7.1. Meaning of Investment Decisions
Investment can be defined as the acquisition of an asset to create wealth using a specific source of income. For instance, a company can use its debt and/or equity capital to purchase an asset such as stock, bonds, or property for the purpose of earning interest or profits. An investment is a process of gaining profit by acquiring and using an asset for a specific period of time.
The investment decisions of a firm are generally known as the capital budgeting, or capital expenditure decisions. A capital budgeting decision may be defined as the firm’s decision to invest its current funds most efficiently in the long-term assets in anticipation of an expected flow of benefits over a series of years. Long-term assets are those that affect the firm’s operations beyond the one-year period. Acquisition of short term assets such as stock which last for less than 1 year is not considered as an investment.
The firm’s investment decisions would generally include expansion, acquisition, modernization and replacement of the long-term assets. Sale of a division or business (divestment) is also as an investment decision. Decisions like the change in the methods of sales distribution, or an advertisement campaign or a research and development programme have long-term implications for the firm’s expenditures and benefits, and therefore, they should also be evaluated as investment decisions.
The key features of investment decisions are:
- The exchange of current funds for future benefits.
- The funds are invested in long-term assets.
- The future benefits will occur to the firm over a series of years.
It is significant to emphasize those expenditures and benefits of an investment should be measured in cash. In the investment analysis, it is cash flow, which is important, not the accounting profit. It may also be pointed out that investment decisions affect the firm’s value. The firm’s value will increase if investments are profitable and add to the shareholders’ wealth. Thus, investments should be evaluated on the basis of a criterion, which is compatible with the objective of the shareholders’ wealth maximization. An investment will add to the shareholders’ wealth if it yields benefits in excess of the minimum benefits as per the opportunity cost of capital. In this unit, we assume that the investment project’s opportunity cost of capital is known. We also assume that the expenditures and benefits of the investment are known with certainty.
7.2. Importance of Investment Decisions
Investment decisions play a significant role in promoting the growth and stakeholders’ wealth maximization. The firm makes investment decisions to acquire assets that will help them to make profits, grow, and compete more effectively. Effective decision making in an organizational context includes financial decision making. Proper utilization of resources is important to achieve long term success of the business. Investment decisions in a company are important for the following reasons:
- Promotes the company’s long term growth
- Influences the risks of the firm
- Involves the use of large sums of money
- Investments are irreversible at substantial loss
- They are the most difficult decision to make in the firm
Growth: the effects of investment decisions stretch beyond the current financial period. They affect the firm’s long term growth in terms of size, speed and direction. Investment in assets determine the future direction of the firm. Choosing a specific type of investment over the other determines whether the company will be profitable enough to grow. A wrong investment decision can be detrimental to the firm’s survival and long term growth. Sustainable growth can be achieved if the business invests in viable projects or businesses.
Risk: Committing the company’s money to a specific type of project or investment comes with a risk. Each investment has its own unique amounts or risks; hence investment decisions affect the company’s risks, uncertainties and complexities. Financial companies should be careful when making investment decisions to ensure that they choose investment options that have the right balance between risks and returns.
Funding: Investment decisions usually involve the commitment of large amounts of funds, which makes it necessary for the company to plan its investment programs carefully and ensure that they have the right sources of funds. Making the right investment decisions ensures that the company utilizes its capital efficiently to maximize profits and minimize costs. A financial manager should assess existing sources of funds and choose the best investment option that can be funded well with existing funds.
Irreversibility: Most investment decisions are irreversible. Once a decision is made, the company ties its resources to the chosen investment for a long period. Wrong decisions leads to massive losses. For instance, a company can invest in a new technology using millions of dollars, and then the technology becomes obsolete almost immediately. A good example is Nokia when it invested in the Symbian operating system, which ultimately failed as Apple’s IOS and Google’s Android worked well for Samsung and other smartphone companies. Nokia was once the biggest mobile company, but its wrong investment decision irreversibly reduced it to a small company.
Complexity: Investment decisions are among the firm’s most difficult decisions. They are an assessment of future events, which are difficult to predict. It is really a complex problem to correctly estimate the future cash flows of an investment. Economic, political, social and technological forces cause the uncertainty in cash flow estimation. Companies need to make good investment decisions in times of uncertainties and heightened business risks to limit losses and ensure the survival of the business.
7.3. Investment Appraisal Techniques
Investment appraisal refers to a decision making process where investments are made today and the benefits occur in the future. Investment appraisal can also be defined as the process of assessing various investments or projects to determine their attractiveness. It plays an important role in identifying long term trends in an industry and assessing the potential of a company in terms of profitability and growth.
The methods of investment appraisal are payback, accounting rate of return and the discounted cash flow methods of net present value (NPV) and internal rate of return (IRR). For each of these methods students must ensure that they can define it, make the necessary calculations and discuss both the advantages and disadvantages.
There are three steps involved in evaluating investments:
- Estimating cash flows
- Estimating the required rate of return (the opportunity cost of capital)
- Applying a decision rule in making a choice
An investment decision rule refers to as capital budgeting technique, or an investment criteria, or an investment appraisal technique. It is the technique or criteria that a company uses to make an investment decision. An appraisal technique is a way of measuring the economic value of an investment project.
Characteristics of an Investment Evaluation Criterion
An appropriate investment evaluation criterion or an appraisal technique has several distinguishing features or characteristics. The primary feature of a sound investment criteria is that it should maximize stakeholder’s wealth. Other characteristics of a sound investment evaluation technique are:
- It should consider all cash flows to determine the true profitability of the project.
- It should provide for an objective and unambiguous way of separating good projects from bad projects.
- It should help ranking of projects according to their true profitability.
- It should recognize the fact that bigger cash flows are preferable to smaller ones and early cash flows are preferable to later ones.
- It should help to choose among mutually exclusive projects that project which maximizes the shareholders’ wealth.
- It should be a criterion which is applicable to any conceivable investment project independent of others.
7.4. Importance of Investment Appraisal Techniques
Investment appraisal is important for a company because it enables them to analyze existing and potential investment projects. The use of investment appraisal techniques to evaluate various investment projects is important for the following reasons:
- Large amounts of capital: investments require a large amount of money to implement. For this reason, a company needs to use investment appraisal to assess the available investment options and ensure that the firm invests its resources in viable projects. The involvement of a large amount of resources necessitates careful evaluation for effective decision making.
- Maximization of Stakeholders’ Wealth: Companies that use equity to raise capital will always focus on the interests of their shareholders. Investment decisions are made with the interests of shareholders in mind because every shareholder wants to see their investments grow. Therefore, one of the major long term objectives of a company is to maximize shareholders’ wealth. Managers conduct investment appraisals to ensure that they invest shareholder’s money on viable projects that will increase the returns on their investments.
- Profitability and Growth: Another important objective of a firm is profitability and growth. This is also related to shareholder’s value because higher profits means higher returns for shareholders. However, earning returns is not an easy thing for companies to achieve because every investment involves risks. Managers use various investment appraisal techniques to investment decisions and choose projects that have the potential of generating higher profits.
- Cost Minimization and Risk Reduction: Investment appraisal techniques are also important because they can be used to minimize costs and reduce risks. Investments always involve a large sum of money, while resources are scarce. Therefore, investment appraisal allows a business to evaluate various projects and choose those that incur less risks and costs. Lower costs means increased profits, and lower risks means less chances of making losses.
- Project Funding: Companies also use investment appraisal techniques to make decisions regarding the sources of funds. Funding a project requires different sources of funds, which are not always appropriate for every project. Funding will be varied depending on the investment needs of the organization as well as the interests of shareholders. Investment appraisal allows the company to determine the funding needs of each project and ensure that there is enough funding before commencing the project.
7.5. Methods of Investment Appraisal
There are various methods of investment appraisal, or investment appraisal techniques. Some of the most commonly used performance appraisal techniques include:
There are various methods of investment appraisal, or investment appraisal techniques. Some of the most commonly used performance appraisal techniques include:
Non-Discounted Cash Flow Methods
- Payback Period
- Accounting Rate of Return (ARR)
Discounted Cash Flows
- Net Present Value (NPV)
- Internal Rate of Return (IRR)
- Profitability Index Method (PI)
1) Payback Period
The payback period (PBP) is one of the most popular and widely recognized traditional methods of evaluating investment proposals. It is based on the assumption that the degree of risk associated with the fixed asset is the length of time required to recover the investment from the firm’s cash flow. Payback period refers to the number of periods or years that a project will take to recover the initial cash outlay invested in a project. This technique applies cash flows and not accounting profits. If the project generates constant annual cash inflows, the payback period can be computed by dividing cash outlay by the annual cash inflow. That is:
Example 7.1: Calculating Payback Period with Constant Cash Flows
Assume that a project requires an outlay of $200,000 and yields annual cash inflow of $40,000 for 9 years. The payback period for the project is:
PB = $200,000/40,000 = 5 years.
Example 7.2: Calculating Payback Period with Uneven Cash Flows
Suppose that a project requires a cash outlay of $20,000, and generates cash inflows of $8,000; $7,000; $4,000; and $3,000 during the next 4 years. What is the project’s payback?
Solution:
Add annual cash inflows
8,000 + 7,000 + 4,000 + 3,000 = 22,000
The total cash inflows of $22,000 exceeds the initial cash outflow of $20,000. To get the payback period, try adding the cash inflows first three years:
8,000 + 7,000 + 4,000 = 19,000
The total cash inflows for three years is less than the initial cash outlay. This means that the payback period lies between three and four years. The remaining amount to recover the initial invested amount is:
$20,000 – $19,000 = $1,000
Assuming that the cash inflow is even throughout the fourth year, the time required to recover the remaining $1,000 is:
(1,000/3,000) 12 months = 4 months.
Thus, the payback period is 3 years and 4 months.
Example 7.3: Comparing two projects
Porojo Company Ltd, a medium sized agricultural company that is currently contemplating two projects: project A requires an initial investment of $42 million and project B requires an initial investment of $45 million. The projected relevant cash flows for the two projects are shown below:
Project A | Project B | |
Initial Investment | $42 million | $45 million |
Annual Cash Inflows | ||
Year 1 | $14 million | $28 million |
Year 2 | $14 million | $12 million |
Year 3 | $14 million | $10 million |
Year 4 | $14 million | $10 million |
Year 5 | $14 million | $10 million |
Average | $14 million | $14 million |
For project A, the Payback period is straightforward because it has a constant cash flow for all the five years:
Payback Period = 42/14 = 3 years.
For Project B, we have to add up cumulative amounts for each year to determine the payback period.
Year | Annual Cash Flows | Cumulative |
Year 1 | $28 million | $28 million |
Year 2 | $12 million | $40 million |
Year 3 | $10 million | $50 million |
Year 4 | $10 million | $60 million |
Year 5 | $10 million | $70 million |
On the cumulative column in the table above, you are adding the cash flows for each year so that you can know which year the initial cash outlay is recovered. For example, in the second row you add first year cash flows to the cash flows of the second year to get $40 million. When you add $10 million for the third year you get $50,000, which is higher than the initial cash outlay of $45 million. Therefore, the payback period is between the second and the third year.
Payback period = 2 + [(45-40)/10] = 2+0.5 = 2.5 years/ 2 years and six months.
Only 50% of year 3 cash inflows of Sh.10million are needed to complete the payback period of the initial investment of Sh. 45million. Therefore payback period of project B is 2.5 years.
Decision criteria:
- If the maximum acceptable Payback period for the company was 2.75 years, Project A would be rejected and project B would be accepted.
- If projects were being ranked, Project B would still be preferred because it recovers the project’s initial investment faster than project A.
- Where the projects are independent the project with the lowest PBP should rank as the first as the initial outlay is recouped within a shorter time period.
- For mutually exclusive projects, the project with the lowest PBP should be accepted.
Advantages and Disadvantages of Payback Period
Payback period is an important investment appraisal technique or capital budgeting technique that allows companies to evaluate the viability or projects. Financial decision makers use payback period to determine the number of years that can take a particular project to return its initial investment. The aim of every organization is to get returns from their investments, but the timing of those returns is important. Projects that take too long to give positive returns indicates that the company’s resources are not utilized efficiently to generate returns quickly.
Furthermore, most assets have a life cycle – a period in which they are able to generate returns. The longer the project takes to recoup its initial outlay, the less desirable it is because the assets have a limited life. For instance, an investment that has a life of 10 years and has a payback period of 7 years is not a viable project because it covers its initial cash outlay only 3 years before the end of its life. If the project has a payback period of 3 years, it is viable because it still has seven more years to make profits. Thus, payback period is advantageous because it provides a clear picture of an investment’s lifetime returns.
Despite having several advantages, payback period as an investment appraisal technique also has numerous limitations or disadvantages. The advantages and disadvantages of using payback period to evaluate the viability of an investment project are listed below:
Advantages
- Payback period is simple to understand and use.
- It is ideal under high risk investment as it identifies which project will payback as soon as possible
- PBP is cost effective as it does not require use of computers and a lot of analysis
- PBP emphasizes on liquidity hence funds which are released as early as possible can be reinvested elsewhere
- Risk shield: The risk of the project can be tackled by having a shorter standard payback period as it may ensure guarantee against loss. A company has to invest in many projects where the cash inflows and life expectancies are highly uncertain
- Liquidity: The emphasis in payback is on the early recovery of the investment. Thus, it gives an insight into the liquidity of the project. The funds so released can be put to other uses
Disadvantages
- Fails to consider the cash inflows earned after the payback period. Some projects may earn proportionately higher returns after the payback period.
- Fails to take into account the cash flow patterns, i.e., magnitude and timing of cash inflows. In other words, it gives equal weights to returns of equal amounts even though they occur in different time periods
- It does not measure the profitability of a project but rather the time it will take to payback the initial outlay
- PBP does not take into account the time value of money
- It does not have clear decision criteria as a firm may face difficulty in determining the minimum acceptable payback period.
- It is inconsistent with the shareholders wealth maximization objective. Share values do not depend on the payback period but on the total cash flows.
2) Accounting Rate of Return (ARR)
The accounting rate of return (ARR) is an investment appraisal technique which is used to measure the percentage rate of return expected from an investment or asset compared to the initial cost of the investment. This capital budgeting technique can be calculated by dividing the average net income that an asset is expected to generate by the average cost of capital. ARR uses a formula that compares the net income of an asset with the initial cost of acquiring that asset. It is the only capital budgeting technique that uses profits rather than cash flows to evaluate the viability of a project. ARR takes into consideration various expenses that are incurred by the asset every year, including depreciation.
Accounting Rate of Return is important for businesses because it can be used to compare several projects or investments to determine the expected rate of return for each profit and decide on the best project. Usually, the project with the highest rate of return is chosen because it gives the company more profits and helps them to grow. The formula for calculating ARR is shown below:
ARR = (Average Annual Profit after Tax ÷ Average Cost of Investment) × 100
Where:
- Average Investment = (Book Value at 1st year + Book Value at End of Useful Life)/2
- Average Annual Profit = Total profit over Investment Period / Number of Years
The outcome of dividing annual profit by cost of capital is multiplied by 100 to get the percentage rate of return.
Steps Used to Calculate the Accounting Rate of Return
Step 1: Calculate the annual net profit of the company – that is, net profit after tax. This includes all revenues minus all annual expenses, including profits, financial costs and depreciation.
Step 2: For a fixed asset such as property, plant and equipment (PPE), subtract the depreciation expense from the annual revenue to get the annual net profit.
Step 3: Divide the annual net profit by the initial cost of the asset or investment. The result of the calculation will yield a decimal. Multiply the result by 100 to show the percentage return as a whole number.
Example 7.4: Simple Calculation of ARR
Chepkonga Traders Ltd wants to implement a project that requires an initial investment capital of $250,000 and is expected to generate revenue of $70,000 annually for the next 5 years.
Solution:
ARR = (annual revenue/initial cost) × 100
= ($70,000/$250,000) × 100
= 28%
Example 7.5: Calculating ARR for a Project with Varying Annual Returns
Juma Entertainment Company is considering to buy equipment at an initial cost of $50 million. Assume the useful life of the equipment is 5 years and has nil residual value. The earnings before depreciation and tax are provided below:
Year | Earnings ($ ‘000) |
1 | 12000 |
2 | 15000 |
3 | 18000 |
4 | 20000 |
5 | 22000 |
Assuming the corporate tax rate is 30% and the depreciation is on straight line basis. Calculate the ARR of the investment.
Solution:
Step 1: Calculate Depreciation
Depreciation = (total cost – residual value) ÷ number of years
= (50 million – 0) ÷ 5 = 10 million
Depreciation for every year is $10 million.
Step 2: Calculate Average Income
Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | |
Earnings before depreciation and tax | 12000 | 15000 | 18000 | 20000 | 22000 |
Depreciation | (10000) | (10000) | (10000) | (10000) | (10000) |
Earnings after Depreciation | 2000 | 5000 | 8000 | 10000 | 12000 |
Tax @ 30% | (600) | (1500) | (2400) | (3000) | (3600) |
Profit after tax | 1400 | 3500 | 5600 | 7000 | 8400 |
NB:
- The values are in thousands (‘000’)
- Tax is calculated as 30% of earnings after tax, e.g. first year tax = 30% × 2000 = 600.
- Tax and depreciation figures are recorded with brackets to show that they are negative values.
- Profit after tax is obtained by subtracting tax amounts from the earnings after depreciation
Calculate the average investment by adding all the annual net income after tax and divide by the total economic life of the investment
Average income = (1400+3500+5600+7000+8400)/5 = 5,180
Remember this was in thousands (‘000’), so:
Average income = 5,180,000
Step 3: Calculate ARR by dividing the average income by the average investment costs. Average investment cost is obtained by adding the initial cost of the equipment with the residual value and dividing the answer by 2. Residual value for the above equipment is 0, so the average cost of investment is: (50 million – 0)/2 = 25 million.
ARR = (5,180,000/25,000,000) × 100
= 20.72%
Decision Criteria:
If the projects are mutually exclusive the project with the highest ARR is accepted. If projects are independent, they should be ranked from the one with the highest ARR which should come first to the one with the lowest as the last.
If the firm has a minimum acceptable ARR, then the decision will be based on the project with a higher ARR as per their preferred rate.
Advantages and Disadvantages of Accounting Rate of Return
Advantages
The main advantages of using the Accounting Rate of Return to assess the viability of an investment project are:
- Simple and straightforward
- Easy to calculate and easy to use
- It is the only investment appraisal method that measures profitability of the firm
- The accounting information used is readily available from the financial statements.
- All the returns in the entire life of the project are used in determining the project’s profitability.
Disadvantages
ARR also has some disadvantages such as:
- It fails to take account of the project life or the timing of cash flows and time value of money within that life
- Ignores time value of money
- It uses accounting profit, hence subject to various accounting conventions
- Does not allow for the fact that profits can be reinvested
- There is no definite investment signal. The decision to invest or not remains subjective in view of the lack of objectively set target ARR
- Like all rate of return measures, it is not a measurement of absolute gain in wealth for the business owners
- The ARR can be expressed in a variety of ways and is therefore susceptible to manipulation
3) Net Present Value (NPV)
The net present value (NPV) is a classic economic method of evaluating investment projects. It is defined as the measure of the difference between the present value of future cash inflows and the present value of cash outflows of a project. The net present value uses a discount rate in its computation. We have already seen that discount rate is the rate of return from an investment, or the opportunity cost of capital. The opportunity cost of capital is the expected rate of return that an investor could earn if the money would have been invested in financial assets of equivalent risk. Hence it’s the return that an investor would expect to earn.
How to Calculate NPV
When calculating the NPV the cashflows are used and this implies that any non-cash item such as depreciation if included in the cashflows should be adjusted for. In computing NPV the following steps should be followed:
Cashflows of the investment should be forecasted based on realistic assumptions. If sufficient information is given one should make the appropriate adjustments for non-cash items
- Identify the appropriate discount rate (It is usually provided)
- Compute the present value of cash flows identified in step 1 using the discount rate in step 2
- The NPV is found by subtracting the present value of cash out flows from present value of cash inflows.
The formula for calculating NPV is:
NPV = PV (inflows) – PV (outflows)
Where:
- ∑ refers to sum or the total of something
- C_{t} = net cash flow at time t
- C_{o} = Cash outflows (initial investment)
- n = period (number of years)
- t = time of the cash flow
- k = discount rate/cost of capital
Sometimes you can find a formula that uses different symbols, but the idea is the same. So the same formula can be given as follows:
NPV_{t} = ∑ X_{t}/(1 + R)^{t} – X_{o}
Where,
- X_{t }= total cash inflow for period t
- X_{o }= net initial investment expenditures
- R = discount rate, finally
- t = total time period count
In either case, the first part of the formula refers to net or total cash inflows for the entire life of the project. It is the projected future values expressed in present value, which means that the present value formula is incorporated in the first section of the NPV formula. The second part of the formula after the minus sign represents the cost of investments in the project. It is the net amount of money used by the investor to pay for the investments. So in simple terms NPV formula just involves subtracting cost of investment from cash inflows received from the investment. Or earnings minus costs. The complication only comes in when the future cash flows are discounted to represent the present value.
Example 7.6
Kenya Investment Ltd wants to invest in a project that has an initial cost of $265,000. The project will receive cash inflows for the next five years as follows:
- Year 1 – $60,000
- Year 2 – $70,000
- Year 3 – $80,000
- Year 4 – $90,000
- Year 5 – $100,000
Required: Find the NPV and conclude whether it is a worthy investment, assuming the rate of return is 10%
Solution:
First, calculate present value of future cash flows for each year
Cash inflow | Calculation [C_{t}/(1+k)^{n}] | Present Value | |
Year 1 | 60,000 | 60,000/(1+0.1)^{1} | 54,545.5 |
Year 2 | 70,000 | 70,000/(1+0.1)^{2} | 57,851.2 |
Year 3 | 80,000 | 80,000/(1+0.1)^{3} | 60,105.2 |
Year 4 | 90,000 | 90,000/(1+0.1)^{4} | 61,471.2 |
Year 5 | 100,000 | 100,000/(1+0.1)^{5} | 62,092.1 |
Sum of the Present Value of Cash Inflows | 296,065.2 |
Secondly, subtract initial cost of investment from the cash inflows
NPV = $296,065.2 – $265,000 = $31,065.2
Decision: invest in the project because it has a positive NPV.
4) Internal Rate of Return (IRR)
The internal rate of return (IRR) is an appraisal technique that utilizes discounted cash flows – taking into account the timing and magnitude of cash flows. It is a rate that the present value of the expected future cash flows with the cost of the investment. In other words, it is the discounting rate that equates NPV to zero. The internal rate of return is also described as the yield on investment, marginal efficiency of capital, time-adjusted rate of internal return, or the rate of return over cost.
How to Calculate IRR
The IRR concept is easy to understand if it deals with one project in one period. As an example, consider an investment whose initial cost is $10,000. Assume that the investment will be worth $10,800 after 1 year. The true rate of return for this one-period investment will be given as:
Rate of Return = (10,800-10,000)/10,000 = 0.08 or 8%.
This means that the return on your investment is $10,800 – $10,000 = $800. The rate of return is 800/10,000*100% = 8%.
So, at the end of 1 year you get your initial investment of $10,000 plus the return of $800. This could be an investment on bonds, shares, property, land, or even fixed deposit in a bank. If your rate of return is negative, then the investment is not worth investing. For instance, if your investment of $10,000 comes to $9,800 after 1 year, the return will be $9,800-10,000 = -200 and the rate of return will be -200/10,000 = -2%.
The rate of return of 8% and the rate of return of -2% make the discounted (present) value of the future cash inflows to be equal to the initial investment of $10,000. Thus, 8% makes the future cash inflows of $10,800 to be equal to the initial cost of $10,000. This is the basic idea of internal rate of return.
The formula for the internal rate of return (r) on an investment C_{0} that generates a single cash flow after period (C_{1}) is given as follows:
r = (C_{1}-C_{0})/C_{0} = (C_{1}/C_{0}) – 1………………………………………………………………… (1)
This equation can be rewritten as:
C_{0}/C_{1} = 1 + r
This is also the same as:
C_{0} = C_{1}/(1+r)………………………………………………………………………………… (2)
Equation 2 shows that the rate of return (r) depends solely on the cash flows of the project, and not any other factor. This is why it is known as the internal rate of return. The internal rate of return (IRR) is the rate that equates the investment outlay with the present value of cash inflow received after one period. This also implies that the rate of return is the discount rate which makes NPV = 0. There is no satisfactory way of defining the true rate of return of a long-term asset. IRR is the best available concept.
Based on the equation involving r and C above, the actual formula for IRR is given as:
…………………………………………. (3)
It can be noticed that the ERR equation is the same as the one used for the NPV method. In the NPV method, the required rate of return, k, is known and the net present value is found, while in the IRR method the value of r has to be determined at which the net present value becomes zero.
The acceptable IRR can be calculated using trial and error and interpolation.
Example 7.7: Calculating IRR Using Trial and Error
A project costs $16,000 and is expected to generate cash inflows of $8,000, $7,000 and $6,000 at the end of each year for next 3 years. Calculate its IRR using the trial and error method.
Solution:
We know that IRR is the rate at which project will have a zero NPV. As a first step, we try (arbitrarily) a 20 per cent discount rate. The project’s NPV at 20 per cent is:
NPV = 8,000(PVF_{1, 0.20}) + 7,000(PVF_{2, 0.20}) + 6,000 (PVF_{3, 0.20}) – 16,000
= (8,000 x 0.833) + (7,000 x 0.694) + (6,000 x 0.579) – 16,000
= 14,996 – 16,000
= -1,004
The NPV is a negative value at a discount rate of 20%. To get the right rate of return that equates NPV to zero, we try a lower rate, say 16%.
