Introduction
After appraising certain projects in terms of market analysis, technical analysis, financial analysis, economic analysis, and environmental analysis, we need criteria to help decide which project to accept and which one to reject before investing scarce resources on any project. There are basically two methods of project evaluation that we can use to help decide whether to proceed with a project idea or to discard the idea altogether. These are: - The static methods, and - The dynamic methods.
The Static Method
The static method consists of:
The Dynamic Method
The dynamic method comprises of:
Let us start with the static method, beginning with the payback period method.
The Payback Period Method
The payback period is defined as the number of years required to recover the initial investment (the cash outlay) of the project. If the project has a constant cash inflows, it is possible to calculate the payback period by dividing the initial investment or cash outplay by the annual cash inflow.
Example
Suppose that a project requires an initial investment or cash outlay of N600,000 and its annual cash inflows is N60,000 for a period of thirteen (13) years. Calculate the payback period.
\[ \begin{eqnarray} \hline \text{Payback Period} &=& \frac{Initial Investment}{Annual Cash Inflow}\\ &=& \frac{600,000}{60,000}\\ &=& 10 years \end{eqnarray} \]
In the case where the annual cash inflows are unequal,then the cash inflows can be summed up until it is equal to the initial investment.
Example:
A project has an initial investment cash outlay of N300,000. The annual cash inflows for six years are: N50,000, N70,000, N90,000, N50,000, N45000, and N25,000. Calculate the payback period.
| Year | Cash Inflows | Cumulative Cash inflows |
|---|---|---|
| 1 | N50,000 | 50,000 |
| 2 | 70,000 | 120,000 |
| 4 | 50,000 | 260,000 |
| 5 | 45,000 | 305,000 |
| 6 | 25,000 | 330,000 |
| ———– | ——————– | ———————– |
The payback period is 5 years.
Advantages of the payback period:
Disadvantages of the payback period:
Accounting Rate of Return Method
This method uses accounting information to measure the profitability of an investment project. It is calculated by dividing the average annual accounting profits or average annual earnings by the average investment. That is, the Accounting Rate of Return (ARR) is computed as follows.
\[ \begin{equation} ARR = \frac{Average Annual Earnings}{Average Investment} \end{equation} \]
Example:
A project’s initial investment cost is N100,000 and has a scrap value of N40,000. The stream of income before depreciation and taxes are N40,000, N50,000, and N60,000 for the first three (3) years. The tax rate is \(50\%\) and depreciation is charged on a straight line basis. Compute the accounting rate of return for this project.
First, calculate depreciation. Depreciation will be equal to the investment cost minus salvage value divided by the number of years of investment. That is,
\[ \begin{eqnarray} Depreciation &=& 100,000 - 40,000\\ &=& \frac{60,000}{3}\\ &=& 20,000 \end{eqnarray} \]
Let us use the following table to calculate earnings before depreciation and taxes, net earnings before taxes, taxes, and net earnings after taxes as follows.
Variable | Year_1 | Year_2 | Year_3 |
|---|---|---|---|
Earnings Before Depreciation and Taxes | 40,000 | 50,000 | 60,000 |
Depreciation | 20,000 | 20,000 | 20,000 |
Net Earnings Before Taxes | 20,000 | 30,000 | 40,000 |
Taxes | 10,000 | 15,000 | 20,000 |
Net Earnings After Taxes | 10,000 | 15,000 | 20,000 |
The Book value of investment is calculated as follows.
Begining | Ending | Average |
|---|---|---|
100,000 | 80,000 | 90,000 |
80,000 | 60,000 | 70,000 |
60,000 | 40,000 | 50,000 |
Let us now calculate the average earnings like so:
\[ Average Earnings = \frac{10,000+15,000+20,000}{3} = 15,000 \] The average investment will be”
\[ Average Investment = \frac{90,000+70,000+50,000}{3} = 70,000 \] Finally, the accounting rate of return would be:
\[ ARR = \frac{15,000}{70,000}\\ = 21.42\% \]
Accept or Reject Decision:
The ARR will accept all those projects whose ARR is greater than the minimum return required by the firm. Thus, of the minimum rate of return is \(15\%\), then the project will be accepted, otherwise it will be rejected.
