Understand Internal Rate Of Return (IRR) (Part 2)

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We have looked at how we compute investment appraisal method using Net Present Value(NPV) and Internal Rate Of Return(IRR) and also understand how to interpret the individual result.

One very good point is that both NPV and IRR are able to eliminate the greatest disadvantage of ignoring the time value of money or present value unlike the other two methods -Payback and ARR.

We now focus on the advantages of using IRR:

IRR is useful for the following reasons:

• If a company had specified it’s “hurdle rate” or a required cost of capital that new projects must achieved in order to be accepted. By just calculating the IRR, it is then compared to the hurdle rate to see whether the IRR is above the rate and the project can be accepted. Incidentally, even without the hurdle rate, if the IRR rate is very high say 32%, this can some sort warrant further analysis as this high IRR rate seems to be much more than the probable opportunity cost of capital.
• IRR is a “true” return (using present value concept) on the investment compared to the other accounting rate of return.

However IRR also has its critique which is as follows:

• IRR does not tell us anything about the size or scope of a potential investment. This is especially important when we are choosing between two mutually exclusive investments, where only one of the investment projects can be chosen.

Say for example, if we are choosing two investment projects with capital outlays of $1,000 and $10,000 and the IRR of the $1,000 is higher. If we use the IRR method than the IRR which is higher will be more attractive. However, the Net Present Value of the other investment could be much high and so we make have made a less than perfect decision. Therefore, the IRR method is not suitable for making comparisons between two investment projects of different scope or differing time horizons.

For illustration purpose that IRR is not suitable to be used when we need to choose between two mutually exclusive investments:

Year	Project A Investment	Cash-flows	Project B Investment	Cash- flows
0	-$100K		-$40K
1		$40K		$20K
2		$50K		$20K
3		$70K		$30K
	NPV @10%	$20K(say)		$10K(say)
	IRR	15%		22%

Project A should be chosen if the NPV method was used whilst Project B should be chosen according to its IRR. But, by taking the differential/remaining cash-flows and calculating the NPV and IRR, we can see that this would have been a less than perfect decision.
Differential Balance of Cash-flow

Year	Investment Project A – B	Cash-flows
0	-$60K
1		$20K
2		$30K
3		$40K
	NPV @10%	$6K(say)
	IRR	14%

The differential table shows that there is still value to be gained to enhance shareholder value by investing the differential.

The other disadvantages of IRR are:

• There is technical disadvantages to using the IRR method when dealing with unconventional cash-flows.

• We can have more than one IRR depending on the flow of the cash-flows. As IRR is determined by mathematical iterations, it is possible to have two IRRs when there is more than one change in the direction of the cash-flows. In a normal investment, in the initial one to two years, there are negative cash-flow but subsequently followed by positive cash-flow. But if an investment has a negative cash flow at the end of its economiclife, the investment would actually have two IRR like in a company which is processing radioactive material materials, it will have to invest heavily at the end of the investment’s life to dispose of the radio-active waste products.

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Understand Internal Rate Of Return (IRR) (Part 1)

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In the previous article on NPV, we noted that a positive NPV denotes that a project can be accepted as it generates excess returns over its cost of finance. Hence, vice-versa, we cannot accept a negative NPV as it cannot generate a return above the cost of finance.

How do we then interpret a zero NPV
Zero NPV is actually the Internal Rate of Return which is therefore the discount rate that causes:
The present value of all the future cash flows – the present value of the initial outlay to yield an NPV of zero.
Using the same cash flow’s details from the NPV case, we shall try to get the IRR:

	Year O	Year 1	Year 2	Year 3	Year 4
Initial Outlay (a)	$100K
Net cash-flows (b)		$20.00K	$30.00K	$40.00K	$50.00K
Using PV factor of 10% NPV=	+$7.15K
Simulating it :
Using PV factor of 15% NPV=	+$0.5K
Using PV factor of 12% NPV=	$0.00K

To calculate the Internal Rate of Return, we can either use the interpolation method which is to take two discount rates, one rate that gives a positive NPV and another discount rate that give a negative NPV and interpolate the IRR.
Or you can use a calculator or a computer model (excel formula for IRR).

Interpretation of IRR:
If the IRR for the project is12% and the cost of capital used to finance it is lesser than 12%,then the project should be accepted.

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Payback Investment Appraisal Method

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Earlier article was on the traditional Accounting Rate Of Return(ARR).

In this article, we look at the Payback Method which seeks to determine how long it takes for the investment project to pay back its initial capital cost.

Illustration:

Let’s say we have two project A & B, having the following initial capital cost, cash inflows and timing

Project A:

Year	Investment	Cash Savings/Inflows	Cumulative Inflows
0	100,000
1		30,000	30,000
2		40,000	70,000
3		30,000	100,000
4

Payback period = 3 years

Project B:

Year	Investment	Cash Savings/Inflows	Cumulative Inflows
0	100,000
1		60,000	60,000
2		40,000	100,000
3		30,000	130,000
4

Payback peiod=2 years

Using the payback period methodology, the analysts merely see how long or how fast the investment can be recouped.

In the aforesaid situation, we see that by investing in Project B, the company has a faster payback period of 2 years instead of Project A which takes a bit longer which is 3 years.

Like the accounting rate of return, payback method also has its advantages and disadvantages.

The advantages are:

• this method is very easy to understand and to explain to other people;
• it requires the proposer to consider and to collect only the forecasts of the initial capital outlay and estimated cash inflows in the next few yeras, typically no more than five years
• it gives a “result” very quickly without much analysis needed-there is no need to compute a discount rate)
• lastly, if forecasts into the future are unlikely to be accurate, due to technological changes for example, it is considered “less risky” because it is only taking into account those cashflows which are easier to forecast well.

However, its following disdvantages outweight the abovesaid advantages:

• this method ignores the time value of money. That is it assumes that if a company has an investment decision rule which sets payback on projects at, say four years, the company will be indifferent as to whether its investment is recouped in the first year of the project or the third year of the project;
• it ignores any cashflows which might occur outside the “Four-year rule”(say). Thus the company may reject a very lucrative project in favor of a less profitable one because the former recoups its investment over a six-year period whilst the latter recoups much less cash but within the four-year(say) payback period;
• this method automatically favors short-term over long-term investments[the company should preferably have a range of investment projects with differing time horizon thus retaining a flexible approach to new opportunities while capitalizing on long-term projects which ensures that the company keeps pace with technological or other research developments that affect its future viability;
• it does not have a clear decision criteria as to whether to accept or reject an investment project. The cut-off point is ambiguous. For example when is the investment stage of a project considered to be finishd? When the investment project begins to generate cash or automatically after the first year? This ambiguiy leads to subjective decision-making rather than clear-cut decision rules and
• thinking that Paybak is “less risk” can be misleading. The opportunity cost of capital takes into account the increased risks associated with forecasting in future years whereas Payback just ignores these cashflows altogehter. This therefore is really not “less risky” but just more inaccurate!

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Accounting Rate Of Return(ARR) Method Of Appraising Investments

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One way of appraising capital investment is the traditional Accounting Rate of Return(ARR) Method or Accounting Return on Book Value.

In this article, there are two parts.

The first part illustrate how to compute Accounting Rate Of Return method and the next part is to discuss its advantages and disadvantages.

About Accounting Rate of Return(ARR):

• The Accounting rate of return is very commonly used as this concept is a very familiar concept to return on investment (ROI), return on capital employed(ROCE) or accounting rate of return(ARR).

• The formula for this method is Average Annual Income/Average Annual Investment

Worked Example:

Let’s say we are evaluating the below said project with the following Initial Outlay/Investment and Net Cash flow ( Revenue minus Costs)

Investment:

	Year 0	Year 1	Year 2	Year 3	Average
Gross Book Value of Investment	100,000	100,000	100,000	100,000
Depreciation		20,000	20,000	20,000
Accumulated Depreciation		20,000	40,000	60,000
Net Book Value	100,000	80,000	60,000	40,000	70,000

Returns/Net “Cash flow (Revenue-Costs)

	Year 1	Year 2	Year 3	Average
Revenue(a)	50,000	70,000	100,000
Costs (b)	20,000	30,000	40,000
Cashflow (a-b)	30,000	40,000	60,000
Depreciation	20,000	20,000	20,000
Net profit	10,000	20,000	40,000	23,300

Accounting Rate of Return

=

Average annual returns

Average annual investments

= $23,300

$70,000

= 33.3%

This Part B looks at the advantages and disadvantages of applying the Accounting Rate Of Return (ARR) method.

Append below a snapshot of the Pro’s and Con’s of ARR:

Pro’s	Con’s
It takes all the years into account when making an investment decision,	There is no account of time value of money. It does not take into account the fact that dollars to be received in the future is not worth as much as money in the hand today.
It’s is easy to use and is familiar concept to managers which they refer to as “ return on investment” or “ return on Capital employed.	It is purely based on accounting figures and not on cash flow. Thus it Does not take into account the working capital requirements that are needed for the investment as working capital is not captured in accounting profit, can be manipulated by changing accounting methods like depreciation rates & methods which have nothing to do with the underlying investment.
	Having calculated the return, we still do not know whether the return is acceptable or not? Perhaps, we can compare it to other companies in the industry. But don’t forget that the other companies might be using different accounting convention, Secondly, high accounting rate of return, the project or investment can be rejected because this cannot be compared to other past returns. This is despite that the high returns are still profitable to the company.

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