NPV v IRR:Question

[S2000magician]

@blackjack21

@S2000magician

@blackjack21

K. Can you give an example where a project having a higher NPV had a lower IRR? In what scenario this might be possible?

Now that you know that it’s possible, you should open up Excel and play with it to come up with your own example; you’ll learn a lot more doing that than merely reading something that someone here writes.

Two projects cost $100,000 each. The first has cash flows of $30,000 at the end of each year for four years. The second has these cash flows at the end of each year (in order): $20,350, $40,350, $20,350, and $40,350. The cost of capital is 7%.

I’ll leave it to you to compute the NPV and IRR for each. Report back when you’re done.

The first project has NPV of ($11,964.42) and the second project has NPV of

($12,097.02)

Both have an IRR of 8%

Both of your NPVs are incorrect.

You need more decimal places on your IRRs: at least 2.

[blackjack21]

@S2000magician

@blackjack21

@S2000magician

@blackjack21

K. Can you give an example where a project having a higher NPV had a lower IRR? In what scenario this might be possible?

Now that you know that it’s possible, you should open up Excel and play with it to come up with your own example; you’ll learn a lot more doing that than merely reading something that someone here writes.

Two projects cost $100,000 each. The first has cash flows of $30,000 at the end of each year for four years. The second has these cash flows at the end of each year (in order): $20,350, $40,350, $20,350, and $40,350. The cost of capital is 7%.

I’ll leave it to you to compute the NPV and IRR for each. Report back when you’re done.

The first project has NPV of ($11,964.42) and the second project has NPV of

($12,097.02)

Both have an IRR of 8%

Both of your NPVs are incorrect.

You need more decimal places on your IRRs: at least 2.

I used the NPV funcion incorrectly.

NPV of first NPV of second

($95,715.33) ($100,001.70) 7.7138

7.6840

[blackjack21]

@blackjack21

@S2000magician

@blackjack21

@S2000magician

@blackjack21

K. Can you give an example where a project having a higher NPV had a lower IRR? In what scenario this might be possible?

Now that you know that it’s possible, you should open up Excel and play with it to come up with your own example; you’ll learn a lot more doing that than merely reading something that someone here writes.

Two projects cost $100,000 each. The first has cash flows of $30,000 at the end of each year for four years. The second has these cash flows at the end of each year (in order): $20,350, $40,350, $20,350, and $40,350. The cost of capital is 7%.

I’ll leave it to you to compute the NPV and IRR for each. Report back when you’re done.

The first project has NPV of ($11,964.42) and the second project has NPV of

($12,097.02)

Both have an IRR of 8%

Both of your NPVs are incorrect.

You need more decimal places on your IRRs: at least 2.

I used the NPV funcion incorrectly.

NPV of first NPV of second

($95,715.33) ($100,001.70) 7.7138

7.6840

NPV of first project is -95,715.33, IRR= 7.7138%

NPV of second project is -100,001.70, IRR= 7.6840%

[S2000magician]

@blackjack21

@blackjack21

@S2000magician

@blackjack21

@S2000magician

@blackjack21

K. Can you give an example where a project having a higher NPV had a lower IRR? In what scenario this might be possible?

Now that you know that it’s possible, you should open up Excel and play with it to come up with your own example; you’ll learn a lot more doing that than merely reading something that someone here writes.

Two projects cost $100,000 each. The first has cash flows of $30,000 at the end of each year for four years. The second has these cash flows at the end of each year (in order): $20,350, $40,350, $20,350, and $40,350. The cost of capital is 7%.

I’ll leave it to you to compute the NPV and IRR for each. Report back when you’re done.

The first project has NPV of ($11,964.42) and the second project has NPV of

($12,097.02)

Both have an IRR of 8%

Both of your NPVs are incorrect.

You need more decimal places on your IRRs: at least 2.

I used the NPV funcion incorrectly.

NPV of first NPV of second

($95,715.33) ($100,001.70) 7.7138

7.6840

NPV of first project is -95,715.33, IRR= 7.7138%

NPV of second project is -100,001.70, IRR= 7.6840%

Your NPVs are still wonky, but your IRRs are correct.

Excel’s NPV function is stupid: it assumes that the first cash flow occurs at time 1, not time 0. So you either have to omit the time 0 cash flow from the function (and add it outside the function), or you have to use all of the cash flows, then project the answer forward one time period (i.e., multiply by (1 + discount rate)).

Try it in your calculator, or do it long hand in Excel (i.e., don’t use the NPV function).

[blackjack21]

@S2000magician

@blackjack21

Cool! No IRR at all…That’s a new addition. When is it possible? Can you give an example?

The two problems with IRR – no IRR, or multiple IRRs – occur only with nonstandard cash flows. (Standard cash flows are: outflow at inception, all other cash flows are inflows. Nonstandard means that there are (net) outflows during the project, not just at inception.)

With that knowledge, you should be able to come up with a simple example of each, though it will take a bit of fiddling. The thing to do is create a set of cash flows in Excel – you can get an example with only 2 or 3 years, so don’t go wild – create a table of discount rates and use Excel’s NPV function to calculate the NPV for each discount rate, then plot NPV vs. discount rate. Finally, fiddle with the cash flows until the graph crosses 0 twice, and fiddle with the cash flows until the graph misses 0 completely.

If you have access to a copy of Schweser’s Mind Maps for Level I, they have examples in there.

Graph will cross zero twice with non standard cash flows.

