Project Evaluation Criteria
Managers are often required to make choices among capital projects that may deliver benefits and may also consume resources on an annual basis over a number of periods. Several standard methods are used in industry to evaluate such projects (Eriona and Nguyen 2013). These include net present value (NPV), internal rate of return (IRR), payback (PB), and profitability index (PI).
1. Net present value where:
NPV = Net present value (dollars)
P = Present investment made to initiate a project activity (dollars)
NCIF(m) = Net cash inflow (dollars) in the period m, which represents revenues earned minus costs incurred = R(m) - C(m)) (dollars) i = Cost of capital (interest) rate (fraction) n = Number of interest period (year)
CR = Capital recovery (dollars), which is the amount regained at the end of the project through resale or other methods of disposition
Note that the first term on the right-hand side is the capital outlay for the project, or an outflow of value (cash). The second term on the right-hand side is the sum of discounted net cash inflow earned over the years. The third term on the right-hand side is the discounted capital recovery of the project.
One major weakness of the NPV equation is that all benefits derived from a project must be expressed in dollar equivalents—within NCIF(m)—in order to be included. Nonmonetary benefits, such as enhanced corporate image, expanded market share, and others, cannot be represented.
For the special case of NCIF(m) = CF = constant
Projects with the largest NPV values are preferable, as NPV represents the net total value added (before tax) to the firm by the project at hand. Note that NPV may be determined only if the project's net cash inflow NCIF(m) is known.
2. Internal rate of return. Rate of return is generally defined as the earnings realized by a project in a percentage of its principal capital.
The IRR is the average rate of return (usually annual) realized by a project in which the total net cash inflow is exactly balanced with its total net cash outflow, resulting in zero NPV value at the end of its project life cycle. In other words, this is the rate realizable when reinvestment of the project earnings is made at the same rate until maturity.
IRR is determined by the following equations:
For NCIG(m) = CF = constant.
The IRR values (before tax) of acceptable projects must be much greater than the firm's cost of capital. Projects with high IRR are preferable.
3. Payback period. The PB is defined as the number of years that the original capital investment for the project will take to be paid back by its annual earnings, or
where:
P = Capital investment
CF = Annual cash flow realized by the project
Cost reduction projects with small PBs (e.g., less than two years) are preferable.
4. Profitability index. PI is defined by the ratio
Projects with large PI values are preferable.
Example 6.6
Your company is currently pursuing three cost reduction projects at the same time.
- • Project A requires an investment of $10 million. It is expected to yield a cost savings of $30 million in the first year and another $10 million in the second year.
- • Project B demands an investment of $5 million. It is expected to produce a cost savings of $5 million in the first year and another $20 million in the second year.
- • Project C needs an investment of $5 million. It is expected to bring about a cost savings of $5 million in the first year and another $15 million in the second year.
After the second year, there will be no receivable benefit or capital recovery from any
of these projects. The cost of capital (interest rate) is 10% per year.
Determine the ranking of these projects on the basis of the evaluation criteria of NPV,
IRR, PB, and PI.
Answer 6.6
Table 6.12 summarizes the results obtained:
P = Present investment
n = 2
CF = Cash flow
CR = Capital recovery = 0
i = 10%
TABLE 6.12
Summary of Results
Project |
Time > |
NPV |
IRR (%) |
PB |
PI |
||
0 |
1 |
2 |
|||||
A |
-10 |
30 |
10 |
25.5 |
230 |
0.5 |
3.55 |
B |
-5 |
5 |
20 |
16 |
156 |
0.4 |
4.22 |
C |
-5 |
5 |
15 |
12 |
130 |
0.5 |
3.39 |
NPV computation
- 1. NPV = - 10 + 30/1.1 + 10/1.1^{2} = $25.537
- 2. NPV = -5 + 5/1.1 + 20/1.1^{2} = $16.074
- 3. NPV = -5 + 5/1.1 + 20/1.1^{2} = $11.942
IRR
- 1. 0 = -10 + 30/(1 + r) + 10/(1 + r)^{2}; r = 2.3%
- 2. 0 = -5 + 5/(1 + r) + 20/(1 + r)^{2}; r = 1.56%
- 3. 0 = -5 + 5/(1 + r) + 15/(1 + r)^{2}; r = 1.3%
PB
- 1. PB = 10/[(30 + 10)/2] = 0.5 year
- 2. PB = 5/[(5 + 20)/2] = 0.4 year
- 3. PB = 5/[(5 + 15)/2] = 0.5 year
PI
- 1. PI = [3.0/1.1 + 10/1.1^{2}]/10 = 3.553
- 2. PI = [5/1.1 + 20/1.1^{2}]/5 = 4.214
- 3. PI = [5/1.1 + 15/1.1^{2}]/5 = 3.3884