Mr Moffat, on this Q3 for June 2010-OKM, part (c(iii)), highlights the issue of several IRRs in a cashfow. But I cannt just get around it. One cash flow can only have one IRR even if some cashflows are negative. I can not imagine a situation where there would several IRRs from a cashflow. Any assistance on this matter will be highly appreciated.

Remember that the IRR is not actually a return, it is simply that rate of interest at which the NPV is zero.

For a ‘normal’ project, the higher the cost of capital, the lower the NPV (and vice versa). So if we have an IRR of (say) 15% we can say that if the cost of capital is less than 15% then the NPV will be positive and therefore we should accept, whereas if the cost of capital is more than 15% then the NPV will be negative and therefore we should reject. Usually there is no problem, there is simply one IRR (or break-even).

However, this ‘works’ because most projects involve one investment at the beginning followed by inflows, and as with any investment the greater the interest that has to be paid, the more inflows are needed to make it worthwhile.

The problem occurs when the signs of the cash flows change. For example, suppose an investment requires an outflow now of $19000, gives an inflow of $45900 in 1 years time, and then requires another outflow of $27350 in 2 years time. You will find that the NPV will be zero at both 7% and at 35% (don’t worry – you would not be expected to calculate multiple IRR’s in the exam, but you can check me by all means 馃檪 ) The reason that this is happening is that over the first year we are investing (as usual) and the NPV will fall with higher interest; however over the second year it is the other way round in that we receive money and then we have to pay out, and so for that bit of it the NPV will fall with lower interest. If you were to calculate the NPV at lots of interest rates (1%, 2% 3% etc.) and put them on a graph then you will find that the NPV starts off being negative, then it increases and becomes positive, but that then it will start to fall and eventually become negative again. The curve will cross the axis at both 7% and 35% (so two IRR’s). The NPV will be positive (and we should therefore accept) if the cost of capital is between 7% and 35%, but if it is below 7% or more than 35% the NPV will be negative and we should reject!!

The reason is the changes in the sign of the cash flows – every time the sign changes there is potentially (not always, but potentially) one more IRR. In my tiny example it starts -‘ve, goes +’ve, then goes -‘ve again – so two changes of sign and therefore two IRR’s.

In calculation parts of questions, the above is not a problem – projects start with outflows and then have inflows (one change of sign, so one IRR). Sometimes there is a small outflow at the end of the project (because of tax) but because it is only ever relatively small, it does not create a problem and if we are asked for the IRR we do it in the normal way and there is only one.

It is only relevant in the exam in the written parts of questions (and even there is not mentioned very often).

Sorry this is such a long reply – it is not easy to explain in just a few words.

Thank you very much. I recalculated to find the IRRs at 7% and 35%. I was quite amazed by this. For now I will let your concise response sink into my consciousness however after some days, if this does settle perfectly in my mind, then I will let you know for any assistance! Once again thank you very much!

Mr Moffat, On this OKM Co. Fixed costs are still a grey area to me. When I tried to solve this question, i had to spend several minutes considering whether to include the fixed costs as relevant cashflows or not. This is a grey matter which could cost marks for me in the exam. What are the rules for making fixed costs as relevant cashflows?

The general rule (as with all costs) is that we are wanting the extra future cash costs that will be incurred as a result of doing the project. In OKM, for part of the fixed costs the money had already been spent and whether or not we go ahead with the project will make no difference to what we have spent. (We can charge whatever we want in the profit statement, but what matters to us are the extra cash flows that will occur each year.)

With regard to the rest of the fixed costs, it very much depends on the wording of the question. If they are extra and will only be incurred if we do the project, then they are relevant for the decision. On the other hand, if it is simply a re-apportionment of existing fixed costs (reapportioned for profit purposes) then that would mean that the total fixed costs would not change and therefore in that case they would be irrelevant.

The way this question was worded implies that the fixed costs (after excluding the part that had already been spent) were additional costs as a result of doing the project (there is no mention of them being an apportionment of existing costs), so they are relevant to the decision.

I understand that when using actual (inflated) cash flows, we should discount with an actual (nominal) rate of return that includes the inflation premium, and not the real rate or event the bank borrowing rate that was used by the trainee accountant.

But, since we’ve calculated after-tax cash flows, shouldn’t we also use an after-tax nominal interest rate? Shouldn’t we adjust the 12% figure provided by the Fisher formula for the tax effect? i.e. multiply by (1 – T) or 0.70 to get an after-tax nominal rate of 8.4%?

We bring tax into the cash flows simply because tax itself is a cash flow and we want to get the actual net cash flows.