NPV = 8,000(PVF_{1, 0.16}) + 7,000(PVF_{2, 0.16}) + 6,000 (PVF_{3, 0.16}) – 16,000
= (8,000 x 0.862) + (7,000 x 0.743) + (6,000 x 0.641) – 16,000
= 15,943 – 16,000
= -57
The answer is still negative, so we still try a lower rate of return, e.g. 15%
NPV = 8,000(PVF_{1, 0.15}) + 7,000(PVF_{2, 0.15}) + 6,000 (PVF_{3, 0.15}) – 16,000
= (8,000 x 0.870) + (7,000 x 0.756) + (6,000 x 0.658) – 16,000
= 16,200 – 16,000
= 200
This is a positive NPV, which shows that the rate of return that equates NPV to zero is between 15% and 16%. At this point we use linear interpolation to determine the most accurate rate of return as follows:
Where:
L = Lower Discount Rate
H = Higher Discount Rate
N_{L} = NPV at lower discount rate
N_{H} = NPV at higher discount rate
Decision Criteria
The accept-or-reject rule, using the IRR method, is to accept the project if its internal rate of return is higher than the opportunity cost of capital (r > k). Note that k is also known as the required rate of return, or the cut-off. The project shall be rejected if its internal rate of return is lower than the opportunity cost of capital (r < k). The decision maker may remain indifferent if the internal rate of return is equal to the opportunity cost of capital. Thus the IRR acceptance rules are:
- Accept the project when r > k.
- Reject the project when r < k.
- The investor is indifferent when r = k.
In case of independent projects, IRR and NPV rules will give the same results if the firm has no shortage of funds.
Strengths & Weaknesses of IRR
The internal rate of return as an investment appraisal technique has several advantages and disadvantages
Strengths/Advantages
The IRR method is like the NPV method. It is a popular investment criterion since it measures profitability as a percentage and can be easily compared with the opportunity cost of capital. IRR method has following merits:
- Like the NPV method, IRR recognises the time value of money.
- It is based on cash flows, not accounting profits. It considers all cash flows occurring over the entire life of the project to calculate its rate of return.
- More easily understood than NPV by non-accountant being a percentage return on investment.
- For accept/ reject decisions on individual projects, the IRR method will reach the same decision as the NPV method.
- Shareholder value: It is consistent with the shareholders’ wealth maximization objective. Whenever a project’s IRR is greater than the opportunity cost of capital, the shareholders’ wealth will be enhanced.
Weaknesses and Disadvantages
Like the NPV method, the IRR method is also theoretically a sound investment evaluation criterion. However, IRR rule can give misleading and inconsistent results under certain circumstances. Here we briefly mention the problems that IRR method may suffer from.
- Does not indicate the size of the investment, thus the risk involve in the investment.
- Assumes that earnings throughout the period of the investment are reinvested at the same rate of return.
- It can give conflicting signals with mutually exclusive project.
- If a project has irregular cash flows there is more than one IRR for that project (multiple IRRs).
- Is confused with accounting rate of return.
- Multiple rates: A project may have multiple rates, or it may not have a unique rate of return.
- Mutually exclusive projects: It may also fail to indicate a correct choice between mutually exclusive projects under certain situations
Relationship between NPV and IRR
The net present value and the internal rate of return methods are two closely related investment criteria. Both are time-adjusted methods of measuring investment worth. In case of independent projects, two methods lead to same decisions. However, under certain situations (to be discussed later in this section), a conflict arises between them. It is under these cases that a choice between the two criteria has to be made. A single project will be accepted if it has a positive NPV at the required rate of return. If it has a positive NPV then, it will have an IRR that is greater than the required rate of return.
We have shown that the NPV and IRR methods yield the same accept-or-reject rule in case of independent conventional investments. However, in real business situations there are alternative ways of achieving an objective and, thus, accepting one alternative will mean excluding the other. Two projects are mutually exclusive if only one of the projects can be undertaken. In this circumstance the NPV and IRR may give conflicting recommendation. The reasons for the differences in ranking are:
- NPV is an absolute measure but the IRR is a relative measure of a project’s viability.
- Reinvestment assumption. The two methods are sometimes said to be based on different assumptions about the rate at which funds generated by the project are reinvested. NPV assumes reinvestment at the company’s cost of capital, IRR assumes reinvestment at the IRR.
Since the NPV and IRR rules can give conflicting ranking to mutually exclusive projects, one cannot remain indifferent as to the choice of the rule.
5) Profitability Index
Profitability Index is a capital budgeting technique which can be defined as the ratio of the present value of cash flows at the required rate of return to the initial cash outflow on the investment. It is also called the benefit –cost ratio because it shows the present value of benefits per dollar of the cost. It is therefore a relative means of measuring a project’s return. It thus can be used to compare projects of different sizes.
- The profitability index (PI) is an investment appraisal method used to determine the attractiveness of a project.
- The PI is calculated by dividing the present value of future expected cash flows of an investment by the initial cash outlay of the investment.
- The investment is acceptable if the PI is greater than 1.0. Projects with higher values are more attractive.
- Under capital constraints and mutually exclusive projects, only those with the highest PIs should be undertaken.
A PI of less than 1 indicates that the present value of the investment’s inflows is less than its initial investment cost.
The components of profitability index are:
- Present value of future cash flows
- Initial investment cost
How to Calculate Profitability Index
PI can be calculated using the following formula:
Profitability Index = PV of future cash flows/initial investment
Based on the above formula, future cash flows of an investment requires the use of time value of money to get the present value. Future cash flows are discounted based on the number of periods of the project to get their present monetary value.
Example:
Dante Hospital wants to buy two mutually exclusive projects. Project A costs $1 million and generates cash flows of $200,000 annually for the next 5 years with a discount rate of 10%. Project B costs $2 million and generates cash flows of $300,000 per year for the next 5 years with a discount rate of 10%.
Project A:
Cash Inflows ($) | Calculation | PV ($) | |
Year 1 | 200,000 | 200,000/(1 + 0.10)^1 | 181,818 |
Year 2 | 200,000 | 200,000/(1 + 0.10)^2 | 165,289 |
Year 3 | 200,000 | 200,000/(1 + 0.10)^3 | 150,263 |
Year 4 | 200,000 | 200,000/(1 + 0.10)^4 | 136,603 |
Year 5 | 200,000 | 200,000/(1 + 0.10)^5 | 124,184 |
NPV | $758,157 |
Profitability index for project A = $758,157/$1,000,000 = 0.758
Project B
Cash Inflows ($) | Calculation | PV ($) | |
Year 1 | 300,000 | 300,000/(1 + 0.10)^1 | 272,727.27 |
Year 2 | 300,000 | 300,000/(1 + 0.10)^2 | 247,933.88 |
Year 3 | 300,000 | 300,000/(1 + 0.10)^3 | 225,394.44 |
Year 4 | 300,000 | 300,000/(1 + 0.10)^4 | 204,904.04 |
Year 5 | 300,000 | 300,000/(1 + 0.10)^5 | 186,276.40 |
NPV | 1,137,236.03 |
Profitability Index for project B = $1,137,236/$2,000,000 = 0.569
Since 0.758 > 0.569, Project A > Project B.
Project A is more attractive than Project B because project A has a higher profitability index. However, since the profitability index for both projects is less than 1, the company may not invest in any of the two projects and look for other opportunities.
Advantages and Disadvantages of Profitability Index
Profitability Index (PI) is a good capital budgeting technique that can enable a company to choose the best business investment, but it also has its own weaknesses and limitations. Some of the advantages and disadvantages of profitability index as an investment appraisal method are listed below:
Advantages:
- PI considers the time value of money: The PI technique is cognizant of the fact that money today is worth much more than the same amount in the future. Since money earns interest and inflation lowers the value of money, considering the time value of money gives a more accurate way of measuring the attractiveness of an investment.
- Enables companies to compare more than two projects because it considers the present value of cash flows rather than totaling the expected cash flows.
- Promotes decision making in an organization by giving managers an objective way to evaluate the attractiveness of investments.
Disadvantages
- Profitability index considers only the initial capital outlay and does not consider future investments or costs of maintaining the investment in the future.
- It does not consider the size of the project – a large project with lower profit margins may have a lower profitability index than smaller projects with high profit margins.
- It may be difficult to determine accurate cash flows and discount rates, which may affect the accuracy of the profitability index. If assumptions used to calculate the PI including discount rate are incorrect, the resulting profitability index will not be accurate.