathematical techniques can range from something as simple as finding the Net Present Value of a promised return to using long tailed distribution math for deciding the right mix of fixed income investments vs stocks in a retirement portfolio.

,Here is an example:

## Discount factor vs discount rate

1.

If you have money today, you can also do stuff with it to make more money out of it.

For example you could put it in a bank account and it could turn into more money.

,2.

Its also better to have money now than in the future because you dont know what will happen in the future.

Money might not be worth anything.

You might not even be alive.

,These are two good reasons why its better to have money today than in ten years.

The discount rate is a measure of this difference between the value of \$1 today (better) vs.

\$1 in the future (worse).

,If you were just thinking about reason #1, you could derive a discount rate by thinking about how much money you could earn by putting \$1 in the bank.

Lets say you have a super magical bank and \$1 will turn into \$10 in 10 years.

So that means each \$1o in ten years is the same as \$1 today.

,If you add a little bit of reason #2 to the mix, you might value the \$1 today even more relative to the \$10 in the future.

Because who knows what is going to happen?