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Posts Tagged ‘Net present value’

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Establishing a value for the target company

In Corporate restructuring, Finance, MBA on October 27, 2010 at 8:11 pm

An acquiring company may be interested in acquiring entire businesses or just acquiring individual assets and selling off the rest of the assets. When considering a merger, companies can use capital budgeting techniques to find the value of the company. If the net present value of the relevant cash flows is positive then a merger is considered acceptable.

If the acquiring company is interested in the whole business rather than in just few assets of the target company then post-merger pro forma statements for the target company should be prepared and the cost of capital of the acquiring company must be adjusted to reflect the cost of capital of the target company.

Test yourself:

ABC Company would like to obtain the assets of BCD Company. BCD Company is a loss maker, it made losses over the last 4 years. However, it has three assets which ABC needs for its operations which are assets a, b and c. BCD is not willing to sell the assets separately but willing to sell the entire company for $95,000. According to the balance sheet of BCD;

  • asset a is worth $25,000,
  • asset b worth $20,000
  • And asset c worth $50,000.
  • BCD also has $5,000 in cash,
  • ABC found out that they can sell accounts receivable and inventory of BCD for $10,000, and
  • BCD’s liabilities account for $70,000.
  • Taking into account merger tax advantages from losses, after the merger, three assets of BCD will generate $15,000 in cash inflows over the next 10 years.
  • ABC’s cost of capital is 12%.

How should ABC establish if it should undertake this investment?

Solution:

BCD requires $95,000. Out of this money, $70,000 will be used to cover liabilities and $25,000 will be going to the owners of the target company. ABC will be able to recover $10,000 from selling accounts receivable and inventory and it will also obtain $5,000 in cash. Therefore, its actual investment is $80,000 ($95,000-10,000-5,000).

Next we need to determine the net present value of the relevant cash flows. Since it is an annuity, we can calculate it very simply. We will use a financial calculator. The calculation is as follows:

PMT: 15,000

N: 10

I: 12

PV: calculate = 84,753

Since investment required is $80,000, we can find the NPV as follows:

84,753 – 80,000 = 4,753

There is another way to calculate NPV using a financial calculator. It is advisable to try them both to make sure that the answer you obtain is correct. The second way is as follows:

CF0: -80,000

CF1: 15,000

Second function Nj: 10

I: 10

Second function NPV: calculate = $4,753

Since both calculations gave us the same answer, we can be confident that the answer is correct.

Since NPV is $4,753 which is higher than zero, a merger with BCD is acceptable.

 

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Capital Rationing

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:38 pm

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.

 

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Annualized Net Present Value (ANPV)

In Cost of Capital, Finance, MBA on October 27, 2010 at 6:37 pm

The annualized Net Present Value (ANPV) technique is the best method to use when comparing mutually exclusive projects which have unequal duration. ANPV is the most efficient technique to convert Net Present Values (NPVs) of projects with unequal duration into an ANPV for each specific project, which can then be compared.

To find ANPV, the following calculation must be made:

1 – Find NPVs for each project

2 – Divide the NPV of each project by PVIFAr,n (Present Value Interest Factor for Annuity) at the project’s required cost of capital and number of periods. The amount for PVIFAr,n can be found in financial tables.

3 – The project with the higher Annualized Net Present Value (ANPV) is preferred.

Alternatively, ANPV can be found by using a financial calculator , as shown below:

PV = use NPV

N = Number of periods over the duration of the project (e.g. number of years)

I = required cost of capital (e.g. 10%)

Find PMT = this will be the annualized net present value (ANPV)

Test yourself

ABC Corporation has two mutually exclusive projects A and B that it can invest in. Initial investments investments required for project A and B are $150,000 and $200,000 respectively. The duration of project A is 4 years and of project B is 3 years. Expected annual cash inflows from project A are $40,000 and from project B is $70,000. The terminal cash flows from projects A and B are $21,000 and $34,000 respectively. The cost of capital of ABC Corporation is 9% and both projects have an average risk, which means that alteration for risk adjusted discount rate is not required. The 9% for cost of capital should be used for both projects.

What is the ANPV for projects A and B?

SOLUTION:

By using a financial calculator, we can find the solution to this problem. First we need to establish the net present value (NPVs) for projects A and B.

NET PRESENT VALUE (NPV) FOR PROJECT A:

Clear calculator: second function, “C ALL”

CFo: -150,000

CF1: 40,000

CF2: 40,000

CF3: 40,000

CF4: 61,000 (40,000 + 21,000)

I: 9

Second function, NPV: 5,534.28

 

NET PRESENT VALUE (NPV) FOR PROJECT B:

Clear calculator: second function, “C ALL”

CFo: -200,000

CF1: 70,000

CF2: 70,000

CF3: 104,000 (70,000 + 34,000)

I: 9

Second function, NPV: 3,444.86

However, because the projects have different duration, we need to convert Net Present Values (NPVs) found above into ANPV for each project.

CONVERTING NPV TO ANPV FOR PROJECT A:

Clear calculator: second function, C ALL

PV: – 5,534.28

N: 4

I: 9

Find PMT: $1,708.26

 

CONVERTING NPV TO ANPV FOR PROJECT B:

Clear calculator: second function, C ALL

PV: – 3,444.86

N: 3

I: 9

Find PMT: $1,360.91

Since the ANPV of project A ($1,708.26) is higher than that of project B ($1,360.91), project A should be selected.

 

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Risk Adjusted Discount Rate: Dealing with Risk in Capital Budgeting

In Capital Budgeting, Finance, MBA on October 27, 2010 at 6:28 pm

Breakeven cash inflow analyses risk adjusted discount rate (RADR) andscenario analyses are tools that facilitate better insight into managing risk in capital budgeting.

Risk in capital budgeting especially refers to variability of the returns (variability of cash inflows), because the initial investment is more or less known with some level of confidence. Therefore, we need to ensure that present value (PV) of cash inflows will be large enough to ensure that project is acceptable.

To adjust the present value of future cash inflows for risk embodied in particular project, we can either adjust cash inflow directly or we can adjust the discount rate. Because adjusting cash inflow is highly subjective, we will rather adjust discount rate. This is when risk adjusted discount rate technique comes into play.

RADR is a discount rate that must be earned to compensate an investor for the risk undertaken. Under RADR the value of the firm must be at least maintained or must increase. Risk adjusted discount rate is the most popular risk adjustment technique that utilize NPV.

The higher is the risk of specific project, the higher RADR will be.

The deployment of RADR is best illustrated by the use of an example:

EXAMPLE

Amanda can invest in two shares, A and B. Both shares presently cost $50 and Amanda wants to hold the shares for 4 years. Annual dividends from share A are expected to be $7. Annual dividends from shares B are expected to be $12. However, share B is more risky.

In 4 years time Amanda expects to be able to sale share A for $55 each and share B for $70 each. Amanda’s required return is 8%. However, for share B she adjusts her return so that her risk adjusted discount rate becomes 12%.

We need to calculate the risk adjusted net present value (NPV) of shares A and B (with the help of deployment of risk adjusted discount rate) and recommend which shares Amanda should purchase. SOLUTION:

We will be using a financial calculator to find a risk adjusted net present value (NPV) of shares A and B.

 

Risk adjusted NPV of shares A:

Clear calculator: second function, “C ALL”

CFo: -50

CF1: 7

CF2: 7

CF3: 7

CF4: 62 (7+55)

I: 8

Second function, NPV: $15.38

 

Risk adjusted NPV of shares B:

Clear calculator: second function, “C ALL”

CFo: -50

CF1: 12

CF2: 12

CF3: 12

CF4: 82 (12+70)

I: 12

Second function, NPV: $30.94

Since investment in shares B offers higher risk adjusted NPV, Amanda should choose to invest in shares B.

The main difficulty in using RADR is in determining level of risk and approximating an appropriate RADR. There is currently no systematic way to adjust the required return to the RADR. Management usually determines a RADR subjectively.

Sometimes a risk index is determined which reflects the RADR for every subsequent level of risk. For example, risk can be categorized into below average, average, above average and very high. Past experience and thecapital asset pricing model (CAPM)can be used to subjectively determine the RADR appropriate for each subsequent level (category) of risk.

 

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Risk Scenario Analysis: Dealing with Risk in Capital Budgeting

In Capital Budgeting, Finance, MBA on October 27, 2010 at 6:27 pm

Breakeven cash inflow analyses ,risk scenario analysis and risk adjusted discount rates are tools that facilitate better insight into managing risk in capital budgeting. Here we focus on risk scenario analyses.

This tool can be used to evaluate the risk of a project. It focuses on developing few alternative scenarios and evaluating the variability between returns, which can be measured by net present value (NPV).

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

The range is found by taking NPV of optimistic outcome and subtracting the NPV of pessimistic outcome, as shown below:

Range (Option 1) = NPV of optimistic outcome – NPV of pessimistic outcome.

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

Range (Option 2) = annual cash inflow from optimistic outcome – annual cash inflow from pessimistic outcome.

Range shows us variability between returns. When conducting risk analysis, remember to always use the MOST positive and negative numbers. Choosing anything between them will not produce the correct result.

 

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Risk in Capital Budgeting

In Capital Budgeting, Finance, MBA on October 27, 2010 at 6:26 pm

Risk in capital budgeting refers to the probability that a project will prove to be unacceptable with a net present value (NPV)less than zero or aninternal rate of return (IRR)less than the cost of capital. Particularly, it refers to variability of the returns (variability of cash inflows) because theinitial investment is more or less known with some level of confidence. Therefore, we need to ensure that cash inflows will be large enough to ensure that project is acceptable. Breakeven cash inflow, scenario analyses and risk adjusted discount rates are tools that facilitate better insight into managing these risks.

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Using a financial calculator

In Capital Budgeting, Finance on October 27, 2010 at 6:25 pm

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 a 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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Profitability index (PI)

In Capital Budgeting, Finance, MBA on October 27, 2010 at 6:24 pm

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.

 

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The Difference Between IRR and NPV

In Finance, MBA, Capital Budgeting on October 27, 2010 at 6:01 pm

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.

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Internal Rate of Return method (IRR)

In Capital Budgeting, Finance, MBA on October 27, 2010 at 6:00 pm

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 one of the sophisticated capital budgeting techniques. It is a widely used technique.

It is also very easy to utilize Internal Rate of Return with the help of afinancial 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.

Lets use a simple example to explain this. IRR is WACC, but only when the WACC results in the NPV equal to zero. That means IRR is another form of cost of capital. IRR is a theoretical number, while WACC is a real number. In simple terms, the IRR is the rate of return that would equate the NPV with zero. If IRR is higher than the cost of capital, then a project should be accepted, and vice versa. If IRR at least equals the cost of capital than we know that the business will at least earn a rate equal to its cost of capital on this particular project.

Example

Let’s see how to utilize Internal Rate of Return method with the help of a financial calculator.

IRR 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

Find IRR: second function, IRR

 

IRR 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

Find IRR: second function, IRR

Both Net present value method (NPV) and Internal Rate of Return method (IRR) will show whether the project is acceptable. However, the ranking of specific acceptable projects may differ between the two techniques.

Test yourself

ABC Corporation has an option to invest in project B. The initial investment for project B is $35,000. Operating cash inflows from project B are 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 the Internal Rate of Return method.

SOLUTION:

With the help of a financial calculator, we can determine the 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 the IRR (3.07%) is below the cost of capital (5%), the project is not acceptable.

TEST YOURSELF:

ABC Corporation has 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 the Internal Rate of Return method, project D is acceptable.

SOLUTION:

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

STEP ONE

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%

STEP TWO

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

Comparing NPV and IRR

You will notice these next two paragraphs appears verbatim on 3 oher pages. There is a reason for this. Understanding the difference between NPV and IRR is critical. Make sure you understand the differences, and are able to apply both techniques.

Theoretically, it is advisable to use Net Present Value method because NPV 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.

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 can be considered a sophisticated and reliable technique.

 

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