Think & Done

Can you answer this question, in evaluating capital projects, the decisions using the NPV methond and IRR method may disagree if

• the projects are independent
• the cash flows pattern is unconvential
• the projects are mutually exclusive
• both b and c

Hi Dawn

the answer is both b and c

The reasoning behind it goes like this that when evaluating mutually exclusive projects, you would have a situation where the size of the two projects is in drastic contrast to each other. and the other reason being that erratic timing of the cash flows can cause the same problem.

Project-A:
   Year.1: $1.2million
   Year.2: $1.9million
   Year.3: $3.1million

Hi Sujai

I would assume that you need to find the IRR or internal rate of return from these cash flows You need to provide me with the initial cash outlay or initial expense at t=0 You have only provided 3 net cash flows beginning at Year 1, you would need to provide the outgoing cash flow at Year 0. Once I have that information, I would be happy to provide you a numerical solution and help you with the MS Excel function too.

Definition of irr, Formula of irr, explanation of the formula,

Hi Vuyolwethu Ngxetwane

You asked for a definition of IRR along with formula and an explanation of the formula

Definition of Internal Rate of Return

IRR is the investor's required rate of return at which the Net Present Value is zero. Think of it this way, if you were to judge the financial viability on an investment whereby you had the initial cash outlay and the expected net cash flows, you know your cost of capital or the discount rate. Now you would need to find the rate of return that will help you decide whether to accept this project or reject it. That is where IRR comes in handy, this rate or return helps you decide whether you should invest in the project or reject it. So you ask how does this help. Well to start off with if the IRR turns out to be higher than your cost of capital ( yielding a positive NPV ) you would make money off the investment. If the IRR turns out to be lower than your cost of capital then the investment is losing proposition since this will yield a negative NPV . If the IRR is the same as the cost of capital or the discount rate the NPV will be zero and no loss or profits are expected.

Formula for Internal Rate of Return

Explanation of Internal Rate of Return Formula

IRR formula is more like an equation which sets equal the initial investment to the present value of the net cash flows. The IRR variable i is found in each of the terms in the denominator. What it actually is the rate at which the discounted net cash flows equal the initial cash out lay. The present value formula to discount an amount R at interest rate i for n periods is R / (1+i)^n

We sum up all the discounted cash flows at a rate that leads to both sides of the equation to be equal. It is not easy to solve this equation with algebraic manipulation (it is virtually impossible to separate the interest rate i from other variables). There exists a mathematical procedure called Newton's method to find the roots but that requires knowledge of advanced calculus. Instead we resort to trial and error method to find the solution for IRR.

Say we had an initial expense of Rand. 100,000 and expected four cash inflows at the end of each of the next four years in the amounts of Rand 50,000 Rand 40,000 Rand 30,000 Rand 10,000

You can go through the attached images for the three step procedure I used to find IRR for this investment project. Keep in mind the answer we arrive at is a close approximation of the actual internal rate of return which you can compute with a financial calculator like Wall Street IRR.

Internal Rate of Return calculation at 10 Percent

Internal Rate of Return calculation at 20 Percent

Linear Interpolation to find Internal Rate of Return

How to calculate internal rate of return on difference finance options provided by bank's as well as leasing company

Hi Kashif

To calculate IRR you would need to have a series of cash flows. For example if you were looking in to different finance options by a given bank in Pakistan such as Habib Bank Ltd, you would need to put together the cash out flow and series of net cash flows

Cash out flow or initial cash outlay is the money going out at t = 0 which is followed by a series of net cash flows. Initial cash outlay is a debt amount and the expected net cash flows may be either negative or positive depending on the difference between any credit and debit amounts

Once you have all the cash flows you could use MS Excel's IRR function

You may type in these cash flows in the A column , and if there were 12 net cash flows and an initial cash outlay, you would type in the following formula

=IRR (A1:A13)

This will give you the internal rate of return. You could compare the IRR from several options you are considering, usually one compares the IRR to cost of capital or the discount rate. The highest IRR which is greater than the cost of capital will be an ideal one. But making a decision solely on the basis of IRR is a flawed approach, you would need to consider other metrics to get a bird's eye view, these include:

• NPV
• MIRR
• Profitability Index
• Discounted Payback Period

how to calculate irr for pjocet worth 50m

Hi Rosli

If that is the cost of the project, you need to provide the benefits in form of cash inflows without cash inflows, we aren't able to find IRR since we need an initial expense followed by a series of net cash flows

From my calculations i realized that my customer from a specific investment has irr 164,58% and i would like to explain that in a following way :

If you have an irr 164.58% by putting a specific money to this investment i could take for a loan a rate bigger than 7% cause this investment it will be attractive to you otherwise...something like that , but i lost it.

Hi Tsilfidou Georgia

An IRR of 164,58% is rather unusual.
Are you sure you computed the IRR correctly?
And if you were to take some money off this investment and expect to pay off a loan at an interest rate higher than 7%, in theory it would have worked but as you say you lost the money. That leads me to believe that your calculation of IRR was incorrect.
How much money did you lose?

can i send you my calculations?

Hi There
Sure send me the calculations, is it in MS Excel file ?
I will have a look at it and will respond to you

yes..it is in excel file , i will send it to you right now...thanks...

Hi Tsilfidou Georgia

Hi There
I looked at the file
You have written off the loan from expenses and did not include its amount -44,864 in calculating IRR and NPV
Your IRR is 4.67%
And your NPV is -4,057.62
Obviously you lost money in discounted amount of -4,057.62

I understand what you say but i borrow someone with this loan and he has to pay off in 25 years , why i have to calculate all of the amount at the begining, i remind you that this is the irr for my customer who take a loan of 45000euros and he will receive 7700 euros every year for this amount, actually i substract the payment of the loan to find out the money that left from his investment, why i have to substract all the loan (45000) and not the yearly payment?
Thanks

Hi Tsilfidou Georgia

The total loan amount is 45000EUROS and which is paid back in yearly amounts of 7700EUROS ( the principal and interest amount.) each year
But the initial expense of 45000 EUROS is at time t=0 and must be included as a whole when computing IRR and NPV

Hi, I want to know what exactly is IRR in layman's terms. For example, if I invest $10,000 for a period of 5 years at an IRR of 10%. What is the absolute return. Is it $15000 (Return component $5000 + plus Investment of $10,000). Is it the correct way to infer or is there some other method. Kindly let me know through an example.
Thanks a lot.

Hi Srinivas

The terms IRR refers to investor's required rate of return which has specific meaning in terms of capital budgeting Usually when there is an cash out flow or initial expense followed by series of cash inflows, you would want to know at what rate the investment will yield a net present value of zero

See the first illustration in the attached MS Excel worksheet, where we have an initial investment of $10,000 that follows 5 cash inflows at the end of each of the next 5 years in the amount of $2638. These cash flows -10000, 2636 , 2636 , 2636 , 2636 , 2636 yield an IRR of 10% and NPV is zero. Thus even though the total cash flows were $13190 our investment didn't yield any profit at 10%. As when we discounted the cash flows in terms of t=0 we only regained the initial investment. Thus if our cost of capital or discount rate (at which we could have invested this money else where ) was less than 10%, then it be meaningful to invest in this project

If you were simply to say that you invested $10,000 and some one promised you in return $15,000 in five years time then your rate is 8.45% as illustrated in the last example in attached file

If you were to invest $10,000 in a bank savings account that promised 10% interest rate and you kept the money in the bank locked up for 5 years than at the end of 5th years your total investment is worth $16488 where $6488 is the interest you earned. See the illustration in the middle section of the attached sheet

Year   Project 1        Project 2
0       -1,250,000        -1,250,000
1       250,000              350,000
2       350,000              350,000
3       450,000              350,000
4       500,000              350,000
5       750,000              350,000

Cost of Capital 15%

What is the IRR and which project should be accepted

Hi Nino

IRR for Project 1 is 20.13%

IRR for Project 2 is 12.38%

As our cost of capital is 15% which is lower than IRR of 20.13% for Project 1, thus project 1 should be accepted as is evident that at a cost of capital of 15%, Project 1 has a positive NPV of $186,683

As for Project2, its IRR is 12.38% which is less than our cost of capital of 15% thus project 1 should be rejected as is evident that at a cost of capital of 15%, Project 2 has a negative NPV of -$76,746

Acceptance Criteria for IRR

At IRR the net present value is zero, and as IRR goes above the cost of capital it yields a positive NPV, and when IRR goes below the cost of capital it yields a Negative NPV. We accept projects when IRR for the specific project is above the cost of capital

I am attaching a MS Excel WorkSheet that shows the IRR and NPV Calculations for Project 1 and Project 2 using the built in IRR and NPV functions.

