Calculatinr IRR

R

runn0010

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  2. It is Jan 1, 2016 and Timco completed the project referenced in questions 4 and 5 above. The project went well. The company is now planning to make a special add-on investment that will enhance the usefulness of the new plane. The changes will cost $3 million in total, with the expenditure occurring at the end of the year three years from today. The changes will bring year-end after-tax cash inflows of $2 million at the end of the two succeeding years. It will then cost $.5 million to dispose of specialized waste generated by the project at the end of the 3rd year of operation.

My First question was about Npv which I figured out so now I have this question Im trying to solve which I know I have to solve the npv for

Year 0 Year 1 Year 2 Year 3
0 0 2 2.5

So I have to calculate for npv which is 2/1.11^2+2.5/1.11^3= 3.45

Now I have to solve for R which is





  2. What is the project's IRR? (2 marks)
 
runn0010 said:
  2. It is Jan 1, 2016 and Timco completed the project referenced in questions 4 and 5 above. The project went well. The company is now planning to make a special add-on investment that will enhance the usefulness of the new plane. The changes will cost $3 million in total, with the expenditure occurring at the end of the year three years from today. The changes will bring year-end after-tax cash inflows of $2 million at the end of the two succeeding years. It will then cost $.5 million to dispose of specialized waste generated by the project at the end of the 3rd year of operation.

My First question was about Npv which I figured out so now I have this question Im trying to solve which I know I have to solve the npv for

Year 0 Year 1 Year 2 Year 3
0 0 2 2.5

So I have to calculate for npv which is 2/1.11^2+2.5/1.11^3= 3.45

Now I have to solve for R which is





  2. What is the project's IRR? (2 marks)
Click to expand...
Can you please tell us the definition of IRR?
 
I might be wrong but from my interpretation of the question that you posted I would get the following cash flows and NPV...
Code: 
All figures are at end of year

               Year 0   Year 1   Year 2   Year 3   Year 4   Year 5   Year 6

Income          0        0        0        0        2        2        0
Change cost     0        0        0        3        0        0        0
Disposal cost   0        0        0        0        0        0        0.5

Total cash
flow (+ve=in)   0        0        0        -3       2        2        -0.5


NPV = -3/(1+r)^3 + 2/(1+r)^4 + 2/(1+r)^5 - 0.5/(1+r)^6      (equation A)
    = $0.043470 million ( if r=0.11 )
    = $43,470

I guess the r=0.11 comes from another part of the question that you didn't post?

--

I have never heard of IRR before today. The "internal rate of return", according to Wikipedia, is the value of r that gives NPV=0. So you can probably just use the "equation A" above to find a value of r that gives 0 NPV.

In other words there is no cost today. The first outlay comes at the end of year 3, which needs to be discounted back to a present day value using <cost>/(1+r)^3. This is taken into account in equation A.

ALTERNATIVELY they might want you to calculate what the IRR would be in three year's time (at the time of the first outlay) but I personally doubt it. I didn't see any statement like this on the Wikipedia page.
 
Do you understand NPV? That a dollar in the future is worth less than a dollar today (if interest rates are positive in the interim).

Imagine a scenario. $80 is invested today. In 5 years it has grown to be $100 (via an interest rate applied every year). So, in this case, the NPV of "$100 in 5 years" is only $80.

--

Anyway, I've plotted a graph of the total NPV given by "equation A". The NPV is 0 when r=0.127 (approximately). So I think that the IRR is 0.127 (or 12.7%).
 
runn0010 said:
Internal rate of return I can figure it out if the initial investment was at the beginning but because its at the end it throws me off
Click to expand...
That is not the definition of IRR. Please define Internal rate of return (IRR) for us.
 
Thanks guys I’ll try that out still unclear how you graph internal rate of return. But I’ll figure it out I have some more time tonight before it’s due if you have any other good links to help me understand let me know.
 
runn0010 said:
  2. It is Jan 1, 2016 and Timco completed the project referenced in questions 4 and 5 above. The project went well. The company is now planning to make a special add-on investment that will enhance the usefulness of the new plane. The changes will cost $3 million in total, with the expenditure occurring at the end of the year three years from today. The changes will bring year-end after-tax cash inflows of $2 million at the end of the two succeeding years. It will then cost $.5 million to dispose of specialized waste generated by the project at the end of the 3rd year of operation.

My First question was about Npv which I figured out so now I have this question Im trying to solve which I know I have to solve the npv for

Year 0 Year 1 Year 2 Year 3
0 0 2 2.5

So I have to calculate for npv which is 2/1.11^2+2.5/1.11^3= 3.45

Now I have to solve for R which is





  2. What is the project's IRR? (2 marks)
Click to expand...
Let's start by pointing out that you miscalculated the npv.

Admittedly, it is a badly worded problem. It is not completely clear if 2 million in positive cash flow is realized at the end of year 4 and again at the end of year 5 or if 2 million is received at the end of year 5. However, an investment that starts with a cash outflow of 3 million and then generates a net cash inflow 2 years later has a negative npv and a negative irr so that reading makes no sense.