I took the following cash flows:

-100000 20350 40350 -20350 40350

and the following “cost of capital”:

2.0000 7.0000 9.0000 11.0000 21.0000

NPV=0 around 6.5%, 10.5%, 15.5%

IRR calculated by using IRR function in Excel in this case comes out to be negative

Whew! It took me close to an hour to do this. I need to learn how to use Excel after L1 ends

[blackjack21]

@S2000magician

@blackjack21

NPV of first project is -95,715.33, IRR= 7.7138%

NPV of second project is -100,001.70, IRR= 7.6840%

Your NPVs are still wonky, but your IRRs are correct.

Excel’s NPV function is stupid: it assumes that the first cash flow occurs at time 1, not time 0. So you either have to omit the time 0 cash flow from the function (and add it outside the function),

I did exactly that after I googled. I used the cash flow (at time t=0) outside the formula for NPV. I was using the wrong cost of capital. The answers calculated were for a cost of capital of 2%.

For 7%, NPV of first project = (95,715.33)

NPV of second project = (96,776.18)

@S2000magician

or you have to use all of the cash flows, then project the answer forward one time period (i.e., multiply by (1 + discount rate)).

If Excel thinks that the first cash flow starts at t=1, shouldn’t I be discounting back my answer by (1+discn rate) instead of multiplying?

[S2000magician]

@blackjack21

@S2000magician

@blackjack21

NPV of first project is -95,715.33, IRR= 7.7138%

NPV of second project is -100,001.70, IRR= 7.6840%

Your NPVs are still wonky, but your IRRs are correct.

Excel’s NPV function is stupid: it assumes that the first cash flow occurs at time 1, not time 0. So you either have to omit the time 0 cash flow from the function (and add it outside the function),

I did exactly that after I googled. I used the cash flow (at time t=0) outside the formula for NPV. I was using the wrong cost of capital. The answers calculated were for a cost of capital of 2%.

For 7%, NPV of first project = (95,715.33)

NPV of second project = (96,776.18)

Your numbers don’t look reasonable. Think of it this way: at a discount rate of 0% the first project will have an NPV of $20,000 (just add up the numbers). You have an outflow of $100,000 and inflows of $120,000; you cannot get an NPV of -$96,000.

@blackjack21

@S2000magician

or you have to use all of the cash flows, then project the answer forward one time period (i.e., multiply by (1 + discount rate)).

If Excel thinks that the first cash flow starts at t=1, shouldn’t I be discounting back my answer by (1+discn rate) instead of multiplying?

No. It’s discounting the first cash flow (-$100,000) for one year, when it should be discounting it for zero years; you have to undiscount it one year (i.e., multiply by (1 + discount rate)) to get it back to where it belongs.

[blackjack21]

@S2000magician

@blackjack21

@S2000magician

@blackjack21

NPV of first project is -95,715.33, IRR= 7.7138%

NPV of second project is -100,001.70, IRR= 7.6840%

Your NPVs are still wonky, but your IRRs are correct.

Excel’s NPV function is stupid: it assumes that the first cash flow occurs at time 1, not time 0. So you either have to omit the time 0 cash flow from the function (and add it outside the function),

I did exactly that after I googled. I used the cash flow (at time t=0) outside the formula for NPV. I was using the wrong cost of capital. The answers calculated were for a cost of capital of 2%.

For 7%, NPV of first project = (95,715.33)

NPV of second project = (96,776.18)

Your numbers don’t look reasonable. Think of it this way: at a discount rate of 0% the first project will have an NPV of $20,000 (just add up the numbers). You have an outflow of $100,000 and inflows of $120,000; you cannot get an NPV of -$96,000.

I entered the rates in the wrong format. The first project’s NPV is 1616.34 and the second project’s NPV is 1656.43. This means that the calculations for the second excel exercise that you gave are wrong too. Phew! I’ll save that for another time.

@S2000magician

@blackjack21

@S2000magician

or you have to use all of the cash flows, then project the answer forward one time period (i.e., multiply by (1 + discount rate)).

If Excel thinks that the first cash flow starts at t=1, shouldn’t I be discounting back my answer by (1+discn rate) instead of multiplying?

No. It’s discounting the first cash flow (-$100,000) for one year, when it should be discounting it for zero years; you have to undiscount it one year (i.e., multiply by (1 + discount rate)) to get it back to where it belongs.

Yeah! I did miss that. Anyways, thanks a lot And thank you for being back. You are a life saver.

[blackjack21]

@S2000magician

@blackjack21

In a way, isn’t IRR too dependent on project size then? Like in this case, project size is small and IRR is large because the return is higher because of a smaller base.

You can say that, but it’s a poor way to look at it.

If you invest $1,000,000 in a stock and make a 1-year profit of $100,000 (and cost of capital is 5%), then your NPV is $47,619, and the IRR is 10%. If you invest only $1,000 in that stock (for a 1-year profit of $100), the NPV is $476, and the IRR is 10%. To say that the IRR depends on the profit versus the initial investment is true, but silly: you aren’t going to earn $100,000 on a $1,000 investment in this stock.

Yes. I get the drift on the importance of NPV now.

[exotichedge]

@blackjack21

@S2000magician

@blackjack21

In a way, isn’t IRR too dependent on project size then? Like in this case, project size is small and IRR is large because the return is higher because of a smaller base.

You can say that, but it’s a poor way to look at it.

If you invest $1,000,000 in a stock and make a 1-year profit of $100,000 (and cost of capital is 5%), then your NPV is $47,619, and the IRR is 10%. If you invest only $1,000 in that stock (for a 1-year profit of $100), the NPV is $476, and the IRR is 10%. To say that the IRR depends on the profit versus the initial investment is true, but silly: you aren’t going to earn $100,000 on a $1,000 investment in this stock.

Yes. I get the drift on the importance of NPV now.

Seems I am late… but everything seems good… as you have understood…

[blackjack21]

Thank you Exotichedge