Keep in mind if you were to compute IRR without a financial calculator or MS Excel, it will be tedious job as there is no straight forward formula to compute IRR. In such a case we resort to trial and error method using Linear Interpolation.

If you would like to see a solution of this problem with Trial and Error method, I will create one for you, let me know.

Frost Company is evaluating the purchase of a rebuilt spot-welding machine to be used in the manufacture of a new product. The machine will cost $170,465, has an estimated useful life of 7 years, a salvage value of zero, and will increase net annual cash flows by $33,880. (Round your answer to 0 decimal places, e.g. 52.)

What is its approximate internal rate of return?

Hi Olga

The IRR for this investment is 9%

Since the salvage value is zero, and there is no tax expense thus we use the cash outlay of $170,465 for the Year 0 and $33,880 as net cash flows from Year 1 to Year 7. You can see the solution with the use of IRR function in MS Excel

Reason Or proper comment when & why we have to calculate or the conditions that we are being forced to calculate IRR for any upcoming projects or investment?

Hi Ashish Gupta

IRR is one of the six different DCF or Discounted Cash Flow techniques we use to evaluate the monetary health of an investment proposal. IRR which stands for internal rate of return is often called the investor's required rate of return, this is so as it gives us the rate at which the Net Present Value for the cash flows is zero. If the IRR turns out to be less than the cost of capital, the NPV will be negative thus incurring a loss. If IRR is higher than the cost of capital this will result in a positive NPV thus we will profit from investing in the project.

We should accept the project if cost of capital or discount rate is lower than the IRR, but we shouldn't just rely solely on the IRR to make the decision, we should look at other metrics in conjunction with IRR such as Discounted Payback Period which will tell us the number of years required to recoup the initial investment. We can get a ratio for comparison of profitability ratio or index which will let us see which one of the projects provide with higher benefits

Your small business has the opportunity to purchase used equipment. It will cost $50,000 for the equipment and another $15,000 to refurbish it for production. This equipment should increase production by 20% over the next 5 years, which will lead to an extra $14,000 each year in profits. Should you purchase the equipment? Why or why not?

Hi Dennis Nowell

IRR comes out to 2.52% thus if your cost of capital is less that 2.52% then it will be a profitable investment

internal rate of return

Year   Project
0       $100,000
1       32,000
2       32,000
3       32,000
4       32,000
5       32,000

Every time I enter a guess into excel to determine the internal rate of return after two years I receive something like #NUM.I have followed the examples provided by excel and still cannot determine the rate. Is the guess always 10%?

Hi Denise Gurley

The cash outflow in year 0 needs to have the minus sign as it is a negative cash outflow.

The Guess is an optional value, so you get the answer when you don't even use it.

I am attaching a MS Excel Worksheet with the calculation and as you can see the IRR is 18.03% regardless of what you type in for the guess

internal rate of return

-50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
100
6

calculate the internal rate of return for these cashflows? discount rate is 5%

Hi Abena

Your answer for IRR is 100%

See the attached MS Excel Worksheet for calculations

An initial outlay of 10,000 resulting in a cash flow of 1993 at the end of each year for the next 10 years, determine the IRR

Hi Debbie

IRR = 15.01%

See the attached MS Excel Worksheet for calculations

an initial outlay of 10,000 resulting in a free cash flow of 2,054 at the end of each year for the next 20 years determine what the internal rate of return on the project.

Hi Debbie

IRR = 20%

See the attached MS Excel Worksheet for calculations

an initial outlay of 10,000 resulting in a free cash flow of 2,843 at the end of each year for the next 5 years determine what the internal rate of return on the project.

Hi Debbie

IRR = 13%

See the attached MS Excel Worksheet for calculations

NPV,PI, and IRR Calculations

Fijisawa Inc is considering a major expansion of its product line and has estimated the following free cash flows associated with such an expansion.The initial outlay associated with the expansion would be $1,950,000, and the project would generate free cash flows of $450,000 per year for six years. the appropriate required rate of return is 9%.

Calculate the net present value
Calculate the profitability index
Should this project be accepted?

Hi Debbie

NPV = $68,663

PI = 1.04

IRR = 10%

Since the IRR is greater than the rate of return, thus the project yields a positive NPV and a profitability index of greater than 1

We should accept the project given that any other project we are comparing it with does not have a NPV greater than this one has.

See the attached MS Excel Worksheet for NPV, and profitability index calculations