Then we discount at the actual cost of money. I don’t know if you have studied weighted average cost of capital yet, but when calculating the cost of debt we do indeed take account of the tax relief on the interest and calculate it after tax (but this has nothing to do with the cash flows themselves – it is simply that the tax relief on the debt makes the borrowing cheaper. However, dividends do not get tax relief and so the cost of equity borrowing is not affected by tax.

Now I get it. All WACC calculations already use an after-tax cost of debt, and of course a flat cost of equity and since WACC is a composite of these two, it already includes the tax effect!

Why did we not use the real weighted average cost of capital (7%) instead we had to use the fisher formula to calculate normal weighted average cost of 12%.

I recall in the previous lecture on inflation (discounted cash flows) we had used the real cost of capital to discount the cashflows. In the lecture we were inflating the cashflows by 5% and discounting by 10%. After the fisher formula we were discounting the current cash flows by 9.52% which is the real cost of capital. Any assistance in this area is highly appreciated.

Either we discount the actual (nominal) cash flows at the actual (nominal WACC); or we discount the real cash flows (ignoring inflation) at the real cost of capital (ignoring inflation).

In the exam, we always do the first option (i.e. calculate the actual cash flows, and then discount at the actual cost of capital, unless the question specifically tells you to do it the other way (which has happened, but is very uncommon in the exam).

If (as in this question) we are given the real cost of capital, then to calculate the actual cost of capital we need to adjust for the general rate of inflation using the Fisher formula.

(The lecture you refer to was simply trying to explain why, in theory, the rate of inflation is irrelevant – as the cash flows change with inflation, then so (in theory) does the cost of capital. However (as I say in the lecture) in practice this is not usually the case because different flows inflate at different rates. The previous lecture explains the way we do it in the exam – inflating the cash flows to get the actual (nominal) cash flows and then discounting at the actual cost of capital.)

boringaccountant says

OKM co’s poor accountant may have lost his job 馃槢

lwitiko says

Mr Moffat, on this Q3 for June 2010-OKM, part (c(iii)), highlights the issue of several IRRs in a cashfow. But I cannt just get around it. One cash flow can only have one IRR even if some cashflows are negative. I can not imagine a situation where there would several IRRs from a cashflow. Any assistance on this matter will be highly appreciated.

John Moffat says

Remember that the IRR is not actually a return, it is simply that rate of interest at which the NPV is zero.

For a ‘normal’ project, the higher the cost of capital, the lower the NPV (and vice versa). So if we have an IRR of (say) 15% we can say that if the cost of capital is less than 15% then the NPV will be positive and therefore we should accept, whereas if the cost of capital is more than 15% then the NPV will be negative and therefore we should reject. Usually there is no problem, there is simply one IRR (or break-even).

However, this ‘works’ because most projects involve one investment at the beginning followed by inflows, and as with any investment the greater the interest that has to be paid, the more inflows are needed to make it worthwhile.

The problem occurs when the signs of the cash flows change. For example, suppose an investment requires an outflow now of $19000, gives an inflow of $45900 in 1 years time, and then requires another outflow of $27350 in 2 years time. You will find that the NPV will be zero at both 7% and at 35% (don’t worry – you would not be expected to calculate multiple IRR’s in the exam, but you can check me by all means 馃檪 )

The reason that this is happening is that over the first year we are investing (as usual) and the NPV will fall with higher interest; however over the second year it is the other way round in that we receive money and then we have to pay out, and so for that bit of it the NPV will fall with lower interest.

If you were to calculate the NPV at lots of interest rates (1%, 2% 3% etc.) and put them on a graph then you will find that the NPV starts off being negative, then it increases and becomes positive, but that then it will start to fall and eventually become negative again. The curve will cross the axis at both 7% and 35% (so two IRR’s). The NPV will be positive (and we should therefore accept) if the cost of capital is between 7% and 35%, but if it is below 7% or more than 35% the NPV will be negative and we should reject!!

The reason is the changes in the sign of the cash flows – every time the sign changes there is potentially (not always, but potentially) one more IRR. In my tiny example it starts -‘ve, goes +’ve, then goes -‘ve again – so two changes of sign and therefore two IRR’s.

In calculation parts of questions, the above is not a problem – projects start with outflows and then have inflows (one change of sign, so one IRR). Sometimes there is a small outflow at the end of the project (because of tax) but because it is only ever relatively small, it does not create a problem and if we are asked for the IRR we do it in the normal way and there is only one.

It is only relevant in the exam in the written parts of questions (and even there is not mentioned very often).

Sorry this is such a long reply – it is not easy to explain in just a few words.

I hope it makes some sense 馃檪

lwitiko says

Thank you very much. I recalculated to find the IRRs at 7% and 35%. I was quite amazed by this. For now I will let your concise response sink into my consciousness however after some days, if this does settle perfectly in my mind, then I will let you know for any assistance! Once again thank you very much!

John Moffat says

You are welcome (and do come back to me if you need to) 馃檪

lwitiko says

Mr Moffat, On this OKM Co. Fixed costs are still a grey area to me. When I tried to solve this question, i had to spend several minutes considering whether to include the fixed costs as relevant cashflows or not. This is a grey matter which could cost marks for me in the exam. What are the rules for making fixed costs as relevant cashflows?

John Moffat says

The general rule (as with all costs) is that we are wanting the extra future cash costs that will be incurred as a result of doing the project.

In OKM, for part of the fixed costs the money had already been spent and whether or not we go ahead with the project will make no difference to what we have spent. (We can charge whatever we want in the profit statement, but what matters to us are the extra cash flows that will occur each year.)

With regard to the rest of the fixed costs, it very much depends on the wording of the question. If they are extra and will only be incurred if we do the project, then they are relevant for the decision.

On the other hand, if it is simply a re-apportionment of existing fixed costs (reapportioned for profit purposes) then that would mean that the total fixed costs would not change and therefore in that case they would be irrelevant.

The way this question was worded implies that the fixed costs (after excluding the part that had already been spent) were additional costs as a result of doing the project (there is no mention of them being an apportionment of existing costs), so they are relevant to the decision.

lwitiko says

Thank you very much. Now everything is so clear on how to treat fixed costs.

John Moffat says

You are welcome – I am pleased that you are clear now 馃檪

nkmile64 says

I understand that when using actual (inflated) cash flows, we should discount with an actual (nominal) rate of return that includes the inflation premium, and not the real rate or event the bank borrowing rate that was used by the trainee accountant.

But, since we’ve calculated after-tax cash flows, shouldn’t we also use an after-tax nominal interest rate? Shouldn’t we adjust the 12% figure provided by the Fisher formula for the tax effect? i.e. multiply by (1 – T) or 0.70 to get an after-tax nominal rate of 8.4%?

John Moffat says

No 馃檪

We bring tax into the cash flows simply because tax itself is a cash flow and we want to get the actual net cash flows.

Then we discount at the actual cost of money. I don’t know if you have studied weighted average cost of capital yet, but when calculating the cost of debt we do indeed take account of the tax relief on the interest and calculate it after tax (but this has nothing to do with the cash flows themselves – it is simply that the tax relief on the debt makes the borrowing cheaper. However, dividends do not get tax relief and so the cost of equity borrowing is not affected by tax.

nkmile64 says

Now I get it. All WACC calculations already use an after-tax cost of debt, and of course a flat cost of equity and since WACC is a composite of these two, it already includes the tax effect!

Thank you Sir.

John Moffat says

You are welcome 馃檪

lwitiko says

Why did we not use the real weighted average cost of capital (7%) instead we had to use the fisher formula to calculate normal weighted average cost of 12%.

I recall in the previous lecture on inflation (discounted cash flows) we had used the real cost of capital to discount the cashflows. In the lecture we were inflating the cashflows by 5% and discounting by 10%. After the fisher formula we were discounting the current cash flows by 9.52% which is the real cost of capital. Any assistance in this area is highly appreciated.

John Moffat says

There are two alternatives:

Either we discount the actual (nominal) cash flows at the actual (nominal WACC); or we discount the real cash flows (ignoring inflation) at the real cost of capital (ignoring inflation).

In the exam, we always do the first option (i.e. calculate the actual cash flows, and then discount at the actual cost of capital, unless the question specifically tells you to do it the other way (which has happened, but is very uncommon in the exam).

If (as in this question) we are given the real cost of capital, then to calculate the actual cost of capital we need to adjust for the general rate of inflation using the Fisher formula.

(The lecture you refer to was simply trying to explain why, in theory, the rate of inflation is irrelevant – as the cash flows change with inflation, then so (in theory) does the cost of capital. However (as I say in the lecture) in practice this is not usually the case because different flows inflate at different rates. The previous lecture explains the way we do it in the exam – inflating the cash flows to get the actual (nominal) cash flows and then discounting at the actual cost of capital.)

nikole25 says

that was so understandable!a really great job!please if you are able,could you help us with more ?

realhams says

Thanks a lot. Helped me save time understanding inflation and tax in investment appraisal

bukky35 says

Excellent and very useful. Thanks a lots.

temi says

lECTURE VERY USEFUL. THNX TO OT

temi says

This is brilliant, so clear and understandable. thumbs up for ot