The document discusses capital budgeting techniques, including methods like payback period, discounted payback, net present value (NPV), profitability index, internal rate of return (IRR), and modified internal rate of return (MIRR). It outlines the importance of these tools for financial managers to evaluate and select investment projects, emphasizing their role in assessing project risks and returns. Additionally, the document highlights the strengths and limitations of each method, guiding decision-making in project approvals.

1. Capital Budgeting
Techniques
By lkjs
Saeed Akbar

2. Topics to be Covered
 The Basics of Capital Budgeting
 The Concept of Capital Budgeting
 The Payback Method and Discounted Payback Period
 The Net Present Value Method
 Profitability Index
 The Internal Rate of Return Method
 Modified Internal Rate of Return

3. Introduction
 We now look at the decision methods that analysts use to determine whether
to approve a given investment project and how they account for a project’s
risk.
 The decision methods for choosing acceptable investment projects are some
of the most important tools financial managers use.
 Capital budgeting is the process of evaluating proposed large, long-term
investment projects.
 Apple Computer’s development of the iPhone was a capital budgeting project.
 Facebook purchasing Instagram and WhatsApp are also capital budgeting
projects.

4. Types of Projects and Decision Practices
 Firms invest in two categories of projects: independent projects and mutually
exclusive projects.
 Independent projects do not compete with each other. A firm may accept
none, one, some, or all from among a group of independent projects.
 Mutually Exclusive projects compete against each other. The best project
from among a group of acceptable mutually exclusive projects is selected.
 Financial managers apply two decision practices when selecting capital
budgeting projects: accept/reject and ranking.
 The accept/reject decision focuses on the question of whether the proposed
project would add value to the firm or earn a rate of return that is
acceptable to the company.
 The ranking decision lists competing projects in order of desirability to choose
the best one.

5. Stages in the Capital Budgeting Process
 1. Finding projects
 2. Estimating the incremental cash flows associated with projects
 3. Evaluating and selecting projects
 4. Implementing and monitoring projects

6. The Payback Period Method
 Payback Period refers to the number of time periods it will take before the
cash inflows of a proposed project equal the amount of the initial project
investment (a cash outflow). We accept the project having minimum payback
period
 Look at the above two projects. Both require an initial investment of $5,000.
Project X recovers its initial investment in two years (2000 in year 1 + 3000 in
year 2). While Project Y recovers its initial investment in 3 years
(2000+2000+1000). So the payback period of Project X is 2 years while project
Y’s payback period is 3 years. Now Project X recovers its initial investment
quicker than Project Y so we accept Project X.

7. The Payback Period Method
 We often face certain projects for which we cannot find the payback period
directly. For example look at the following project A.
Year Project A (Cash flows)
0 ($100,000)
1 30,000
2 30,000
3 30,000
4 20,000
5 10,000
6 5,000
Now we cannot find the payback period of the above project directly. So we
use a formula to find the exact payback period.
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 = 𝑎 +
𝑏 − 𝑐
𝑑

8. The Payback Period Method
Year Cash Flows Cumulative Cash flows
0 ($100,000) b -----------
1 30,000 30,000
2 30,000 60,000
3 (a) 30,000 90,000 (c)
4 25,000 (d) 115,000
5 10,000 125,000
6 5,000 130,000
 Now we will allocate the values of the formula, i.e. a, b, c and d.
 We will look into the cumulative cash flows column and take the value which is the
closest to the initial investment before it exceeds the initial investment. Here, the
value is 90,000. So this is ‘c.’ The very next value in the cash flows column will be
‘d’ which is 25,000. The number of year straight to ‘c’ is ‘a’ which is 3 in this case
and initial investment will always be ‘b.’
Here we add another column, the
Cumulative Cash Flows.

9. The Payback Period Method
 Now let's put the values in the formula
 𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 = 3 +
100,000−90,000
25,000
 Payback Period = 3.4 years.
 here, 3.4 cannot be interpreted accurately. So we convert .4 into months by
multiplying it with 12.
.4 x 12 = 4.8 months
 now we can say that the payback period is 3 years and 4.8 months. We can also
round of 4.8 to 5 to make it 5 months but let's go towards more accurate payback
period by multiplying .8 by 30 to convert it into days.
 So .8 x 30 = 24 days
 No we have reached the exact payback period which is 3 years, 4 months and 24
days.

10. The Payback Period Method
 Problems with the Payback period method.
Since payback period is used due to its simplicity but it has several limitations.
1. It does not consider cash flows after the payback period. For example, let’s look
into these projects again.
We have accepted the project X as it returns its initial investment quicker than
Project Y. Now, if we look at the cash flows of Project X after the payback period,
its 500 and then 0. While Project Y has another cash flow of 2000 after the
payback period but still payback period method does not consider these cash flows
and accepts project X.
2. Another problem is that it does not consider time value of money.
Because the payback method does not factor in the time value of money, nor the cash
flows after the payback period, its usefulness is limited.

11. The Discounted Payback Period Method
 We discussed the limitation of the payback period method that it does not
consider time value of money. In order to overcome this limitation, another
version of the payback period is used, called the discounted payback period
method. This method discounts the cash flows and then finds the payback
period method.
 Recall the time value of money chapter. In order to discount an amount, we
use the following formula.
 𝑃𝑉 = 𝐹𝑉 𝑋
1
(1+𝑘)𝑛
 Where
1
(1+𝑘)𝑛 is the discount factor. So we will multiply all the incremental
cash flows of the project with this discount factor and then find out the
payback period.

12. The Discounted Payback Period Method
Consider the following project
Year Cash Flows x Discount factor @ 12% Discounted Cash Flows
0 ($100,000) x 1
1 35,000 x
1
(1+0.12)1 = 0.893 = 31255
2 35,000 x
1
(1+0.12)2 = 0.797 = 27895
3 33,000 x
1
(1+0.12)3 = 0.711 = 23463
4 25,000 x
1
(1+0.12)4 = 0.635 = 15875
5 20,000 x
1
(1+0.12)5 = 0.567 = 11340
6 10,000 x
1
(1+0.12)6 = 0.506 = 5060
 Now, as we have the discounted cash flows, we will proceed to find out the
payback period.

13. The Discounted Payback Period Method
Rest of the procedure is same as we did for simple payback period method. We will add another
column, cumulative cash flows, and then allocate a, b, c and d.
Year Discounted Cash Flows Cumulative Cash Flows
0 ($100,000) (b) -------------
1 31255 31255
2 27895 59150
3 23463 82613
4 (a) 15875 98488 (c)
5 11340 (d) 109828
6 5060 114888
𝑃𝑎𝑦𝑏𝑎𝑐𝑘 𝑃𝑒𝑟𝑖𝑜𝑑 = 𝑎 +
𝑏 − 𝑐
𝑑
= 4 +
100000 − 98488
11340
= 4.133
Let’s convert .133 into months by multiplying it by 12.
So .133 x 12 = 1.596 or 1.6 days. Again converting .6 into days by multiplying it by 30 we get
.6 x 30 = 18. So the discounted payback period for this project is 4 years, 1 month and 18 days

14. The Net Present Value (NPV) Method
 The net present value (NPV) of a capital budgeting project is the dollar
amount of the change in the value of the firm as a result of undertaking the
project. The change in firm value may be positive, negative, or zero,
depending on the NPV value.
 If a project has an NPV of zero, it means that the firm’s overall value will not
change if the new project is adopted. Why? Because the new project is
expected to generate exactly the firm’s required rate of return—no more and
no less. A positive NPV means that the firm’s value will increase if the project
is adopted because the new project’s estimated return exceeds the firm’s
required rate of return. Conversely, a negative NPV means the firm’s value
will decrease if the new project is adopted because the new project’s
estimated return is less than what the firm requires.
 Therefore, if a project’s NPV is positive, we will accept that project while
reject the project if its NPV is negative. If all the project has positive NPV’s
then we will accept the project with the highest NPV.

15. The Net Present Value (NPV) Method

16. The Net Present Value (NPV) Method
 Let’s calculate NPV for the following projects if the required rate of return is
10%
= -$526.822

17. The Net Present Value (NPV) Method
 Now for Project Y.
 As the NPV of project Y is positive while the NPV of Project X is negative so we will
accept the Project Y and reject project X.
 Recall that when we applied the Payback period method, the Project X was
accepted while here, it is rejected. This is because of the two limitations of the
Payback Period method.

18. The Net Present Value (NPV) Method
 Problems with the NPV Method: Although the NPV method ensures that a
firm will choose projects that add value to a firm, it suffers from two
practical problems. First, it is difficult to explain NPV to people who are not
formally trained in finance. Few nonfinance people understand phrases such
as “the present value of future cash flows” or “the change in a firm’s value
given its required rate of return.” As a result, many financial managers have
difficulty using NPV analysis persuasively.
 A second problem is that the NPV method results are in dollars, not
percentages. Many owners and managers prefer to work with percentages
because percentages can be easily compared with other alternatives; Project
1 has a 10 percent rate of return compared with Project 2’s 12 percent rate
of return. The next method we discuss, the internal rate of return, provides
results in percentages.

19. The Profitability Index
 Profitability Index is a Capital Budgeting Technique in which the costs and
benefits of the project are compared. We calculate the profitability index by
dividing the present value of all the cash flows by the initial investment.
 𝑃𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝐼𝑛𝑑𝑒𝑥 =
𝑃𝑉 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑓𝑢𝑡𝑢𝑟𝑒 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤𝑠
𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
 If the value of profitability index is greater than 1, we accept the project and
reject it if the value is less than 1.
 To find the PV of the future cash flows, we use the formula
 PV of future cash flows =

20. The Profitability Index
 Let’s calculate the Profitability Index for the Project Y which we used in the
calculation of NPV.
 PI = ÷ 5000
÷ 5000
= 1.117
 As the profitability index of project Y is 1.117 which is greater than 1, so
we accept the project Y.

21. Internal Rate of Return (IRR) Method
 The Internal Rate of Return (IRR) is the estimated rate of return for a
proposed project, given the project’s incremental cash flows. In simple
words, IRR is the rate at which NPV becomes 0. So we will use the NPV
formula and find out a rate (i) at which NPV becomes 0 and that rate will be
the IRR of the project.
 Just like the NPV method, the IRR method considers all cash flows for a
project and adjusts for the time value of money. However, the IRR results are
expressed as a percentage, not a dollar figure.
 When capital budgeting decisions are made using the IRR method, the IRR of
the proposed project is compared with the rate of return management
requires for the project. The required rate of return is often referred to as
the hurdle rate. If the project’s IRR is greater than or equal to the hurdle
rate (jumps over the hurdle), the project is accepted. In the case of mutually
exclusive projects, the project with highest IRR is selected.

22. Internal Rate of Return (IRR) Method
 In order to calculate the IRR, we use two methods: Trial-and-Error Method
and the Interpolation Method
 In Trial-and-Error method, we apply a rate (i) through our own guess till the
NPV becomes 0 or at least close to 0. This method is quite time consuming.
Let’s calculate IRR for project X through Trial-and-Error method.

23. Internal Rate of Return (IRR) Method

24. Internal Rate of Return (IRR) Method

25. Internal Rate of Return (IRR) Method
 Now we use Interpolation method to find the exact IRR at which NPV becomes
0. In this method, we take two rates (i), one at which NPV is negative and
other at which NPV is positive. No matter which rates we chose, all we need
are two NPV’s, one is negative while other is positive. Let’s calculate IRR for
the same project via Interpolation.
 We have already applied two rates, i.e. 5% and 6% at which NPV is $57.77 and
-$23.41 respectively. Now we will use the formula of Interpolation to find the
exact IRR.
 𝐼𝑅𝑅 = 𝑙𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑒 +
𝑁𝑃𝑉 𝑎𝑡 𝑙𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑒
𝑁𝑃𝑉 𝑎𝑡 𝑙𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑒−𝑁𝑃𝑉 𝑎𝑡 𝑢𝑝𝑝𝑒𝑟 𝑟𝑎𝑡𝑒
𝑢𝑝𝑝𝑒𝑟 𝑟𝑎𝑡𝑒 − 𝑙𝑜𝑤𝑒𝑟 𝑟𝑎𝑡𝑒
 𝐼𝑅𝑅 = 0.05 +
57.77
57.77 −(−23.41)
0.06 − 0.05
 IRR = 0.05 + 0.007 = 0.0571 or 5.71%
 So the IRR of project X is 5.71% which means that the NPV for project X will
be 0 at 5.71%.

26. Internal Rate of Return (IRR) Method
 Benefits of the IRR Method: The IRR method for selecting capital budgeting
projects is popular among financial practitioners for three primary reasons:
1. IRR focuses on all cash flows associated with the project.
2. IRR adjusts for the time value of money.
3. IRR describes projects in terms of the rate of return they earn, which makes
it easy to compare them with other investments and the firm’s hurdle rate.
 Problems with the IRR method:
1. because the IRR is a percentage number, it does not show how much the value
of the firm will change if the project is selected. If a project is quite small,
for instance, it may have a high IRR but a small effect on the value of the
firm.
2. If the primary goal for the firm is to maximize its value, then knowing the
rate of return of a project is not the primary concern. What is most important
is the amount by which the firm’s value will change if the project is adopted,
which is measured by NPV.

27. Modified Internal Rate of Return (MIRR) Method
 One problem with the IRR method that was not mentioned earlier is that the
only way you can actually receive the IRR indicated by a project is if you
reinvest the intervening cash flows in the project at the IRR. If the
intervening cash flows are reinvested at any rate lower than the IRR, you will
not end up with the IRR indicated at the end of the project.
 For example, assume you have a project in which you invest $100 now and
expect to receive four payments of $50 at the end of each of the next four
years:
t0 t1 t2 t3 t4
–100 +50 +50 +50 +50
 If you calculate the IRR of this project, it is 34.9% which seems very good. But
you would only get this IRR if you are able to reinvest each cash flow at
34.9%. If you can’t reinvest each $50 payment at the IRR of 34.9 percent,
forget it; you won’t end up with an overall return of 34.9 percent.

28. Modified Internal Rate of Return (MIRR) Method
 To see why, consider what would happen if, for example, you simply put each
$50 payment in your pocket. At the end of the fourth year you would have
$200 in your pocket. Now, using Equation 8-6, calculate the average annual
rate of return necessary to produce $200 in four years with a beginning
investment of $100:
Actual return on the investment
𝑖 = (
𝐹𝑉
𝑃𝑉
)
1
𝑛 −1
𝑖 = (
200
100
)
1
4 −1 = .189, or 18.9% (not 34.9%)
 Despite the fact that the IRR of the investment was 34.9 percent, you only
ended up with an 18.9 percent annual return. The only way you could have
obtained an annual return of 34.9 percent was to have reinvested each of the
$50 cash flows at 34.9 percent. This is called the IRR Reinvestment
Assumption.

29. Modified Internal Rate of Return (MIRR) Method
 The MIRR method calls for assuming that the intervening cash flows from a
project are reinvested at a rate of return equal to the cost of capital. To find
the MIRR, first calculate how much you would end up with at the end of a
project, assuming the intervening cash flows were invested at the cost of
capital. The result is called the project’s terminal value. Next, calculate the
annual rate of return it would take to produce that end amount from the
beginning investment. That rate is the MIRR.
 Here is the MIRR calculation for the project in our example, in which $100 is
invested at time zero, followed by inflows of $50 at the end of each of the
next four years. Let us assume for this example that the cost of capital is 10
percent.

30. Modified Internal Rate of Return (MIRR) Method

31. Modified Internal Rate of Return (MIRR) Method
 Step 2: Calculate the annual rate of return that will produce the terminal
value from the initial investment:
 Project’s Terminal Value: $232.05
 PV of Initial Investment: $100

32.  Try to solve the Self-Test questions and problems in the exercise and
let me know if you face any difficulty in solving a problem.
 The Youtube link for the video lecture of this chapter is: