Tag Internal rate of return

The Hurdle Rate

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The hurdle rate is also called minimum acceptable rate of return (abbreviated MARR) or break-even yield. It refers to the minimum rate of return that is required before any project can be undertaken. The hurdle rate is used in the capital budgeting and is the same as the required rate of return in the discounted cash flow analysis of long-term investment opportunities. It is a discount rate used when different investment alternatives are considered.

If the expected return on the proposed investment is below the hurdle rate, than the investment is not acceptable and vice versa. Sometimes the hurdle rate also refers to the minimum internal rate of return (IRR) for the project to be undertaken.

The hurdle rate should be equal to the marginal cost of capital, which is also referred to as the incremental cost of capital. The hurdle rate is also a rate of return which is necessary to maintain market value of the firm. The market value of the firm refers to the firm’s current market price of shares.

Organizations use hurdle rates to evaluate long-term investment projects using discounted cash flow techniques (capital budgeting). This allows assessing potential projects more systematically. Such evaluation allows having better confidence that selected long-term investments will at least have returns equal to the marginal cost of capital.

Hurdle rates should be set for each project or at least for each business unit or division to account for differences in risk profiles across the enterprise.

 

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Capital Rationing

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Many firms operate under capital rationing. Firms ration capital because more often than not firms do not have unlimited funds to invest. Therefore, not all acceptable projects can be actually accepted. This is, of course, contradictory with goal of maximizing shareholders value.

We can formally define the rationing of capital as follows: It is a situation when firms do not accept all acceptable projects due to a limited amount of funds or due to limits imposed on investments. The goal is to select portfolio of projects with the highest net present value.

Under situations involving scarce capital, businesses will select a portfolio of projects with the highest NPV and which does not exceed the allocated budget. There are two commonly used techniques to select projects in these situations, the net present value NPV approach and the internal rate of return (IRR) approach.

The IRR approach graphs return against the total investment on the investment opportunities schedule (IOS) and by drawing the budget constraint shows the group of projects that are acceptable to be invested in. The NPV approach ranks projects by IRR and than generates a portfolio of projects with the highest overall present value.

When selecting projects, the net present value (NPV) approach is preferred because it maximizes shareholders’ returns whereas an internal rate of return (IRR) approach just generates a portfolio of acceptable projects.

 

Risk in Capital Budgeting

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When it comes to capital budgeting, risk refers to probability that project will proof to be unacceptable with net present value (NPV) less than zero or internal rate of return (IRR) less than cost of capital. Particularly, it refers to variability of the returns.

To find the minimum cash inflow level acceptable, we need to calculate breakeven cash inflow.

Breakeven cash inflow refers to the minimum cash inflow that it required for the project to be acceptable. It is calculated as follows:

PV – Initial investment

N – number of periods over which cash inflow is received

I – required cost of capital

Find PMT – breakeven cash inflow

Test yourself:

ABC Corporation have an option to invest in project A which requires investment of $120,000. The duration of the project is 5 years and ABC’s cost of capital is 9%. What is the breakeven cash inflow?

Solution:

We can find breakeven cash inflow of project A with the help of financial calculator.

PV: -120,000

N: 5

I: 10

Find PMT: $31,448.94

The above calculation helps us to determine that the minimum annual cash inflow that will be acceptable for project A is $31,448.94.

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Using a financial calculator

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Using a financial calculator is a skill, similar to typing. You just need to know which steps to take and then you need to practice to the point when you feel comfortable with using a calculator.

In all explanations with a financial calculator we will be using an HP 10bll. Other financial calculators are similar, yet we find it easier to work with the HP. Most text books use HP calculators when providing guidance on using a financial calculator, so if you have a different calculator you may need to spend more time learning slightly different calculation steps. Before investing further time, it may be wise to get a universally used calculator.

