What are the popular evaluation techniques?
Several methods of evaluating investment projects are as follows:

  • Payback period
  • Discounted payback period
  • Accounting (simple) rate of return (ARR)
  • Net present value (NPV)
  • Internal rate of return (IRR) (or time adjusted rate of return)
  • Profitability index (or present value index)

The NPV method and the IRR method are called discounted cash flow (DCF) methods. Each of these methods is discussed below.

How do you determine the payback period?
The payback period measures the length of time required to recover the amount of initial investment. When the annual cash flows are constant and of equal amounts, then the payback period can be calculated by dividing the initial investment by the cash inflows through increased revenues or cost savings.

Cost of investment: $18,000
Annual after-tax cash savings: $3,000
Then, the payback period is:

Payback period =(INITIAL INVESTMENT)/(COST SAVINGS)=($18.000)/($3000)=6 YEARS

Decision rule: Choose the project with the shorter payback period. The rationale behind this choice is: The shorter the payback period, the less risky the project, and the greater the liquidity. NOTE: When periodic cash flows are not equal, then cal­culation of the payback period is more complex.

Consider the two projects whose after-tax cash inflows are not even. Assume each project costs $1,000.

When cash inflows are not even, the payback period has to be found by trial and error. The payback period of project A is ($1,000= $100 + $200 + $300 + $400) 4 years. The payback period of project B is $1,000 = $500 + $400 + $100):

2 years +$100/$300=2*1/3 years

Project B is the project of choice in this case, since it has the shorter payback period.

What are the pros and cons of the payback period method?
The advantages of using the payback period method of evaluating an investment project are that (1) it is simple to compute and easy to understand, and (2) it handles investment risk effectively . The shortcomings of this method are that (1) it does not recognize the time value of money, and (2) it ignores the impact of cash inflow received after the payback period; essentially, cash flows after the payback period determine profitability of an investment.

How do you determine the discounted payback period?
You can take into account the time value of money by using the discounted payback period. The payback period will be longer using the discounted method since money is worth less over time.
Discounted payback is computed by adding the present value of each year`s cash inflows until they equal the initial investment.

Discounted payback = (Initial cash outlays)/ Discounted annual cash inflows

You invest $40,000 and receive the following cash inflows. The discounted payback period is calculated as follows:


$30,165 +($40,000 - 3,0165)/$21,036 = 2 years + .47 = 2.47 years

What is the accounting rate of return?

Accounting rate of return (ARR) measures profitability from the conventional accounting standpoint by relating the required investment-or sometimes the average investment-to the future annual net income.
Decision rule: Under the ARR method, choose the project with the higher rate of return.


Consider the following investment:

Initial investment: $6,500
Estimated life: 20 years
Cash inflows per year :$1,000
Depreciation per year (using straight line method): $325
ARR = (Project`s Averange Annual Income)/(Initial (or Average) Investment)

Average investment is defined as follows:

Average investment = (I - S)/2 + S

where I = initial (original) investment and S = salvage value.
When there is no salvage value, the average investment = I / 2
Decision rule: Under the ARR method, choose the project with the higher rate of return.

What are the benefits and drawbacks of the ARR method?
The advantages of this method are that it is understandable, simple to compute, and recognizes the profitability factor.
The shortcomings of this method are that it fails to recognize the time value of money, and it uses accounting instead of cash flow data.

What is internal rate of return?
Internal rate of return (IRR) is defined as the rate of interest that equates I with the PV of future cash inflows. In other words, at IRR,
I = PV
NPV = 0

Decision rule: Accept the project if the IRR exceeds the cost of capital. Otherwise, reject it.

Consider the following investment:
Initial investment: $37,910
Estimated life: 5 years
Annual cash inflows after taxes: $10,000
Cost of capital (minimum required rate of return):8%

We set the following equality (I = PV):

$37,910 = $10,000 . T4(i,5 years)

T4(i,5 years) =$37,910/$10,000 = 3.791

which is right on 10% in the 5-year line of Table 4.4.

Since the IRR of the investment is greater than the cost of capital (8 percent), accept the project. Note that the cost of capital is also called as a hurdle rate or minima required rate of return.

What are the benefits and drawbacks of the IRR method?
The advantage of using the IRR method is that it considers the time value of money and, therefore, is more exact and realistic than the ARR method. The shortcomings of this method are that (1) it is time-consuming to compute, especially when the cash inflows are not even, although
most business calculators and spreadsheet software have a program to calculate IRR, and (2) it fails to recognize the varying sizes of investment in competing projects.
NOTE: When cash inflows are not even, IRR is computed by the trial and error method, which is not discussed here. Financial calculators such as Texas Instruments and Sharp have a key for IRR calculations.

What is net present value?
Net present value (NPV) is the excess of the present value (PV) of cash inflows generated by the project over the amount of the initial investment (I):
NPV = PV - I
The present value of future cash flows is computed using the so-called cost of capital (or minimum required rate of return) as the discount rate. In the case of an annuity, the present value would be
PV = A * T4 (i, n)
where A is the amount of the annuity. The value of T4 is found in Table 4.4 of Chapter 4.

Decision rule: If NPV is positive, accept the project. Otherwise reject it.

Assume the same data given in Example 5.5 and the net present value of the cash inflows is:

Present value of the cash inflows is:

PV = A * T4 (i, n)
= $10,000. T4(8%,5 years)
= $10,000 (3.993)
Initial investment (I) 37,910
Net present value (NPV = PV - I) $ 2,020

Since the NPV of the investment is positive, the investment should be accepted.

What are the pros and cons of the NPV method?
The advantages of the NPV method are that it obviously recognizes the time value of money and it is easy to compute whether the cash flows are in the form of an annuity or vary from period to period.

Can a Computer Help?
Spreadsheet programs can be used in making IRR calculations. For example, Excel has a function IRR(values, guess). Excel considers negative numbers as cash outflows such as the initial investment, and positive numbers as cash inflows. Many financial calculators have similar features. As in Example 3, suppose you want to calculate the IRR of a $37,910 investment (the value --37910 entered in year 0 that is followed by 5 monthly cash inflows of $10,000). Using a guess of 8% (the value of 0.08), which is in effect the cost of capital, your formula would be @IRR(values, 0.08) and Excel would return 10%, as shown below.

Note: The Excel formula for NPV is NPV (discount rate, cash inflow values) + I, where I is given as a negative number.

How does the profitability index work?
The profitability index uses the same variables as NPV but combines them differently. Profitability index (P1) is defined as the ratio of the total PV of future cash inflows to the initial investment, that is, PV/I. This index is used as a means of ranking projects in descending order of attractiveness. Normally, when comparing more than one project, the one with the higher PI is the more profitable. CAUTION: A higher PI does not always coincide with the project with the highest NPV.

Decision rule: If PI is greater than 1, then the project is a good candi­date for investment.

Using the data in Example 5.5, the profitability index is

PV/I= $39,930/$37,910= 1.05

Since this project generates $1.05 for each dollar invested (i.e., its profitability index is greater than 1), accept the project.
The profitability index has the advantage of putting all projects on the same relative basis regardless of size.

What is capital rationing?
Capital rationing occurs whenever a company cannot or will not undertake all investment projects with NPV greater than or equal to zero. Usually the company has set an upper limit to its capital budget, thereby preventing it from under­taking all projects.

How do you select the best mix of projects with a limited budget?
Many firms specify a limit on the overall budget for capital spending. Capital rationing is concerned with the problem of selecting the mix of acceptable projects that provides the highest overall NPV. The profitability index is used widely in ranking projects competing for limited funds.

A company with a fixed budget of $250,000 needs to select a mix of acceptable projects from the following:

The ranking resulting from the profitability index shows that the company should select projects A, B, and D.

A $70,000 $112,000
B 100,000 145,000
D 60,000 79,000
$230,000 $336,000


NPV = $336,000 - $230,000 = $106,000

How do the projects relate to each other?
Investment projects are either independent or mutually exclusive. They are independent if both can be undertaken simultaneously. When this occurs, there`s no need to rank one project over another. Projects are mutually exclusive when only one project can be carried out. Then it is necessary to rank the projects to determine which is most attractive.

How do you choose between mutually exclusive investments?
A project is said to be mutually exclusive if the acceptance of one project automatically excludes the acceptance of one or more other projects (for example, two alternative uses of a single plot of land). In the case where one must choose between mutually exclusive investments, the NPV and IRR methods may result in contradictory indications. The conditions under which contradictory rankings can occur are:
1. Projects that have different life expectancies.
2. Projects that have different sizes of investment.
3. Projects whose cash flows differ over time. For example, the cash flows of one project increase over time, while those of another decrease.

The contradictions result from different assumptions with respect to the reinvestment rate on cash flows from the projects.
1.  The NPV method discounts all cash flows at the cost of capital, thus implicitly assuming that these cash flows can be reinvested at this rate.
2.  The IRR method assumes that cash flows are reinvested at the often unrealistic rate specified by the project`s internal rate of return. Thus, the implied reinvestment rate will differ from project to project.

Thus, the relative desirability of mutually exclusive projects depends on what rate of return the subsequent cash flows can earn. The NPV method generally gives correct ranking, since the cost of capital is a more realistic reinvestment rate. The cost of capital tends to give a close approximation for the market rate of return.


Assume the following:

Cash Flows

0 1 2 3 4 5
A (100) 120
B (100) 201.14

Computing IRR and NPV at 10 percent gives the following different rankings:

IRR NPV at 10%
A 20% 9.08
B 15% 24.90

The difference in ranking between the two methods is caused by the methods` reinvestment rate assumptions. The IRR method assumes Project A`s cash inflow of $120 is reinvested at 20% for the subsequent 4 years and the NPV method assumes $120 is reinvested at 10%. The correct decision is to select the project with the higher NPV (that is, Project B), since the NPV method assumes a more realistic reinvestment rate, that is, the cost of capital (10% in this example).

The net present values plotted against various discount rates (costs of capital) results in the NPV profiles for projects A and B (Figure 5.1). An analysis of Figure 5.1 indicates that at a discount rate larger than 14 percent, A has a higher NPV than B. Therefore, A should be selected. At a discount rate less than 14 percent, B has the higher NPV than A, and thus should be selected.



The correct decision is to select the project with the higher NPV, since the NPV method assumes a more realistic reinvestment rate, that is, the cost of capital.

Which is the preferable project if NPV and IRR do not give consistent signals?
In order to resolve this conflict, you need to know the interest rate or rates at which the company will be able to reinvest net cash inflows from the projects as these funds are generated. In other words, you need to forecast future or compound values of the net cash inflows as of the end of the expected life of the projects.

What is the use of Modified Internal Rate of Return?
The modified internal rate of return (MIRR) is defined as the discount rate which forces the Initial cash outlay = present value of terminal (future) value compounded at the cost of capital.
The MIRR forces cash flow reinvestment at the cost of capital rather than at the project`s own IRR, which was the problem with the IRR. MIRR avoids the problem of multiple IRRs. However, conflicts can still occur in ranking mutually exclusive projects with differing sizes. NPV should again be used when this occurs.

Refer back to Example 5.9, where computing IRR and NPV at 10% gives the following different rankings:

Projects IRR NPV at 10%
A 20% $ 9.08
B 15% 24.90

As noted, the correct decision is to select the project with the higher NPV (Project B), since the NPV method assumes a more realistic reinvestment rate, that is, the cost of capital (10% in this example). The MIRR overcomes this problem.

Project A`s MIRR:

First, compute the project`s terminal value at a 10% cost of capital.
120 x T1(10%, 4 years) = 120 x 1.4641 =175.69

Next, find the IRR by setting:

100 = 175.69 T3(MIRR, 5 years)
T3 = 100/175.69 = 0.5692, which gives MIRR = about 12%

Now we see the consistent ranking from both the NPV and MIRR methods.

MIRR NPV at 10%
A 12% $ 9.01
B 15% 24.90

Note: Microsoft Excel has a function MIRR(values, finance_rate, reinvest_rate).

Full course available on the App Store:

for iPhone:

for iPad:

for Mac:

Web Version of course will be available soon.