Advantages:
Disadvantages:
Discounted Cash Flow (DCF) Methods
The discounted cash flow methods are superior to the previous methods in that they consider the time value of money and the timing of cash flows. The main DCF methods are:
The NPV Method
Cash flows arise at different time periods and thus differ in value. The cash flows can only be comparable if we can find their equivalent present value. To compute the NPV, we need to:
Decision Rule:
If the NPV is positive, accept the investment project; if it is negative, reject the investment project.
One can interpret the NPV of an investment project as follows:
Example:
A project cost an initial outlay of N500,000. The roject’s cash flows are N150,000, N300,000, and N400,000 over a three year period. The required rate of return is \(10\%\). Calculate the NPV of this project.
Solution:
Create a table to calculate the NPV as follows:
Year | Cash_inflows | Discount_factor | Present_value | Total | Less_Capital_Investment | NPV |
|---|---|---|---|---|---|---|
1 | 150,000 | 0.909 | 136,350 | |||
2 | 300,000 | 0.826 | 247,800 | |||
3 | 400,000 | 0.751 | 300,000 | 684550 | -500000 | 184500 |
In general, the NPV can be calculated as follows:
\[ NPV = \frac{CIF_1}{(1+i)^1}+\frac{CIF_2}{(1+i)^2}+\frac{CIF_3}{(1+i)^3}+...\frac{CIF_T}{(1+i)^T}-C \]
Advantages:
Disadvantages:
Internal Rate of Return Method
The internal rate of return is the rate that equalizes the present value of cash inflows with the present value of cash outflows of an investment project. It is the rate at which the NPV equals zero. It is called IRR because it depends solely on the cash outlay and cash inflows of the project and not on any rate determined outside the investment project.
To calculate the IRR. Let:
Then the formula is given as follows:
\[ IRR_t = \frac{CIF_1}{(1+r)^1}+\frac{CIF_2}{(1+r)^2}+\frac{CIF_3}{(1+r)^3}+...\frac{CIF_T}{(1+r)^T}-C = 0 \]
The value of \(r\) which equalizes total cash outlays to the total cash inflows is called the internal rate of return.
Calculating the value of r:
In calculating the value of \(r\), one can use trial and error. In doing so, one can try a lower rate if the present value of cash inflows is lower than the present value of cash outflows. Alternatively, one can try a higher rate if the present value of cash inflows is greater than the present value of cash outflows. The value of \(r\) in the equation where total cash outlays equal total cash inflows is the internal rate of return.
Example:
A saloon’s shop costs N320,400 to establish and its expected cash inflows are N160,000, N140,000, N120,000 over its life of three years. Calculate the internal rate of return.
Solution:
Using the trial and error method, start by trying \(16\%\). The table of values will appear like so:
Variable | Cash_inflows | Discount_factor | Present_value | Total | Cash_outlay | NPV |
|---|---|---|---|---|---|---|
1 | 160,000 | 0.862 | 130,792 | |||
2 | 140,000 | 0.743 | 110,402 | |||
3 | 120,000 | 0.641 | 70,692 | 310886 | 320400 | -9514 |
Now try a lower rate, say, \(14\%\). Then, you would get:
Variable | Cash_inflows | Discount_factor | Present_value | Total | Cash_outlay | NPV |
|---|---|---|---|---|---|---|
1 | 160,000 | 0.877 | 140,320 | |||
2 | 140,000 | 0.763 | 107,660 | |||
3 | 120,000 | 0.675 | 81,000 | 328980 | 320400 | 8580 |
The NPV is now positive. This means the internal rate of return lies between \(16\%\) and \(14\%\).
Decision Rule:
IRR can be interpreted as the highest rate of interest a firm will be willing to pay on funds borrowed to finance the project without being financially worse off by repaying the principal and accrued interest out of the cash inflows generated by the project.
Advantages:
Disadvantages: