Category MBA

Risk Scenario Analysis: Dealing with Risk in Capital Budgeting

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Another way to evaluate risk of the project is to undertake scenario analysis.

Scenario analysis focus on developing few alternative scenarios and evaluating variability between returns, which can be measured by net present value (NPV).

For example, we can generate 3 scenarios (optimistic, most likely and pessimistic) and than find NPVs for each of the scenarios. When we know net present values for each scenario, we can find the range.

The range here is found by taking NPV of optimistic outcome less NPV of pessimistic outcome, as shown below:

range (1) = NPV of optimistic outcome – NPV of pessimistic outcome

Alternatively, the range is found by taking annual cash inflow from optimistic outcome and subtracting annual cash inflow from pessimistic outcome, as shown below:

range (2) = annual cash inflow from optimistic outcome – annual cash inflow from pessimistic outcome

Range shows us variability between returns.

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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Profitability index (PI)

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Profitability Index (PI) is another sophisticated technique used in capital budgeting decisions. PI is related to NPV as it indicates the net present value (NPV) per each dollar invested. PI is calculated as follows:

PI =

Total present value (PV) of cash inflows divided by Initial investment.

PI is an especially advantageous technique if the company operates under capital rationing. If the PI is greater than one, the project is acceptable.

 

Equivalent Annual Annuity Approach (EAA)

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Equivalent Annual Annuity approach (EAA) is another sophisticated technique used in capital budgeting decisions. EAA determines the annual cost of the project over its economic life. It is determined by dividing net present value (NPV) of the project by the present value interest factor for annuity (PVIFAr,n) for a specific period and at a specific discount rate. PVIFAr,n can be found in financial tables.

EAA is helpful when a project has to be selected from mutually exclusive projects with unequal lives. The project with the highest Equivalent Annual Annuity (EAA) is more attractive. If two mutually exclusive projects have equal EAA than the project with the shorter economic life is more acceptable.

 

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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Unsophisticated capital budgeting techniques

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Simple (unsophisticated) capital budgeting techniques include average rate of return (ARR) and the payback method (also called PB or payback period).

Average Rate of Return

Average Rate of Return (ARR) is an unsophisticated budgeting technique and generally considered to be ineffective. Average Rate of Return (ARR) evaluates relative profitability of the investment. In other words, it evaluates how project affects accounting profits. Average Rate of Return (ARR) is calculated as follows:

ARR = Average income / Average investment

Average income refers to annual average net profits after tax (refer to income statement to see how net profits after tax are determined). Annual average net profits after tax is found by taking total net profits after tax over the useful life of the project and dividing it by number of years over useful life of the project. Average investment refers to average investment over the economic life of the project. The ARR capital budgeting technique does not consider the time value of money. It also considers net profits rather than cash inflows. Consequently, the technique overlooks the possibility of reinvestment of returns.

The positive side of this technique, as compared to payback period discussed below, is that it considers returns on investment over entire useful life of the project. However, this technique is generally not recommended.

Payback method

Payback period (PB), also called a payback method, is another unsophisticated budgeting technique. It determines how long it takes to recover the initial investment by taking into account cash inflows from the investment. If we deal with an annuity (an equal periodic cash flow over a specific period) than all we need to do is to divide initial investment by an annuity.

However, if we deal with a mixed stream of cash inflows (unequal cash flows during specific period with no precise pattern) than we need to add up cash flows until the initial investment is recovered.

Management needs to subjectively determine the maximum payback period and then projects are evaluated according to this. If the project’s payback period is below maximum than the project is acceptable and vice versa.

The payback period budgeting technique measures business’s risk exposure because the project’s risk level depends on how long it takes to recover the initial investment. However, it does not explicitly consider the time value of money.

Moreover, this budgeting technique is weak because it is subjective in nature since the minimum payback period is subjectively determined. Furthermore, it does not take into account the cash flows that occur after the payback period.

A variation of payback period capital budgeting technique allows to account for time value of money and risk (due to usage of discount rate which incorporates risk). Such variation is called discounted payback period technique. This technique determines how long it takes for discounted cash flows to recover the investment. However, this variation still does not consider cash flows after the payback period.

Test Yourself

ABC Corp has a proposed project A, which has expected cash inflows of $4,000 over 10 years period. The initial investment is $30,000. Find the payback period.

SOLUTION:

Payback period = 30,000/4,000 = 7.5 years

This means that it will take 7.5 years for ABC to recover its investment in project A.

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Terminal Cash flow in capital budgeting decisions

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Terminal cash flow refers to the cash flow, which takes place at the end of the project life. Terminal cash flow takes into account a net salvage value received at the end (liquidation) of the project (such as sale of the asset).

Terminal cash flow excludes operation cash inflow from the last year of the project but includes cash flow due to change in net working capital. Generally, change in net working capital results in the cash inflow which is the recovered amount of cash outflow (due to increase in net working capital) that were taken into account at the beginning of the project (when calculating the initial investment).

The calculation of the terminal cash flow is as follows:

After-tax proceeds from the new asset

LESS: After-tax proceeds from the old asset

LESS/ADD: Change in net working capital

= TERMINAL CASH FLOW

As stated above, when we calculate a terminal cash flow, we reverse the change in net working capital, which was taken into account during the calculation of the initial cash outflow (initial investment) .

If there was an increase in net working capital at the beginning of the project than we see it as inflow when calculating the terminal cash flow and vice versa. In other words, if there was an outflow due to change in net working capital at the beginning of the project than we reverse it by adding it back during calculation of the terminal cash flow.

Tax considerations in calculation of the terminal cash flow are the same as explained in initial cash outflow (initial investment) section earlier.

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Operating Cash Inflows

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Operating cash inflows is a second variable that we must take into account when determining cash flows from the project. It refers to incremental (additional) cash inflows over the duration of the project. The cash inflows do not take into account interest payments and are calculated as follows:

Revenue

LESS: Expenses (excluding depreciation and interest

 

= EBDIT (Earnings before depreciation, interest and taxes)

LESS: Depreciation

 

= EBIT (Earnings before interest and tax)

LESS: Taxes

 

= NOPAT (Net operating profit after taxes)

ADD: Depreciation

 

= OPERATING CASH INFLOWS