Before using a financial calculator to make specific calculations such as calculating NPV or IRR, it is important to make sure that you:

1 – Clear the calculator – by pressing second function followed by “C All”

2 – Set calculator for the “END” by pressing second function followed by “BEG/END” and ensuring that the word “BEGIN” is not displayed. Exceptions to this rule occur when it is specifically stated in the problem that cash flows occur at the beginning of the period (for example, at the beginning of the year).

Again, if no sign appears on the display then you do not need to reset it as it is set for “END” by default. If it says “BEGIN” on the display, you need to press second function followed by “beg/end.”

When you set the calculator for the “END” of the period you do that because in the problem you are working with, cash inflow or outflow occurs at the end of the period. If the problem does not state when cash flows occur, you need to assume that it occurs at the “END” of the period.

The majority of calculations will require the “END” setting. If it is by mistake set for “BEGIN” but cash flows occur at the end of the period, then incorrect answers will be generated.

Therefore, it is advisable to keep it set for the “END” at all times as a default and only reset it for “BEGIN” when a calculation requires that to be done. Right after a calculation is completed that requires the “BEGIN” setting, it is important to develop a habit to reset it to the “END”.

In the explanations using a financial calculator, for convenience and clarity purposes, we will generally display explanations of calculations as presented in the example below:

PV: -900 I: 7 N: 5 FV: 1,262.3

When using a HP 10bll financial calculator, or using any financial calculator, you need to first insert the number (number, e.g. -900) and then insert the purpose of the number (e.g. PV).

For example, as per above, you need to press:

900 followed by the minus sign followed by PV

7 followed by I

5 followed by N

Than press FV, and the calculator will display the correct answer

Financial calculators sometimes give false answers. It is advisable to check each calculation 3-4 times to make sure that the same answer is given consistently.

Throughout the site, if you ever struggle with a calculation, always come back to this page for some simple tips on using a financial calculator.

Test yourself

ABC Corporation plans to invest in project C which has an initial investmentof $500,000. ABC’s cost of capital is 8%. The operating cash flows to be generated from the project will be as follows:

End of 1st year: $100,000 End of 2nd year: $300,000 End of 3rd year $250,000

1 – What is the Profitability Index (PI) for project C?

2 – What is the NPV for project C?

3 – Taking the NPV found in the previous step into account, is the project acceptable according to the NPV technique?

4 – Based on the Profitability Index (PI), is project C acceptable?

SOLUTION:

1 – First we need to find present values of the mixed stream of operating cash inflows. Using a financial calculator, we need to take the following steps:

End of 1st year:

FV: $100,000

N: 1

I: 10

Calculate PV: $90,909.09

End of 2nd year:

FV: $300,000 N: 2

I: 10

Calculate PV: $247,933.88

End of 3rd year:

FV: $250,000

N: 3

I: 10

Calculate PV: $187,828.7

Next we need to add up all present values from operating cash inflows to obtain the total PV of operating cash inflows:

= $90,909.09 + $247,933.88 + $187,828.7

Total PV of operating cash inflows = $526,671.67

Next we will follow the equation for Profitability Index (PI):

PI = Total present value of cash inflows/Initial investment

PI=$526,671.67/$500,000

PI=1.05

Therefore, the profitability index (PI) for project C is 1.05.

2 – To find NPV, we follow the formula for NPV:

NPV=Present value of cash inflows – Initial investment

Therefore, NPV for project C = $526,671.67 – $500,000

NPV for project C = $26,671.67

3 – Since NPV is more than zero ($26,671.67), project C is acceptable according to NPV technique.

4 – Since Profitability Index (PI) is greater than 1 (1.05), the project may be considered to be acceptable.

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The Difference Between IRR and NPV

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This article answers two questions:

1 – What is important difference between IRR and NPV?

2 – Based on these differences and other considerations, which method is more popular and which method is theoretically superior?

What is important difference between IRR and NPV?

Net Present Value method assumes that cash inflows are reinvested at cost of capital, which is more realistic than assumption made in Internal Rate of Return method (IRR) that cash inflows are reinvested at IRR.

Based on these differences other considerations, which method is more popular and which method is theoretically superior?

Theoretically, it is advisable to use the Net Present Value method because it assumes that cash inflows are reinvested at cost of capital. However, in real life, the Internal Rate of Return method is more common because it considers the rate of return instead of dollar amount considered in the Net Present Value method and the former seems to be more intuitive to users of techniques. There are, however, ways to deal with shortcomings of Internal Rate of Return method and therefore IRR is still considered a sophisticated and reliable technique.

Internal Rate of Return method (IRR)

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Sophisticated capital budgeting techniques include Net present value method (NPV), Internal Rate of Return method (IRR), Profitability index (PI) and Equivalent Annual Annuity (EAA). Internal Rate of Return method (IRR) is discussed below.

Internal Rate of Return (IRR) is a widely used technique.

It is also very easy to utilize Internal Rate of Return with the help of a financial calculator. It is much more challenging to calculate it by hand. Again, as in utilizing the NPV method, it is important to first understand the logic behind the calculation.

In simple terms, the IRR is the rate of return that would equate NPV with zero. If IRR higher than cost of capital than project should be accepted and vice versa. If IRR at least equals cost of capital than we know that business will earn at least rate equal to its cost of capital on this particular project.

Below is shown how to calculate IRR using the financial calculator.

IRR for annuity is calculated as follows:

Initial investment, minus sign – CFi

Annual cash inflow – CFi1

Number of periods – second function Ni

Second function IRR

IRR for a mixed stream is calculated as follows:

Initial investment, minus sign – CFi

Put in each cash inflow separately following with CFi1, CFi2 etc

Second function IRR

Both NPV and IRR will show whether the project is acceptable. However, the ranking of specific acceptable projects may differ between two techniques.

Test yourself

ABC have an option to invest in project B. The initial investment for project B is $35,000. Operating cash inflows from project B expected to be $5,000 per year for 8 years. The cost of capital of ABC is 5%.

What is the Internal Rate of Return (IRR) for project B?

Find out if project B is acceptable based on IRR calculation.

Solution:

With the help of financial calculator, we can determine IRR of project B as follows:

CFio: -35,000

CFi1: 5,000 (annual operating cash inflow)

Second function Nj: 8 (8 years)

Second function IRR: calculate – 3.07

The IRR of project B is 3.07%. The cost of capital of ABC is 5%. Since IRR (3.07%) is below cost of capital (5%), the project is not acceptable.

Test yourself

ABC have an option to invest in project D. The initial investment is $300,000. The operation cash inflows are expected to be $100,000 at the end of year 1, $110,000 at the end of year 2 and $130,000 at the end of year 3. The cost of capital of ABC is 10%.

  1. Calculate IRR
  2. Recommend if based on IRR technique project D is acceptable.

Solution:

1. With the help of financial calculator, the calculation is as follows:

Clear calculator: second function followed by C ALL

CFo: -300,000

CF1: 100,000

CF2: 110,000

CF3: 130,000

Second function IRR: calculate – 6.24%

2. Since cost of capital of ABC is 10% and IRR is only 6.24% (less than cost of capital), based on IRR technique, project D is not acceptable.

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Net Present Value Method

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Sophisticated capital budgeting techniques include Net present value method (NPV), Internal Rate of Return method (IRR), Profitability index (PI) and Equivalent Annual Annuity (EAA). NPV is discussed below.

NPV is a sophisticated capital budgeting technique. Theoretically, Net Present Value (NPV) is the best technique out of sophisticated capital budgeting techniques but it is difficult to use it in practice. Sometimes Net Present Value method is referred to as the “gold standard” for investment decisions.

It is very easy to use Net Present Value with the help of a financial calculator if all necessary data is available. However, it is important to firstly understand the logic behind this calculation. NPV is determined by finding present value of cash inflows and then subtracting an initial investment.

NPV=Present value of cash inflows – initial investment

Now, after we understand the logic behind usage of Net Present Value method, we can calculate NPV using a financial calculator. We will always use a HP 10bll financial calculator throughout the website. Other calculators are similar but may have some small differences.

Before you make any calculations, make sure that you:

1 – Clear the calculator – by pressing the second function followed by “C All”

2 – Ensure that it is set for end if cash flows occur at the end of the period and that it is set for beginning if cash flows occur at the beginning of the period.

To set for end/beginning – press second function followed by beg/end. If it is set for the beginning than word “begin” will be displayed. If it is set for the end than no word will be displayed.

Majority of calculations will be with the “end” setting (used when cash flows occur at the end of the period). Therefore, it is important to acquire a habit of re-setting your calculator to the “end” setting after every calculation with the “begin” setting. Otherwise, you are running a risk of forgetting to re-set the calculator and obtaining an incorrect result from future calculations.

NPV FOR ANNUITY IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Annual cash inflow: amount, CFi1

Number of periods: number of periods, second function, Ni

Cost of capital: number, i

Find NPV: second function, NPV

NPV FOR A MIXED STREAM IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Put in amount for each cash inflow separately following with CFi1, CFi2 etc

Cost of capital: number, i

Find NPV: second function, NPV

If NPV is higher than zero than we know that this project will earn returns higher than the business’s cost of capital. Further, the owner’s wealth will increase by the amount equal to NPV.

Test yourself

ABC Corporation has an option to invest in projects A. Project A has aninitial investment of $15,000, and operating cash inflows of $3,000 over the economic life of the project, which is 8 years. The cost of capital (also called discount rate or rate of return) is 8%.

Find the net present value (NPV) of project A?

SOLUTION:

With the use of a financial calculator, we can find the net present value (NPV) as follows:

Clear the calculator by pressing second function followed by “C ALL”.

Make sure calculator is set to the “end”. This setting is used because in this problem cash flows occur at the end of each period. It is commonly accepted that if problem does not state when cash flows occur, you need to assume that cash flows occur at the end of the period, not at the beginning of the period.

WE KNOW THAT NPV FOR AN ANNUITY IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Annual cash inflow: amount, CFi1

Number of periods: number of periods, second function, Ni

Cost of capital: number, i

Find NPV: second function, NPV

NOW YOU NEED TO PLUG IN THE NUMBERS:

NPV for annuity:

Initial investment: 15000, minus sign, CFi

Annual cash inflow: 3000, CFi1

Number of periods: 8, second function, Ni

Cost of capital: 8, i

Find NPV: second function, NPV

= $2,239.92

The above calculation makes it clear that project A is an acceptable project for ABC because the NPV is higher than zero ($2,239.92).

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Capital Budgeting Techniques

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The Capital budgeting techniques discussed here focus on financial considerations, although, there are financial and non-financial considerations that should be taken into account when selecting a project for capital expenditure.

There are unsophisticated (simple) and sophisticated (advanced) techniques.

1 – Unsophisticated techniques include payback period (PB, also called payback method) and average rate of return(ARR).

2 – Sophisticated techniques include net present value (NPV), internal rate of return (IRR), equivalent annual annuity (AEE) and profitability index (PI).

Out of this range of techniques, payback period is the most popular unsophisticated technique. From the sophisticated techniques, the most popular methods are net present value (NPV) and internal rate of return (IRR).

Capital budgeting techniques used to select most profitable projects for capital expenditure, which is aligned with enterprise’s objective of maximizing shareholder’s wealth. Sophisticated techniques are considered to be the most effective means of selecting the most appropriate projects for capital expenditures. Such techniques take into account risk, the time value of money and focus on cash flows rather than on accounting profits.

The result of educated usage of capital budgeting techniques knowledge generated on which projects and in which order should be accepted based on the available funds for investment.