You did not give a date at which the npv is calculated so it is impossible to calculate the npv because present values are always computed relative to a date.

In any case your computation is clearly wrong because the cash flow in the final year is 2 - 0.5 = 1.5 rather than 2.5 and you forgot to take the initial outflow of 3 into account at all.

As for the irr, they are frequently solvable only by numeric methods that require an initial guess and may generate multiple answers. This one can be solved using the quadratic formula.

Here is the equation

[MATH]\dfrac{-\ 3}{1 + r)^0} + \dfrac{2}{(1 + r)^1} + \dfrac{2 - 0.5}{(1 + r)^2} = 0 \implies[/MATH]
[MATH]-\ 3(1 + r)^2 + 2(1 + r) + 1.5 = 0.[/MATH]
If you solve that, what do you get for r. (You may find it helpful to do a u-substitution.)

If this is too mathy for you, excel will calculate an irr for you.
 
JeffM said:
Let's start by pointing out that you miscalculated the npv.

Admittedly, it is a badly worded problem. It is not completely clear if 2 million in positive cash flow is realized at the end of year 4 and again at the end of year 5 or if 2 million is received at the end of year 5. However, an investment that starts with a cash outflow of 3 million and then generates a net cash inflow 2 years later has a negative npv and a negative irr so that reading makes no sense.

You did not give a date at which the npv is calculated so it is impossible to calculate the npv because present values are always computed relative to a date.

In any case your computation is clearly wrong because the cash flow in the final year is 2 - 0.5 = 1.5 rather than 2.5 and you forgot to take the initial outflow of 3 into account at all.

As for the irr, they are frequently solvable only by numeric methods that require an initial guess and may generate multiple answers. This one can be solved using the quadratic formula.

Here is the equation

[MATH]\dfrac{-\ 3}{1 + r)^0} + \dfrac{2}{(1 + r)^1} + \dfrac{2 - 0.5}{(1 + r)^2} = 0 \implies[/MATH]
[MATH]-\ 3(1 + r)^2 + 2(1 + r) + 1.5 = 0.[/MATH]
If you solve that, what do you get for r. (You may find it helpful to do a u-substitution.)

If this is too mathy for you, excel will calculate an irr for you.
Click to expand...
teacher states that the intial investment is in year 3 with 2 million dollar inflows occurring after for two years and then the cost of clean up
 
runn0010 said:
teacher states that the intial investment is in year 3 with 2 million dollar inflows occurring after for two years and then the cost of clean up
Click to expand...
OK then. That is what made sense. I have given you the equation.
 
JeffM said:
Let's start by pointing out that you miscalculated the npv.

Admittedly, it is a badly worded problem. It is not completely clear if 2 million in positive cash flow is realized at the end of year 4 and again at the end of year 5 or if 2 million is received at the end of year 5. However, an investment that starts with a cash outflow of 3 million and then generates a net cash inflow 2 years later has a negative npv and a negative irr so that reading makes no sense.

You did not give a date at which the npv is calculated so it is impossible to calculate the npv because present values are always computed relative to a date.

In any case your computation is clearly wrong because the cash flow in the final year is 2 - 0.5 = 1.5 rather than 2.5 and you forgot to take the initial outflow of 3 into account at all.

As for the irr, they are frequently solvable only by numeric methods that require an initial guess and may generate multiple answers. This one can be solved using the quadratic formula.

Here is the equation

[MATH]\dfrac{-\ 3}{1 + r)^0} + \dfrac{2}{(1 + r)^1} + \dfrac{2 - 0.5}{(1 + r)^2} = 0 \implies[/MATH]
[MATH]-\ 3(1 + r)^2 + 2(1 + r) + 1.5 = 0.[/MATH]
If you solve that, what do you get for r. (You may find it helpful to do a u-substitution.)

If this is too mathy for you, excel will calculate an irr for you.
Click to expand...
In your formula why do you use the exponent of 2 and none for year two of the last year with the cost I figured it would be ^3 for the initial investment then ^4 then ^5 at the end because the initial investment is the third year then the next two years are the fourth and fitth
 
Cubist said:
Do you understand NPV? That a dollar in the future is worth less than a dollar today (if interest rates are positive in the interim).

Imagine a scenario. $80 is invested today. In 5 years it has grown to be $100 (via an interest rate applied every year). So, in this case, the NPV of "$100 in 5 years" is only $80.

--

Anyway, I've plotted a graph of the total NPV given by "equation A". The NPV is 0 when r=0.127 (approximately). So I think that the IRR is 0.127 (or 12.7%).
Click to expand...
Can I see your formula
 
runn0010 said:
In your formula why do you use the exponent of 2 and none for year two of the last year with the cost I figured it would be ^3 for the initial investment then ^4 then ^5 at the end because the initial investment is the third year then the next two years are the fourth and fitth
Click to expand...
Are you talking about the irr formula? I do see that I made a slight error. The -0.5 comes a year after the last cash inflow I guess. That generates an ugly cubic. I probably misread the problem because I thought that they would give you a reasonable equation to solve.

The point is that you can start the irr calculation at any date. It always simplifies to the initial cash flow being discounted by (1 + r)^0, which equals 1.

If we start it now, we have, as you thought,

[MATH]\dfrac{0}(1.11^0} + \dfrac{0}{1 + r)^1 + \dfrac{-\ 3}{(1 + r)^2} + \dfrac{2}{(1 + r)^3 + \dfrac{2}{(1 + r)^4} + \dfrac{-\ 0.5}{(1 + r)^5} = 0 \implies[/MATH]
[MATH]\dfrac{-\ 3}{(1 + r)^2} + \dfrac{2}{(1 + r)^3 + \dfrac{2}{(1 + r)^4} + \dfrac{-\ 0.5}{(1 + r)^5} = 0 \implies[/MATH]
[MATH](1 + r)^2 * \left ( \dfrac{-\ 3}{(1 + r)^2} + \dfrac{2({(1 + r)^3 + \dfrac{2}{(1 + r)^4} + \dfrac{-\ 0.5}{(1 + r)^5} \right ) = (1 + r)^2 * 0 \implies[/MATH]
[MATH]\dfrac{-\ 3}{(1 + r)^0} + \dfrac{2({(1 + r)^1} + \dfrac{2}{(1 + r)^2} + \dfrac{-\ 0.5}{(1 + r)^3} = 0.[/MATH]
That is where I would normally start. That leads to

[MATH](1 + r)^3 * \left ( \dfrac{-\ 3}{(1 + r)^0} + \dfrac{2({(1 + r)^1 + \dfrac{2}{(1 + r)^2} + \dfrac{-\ 0.5}{(1 + r)^3} \right ) = (1 + r)^3 * 0 \implies[/MATH]
[MATH]-\ 3(1 + r)^3 + 2(1 + r)^2 + 2(1 + r)^1 - 0.5 = 0.[/MATH]
Now you can solve that by using the cubic formula, the Newton-Raphson method, or excel.

The answer I get from excel is r approximately equals 12.7%.

Let's check..

[MATH]\dfrac{-\ 3}{1.127^0} +\dfrac{2}{1.127^1} + \dfrac{2}{1.127^2} + \dfrac{-\ 0.5}{1.127^3} \approx 0.[/MATH]
I have to tell you that I have never thought that the irr calculation makes much sense. It's not the math that is at fault; it is the economic assumption behind it. The fact that it may give multiple answers should be enough to indicate that it has little to do with reality. Of course, you have to learn it to pass. Then you can forget all about it.
 
I am asking why are we discounting the the last two cash inflows as year 1 and 0 if the investment is being adjusted for year 3, The question states they are succeeding so that means aftwards.
 
runn0010 said:
I am asking why are we discounting the the last two cash inflows as year 1 and 0 if the investment is being adjusted for year 3, The question states they are succeeding so that means aftwards.
Click to expand...
My goodness, I did not discount the two positive cash flows by exponents of 1 and 0, but by exponents of 1 and 2, because they come 1 and 2 years respectively after the first cash flow. IRR calculations do not have to be present dated. They can be dated relative to the first cash flow in time, whether it is positive or negative.

I actually showed you mathematically that you can do it your way or my way, and they are mathematically identical.

I don't think you understand the logic of irr. Net present value computes a discounted value as of some particular date. It is typically as of the date the first cash flow occurs. If you choose a different date, you will get a different value (unless the value is zero). Because the irr calculation focuses on a zero net present value, you can discount zero by anything, and it is still zero. The irr calculation is thus independent of date. You can pick any date you want, and, so long as you are consistent, you will get the same answer.
 
runn0010 said:
Can I see your formula
Click to expand...

I used the "equation A" as written in my first post on this thread. This is it:-

NPV = -3/(1+r)^3 + 2/(1+r)^4 + 2/(1+r)^5 - 0.5/(1+r)^6

For IRR, NPV=0.

JeffM has given several methods for solving this type of equation. Another method, if you have a graphing calculator/ app you can plug in:-

-3/(1+x)^3 + 2/(1+x)^4 + 2/(1+x)^5 - 0.5/(1+x)^6
Substitute "x" for "r" since most graph plotters expect y=<expression in x>

Where this graph crosses 0, the x value is approximately 0.127. Obviously r=x. You can zoom for extra accuracy.
 
Cubist said:
Where this graph crosses 0, the x value is approximately 0.127. Obviously r=x. You can zoom for extra accuracy.
Click to expand...

NOTE there is another solution at r = -1.67833 ( minus 167% ).

You should assume the solution where r>0 is correct, unless people are starting to store their money under their mattresses :)
 
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