Capital Budgeting - Introduction
Readings: Chapter 10
At the end of this unit students should be able to:
Define capital budgeting and explain why it is important.
List the steps involved in evaluating a capital budgeting project.
Classify capital budgeting project proposals
Calculate payback period, discounted payback period, Net Present Value (NPV), and Internal Rate of Return (IRR) for a given project and evaluate each method.
Explain the rationale behind the NPV and IRR methods, their reinvestment rate assumptions, and which method is better when evaluating independent versus mutually exclusive projects.
Define and construct NPV profiles
Briefly explain the problem of multiple IRRs and when this situation could occur.
Calculate the Modified Internal Rate of Return (MIRR) for a given project and evaluate this method.
Identify and explain the purposes of the post-audit in the capital budgeting process.
Capital
budgeting is also known as 'capital investment appraisal'. It is the process of using the
company's resources to acquire long-term assets, which allows the company to
carry on its operations. These decisions are different from current expenditure,
which is concerned with short-term assets. They are also different from
portfolio investments (which is the allocation of excess cash to acquire
financial assets). However, the portfolio investment process is similar to the
capital budgeting process.
1.
Capital budgeting decisions are important since they normally involve all
ranks of management
2.
Once the decision is taken it normally locks the company into a fixed
path of production for some time
3.
It also involves large sums of money, which can be recovered only over
several years.
The
main objective of capital budgeting is the selection and implementation of those
projects, which increases the value of the firm, that is, increases shareholders'
wealth.
There
is a four-step process to capital budgeting:
1.
Identify the opportunities available to the company
2.
Obtain and collate all pertinent information
3.
Apply one or more of the decision rules and select the best alternative
or alternatives
4.
Complete a post-audit, That is, revisit the information gathering and the
decision making process with the aim of improving them for future use.
Expansion vs Replacement Projects
There
are basically two broad classifications of projects
1.
The expansion-type project - the company acquires resource machinery
in order to produce new products or to enter into new markets.
2.
The replacement type project. This is aimed at replacing obsolete machinery
in order to maintain current operations
Mutually Exclusive vs Independent Projects
Mutually exclusive projects are those where the decision to accept one precludes the acceptance of any other. Normally, mutually exclusive projects are aimed at achieving the same end but only one can be selected. Independent projects on the other hand are those where the acceptance of one does not affect the decision to accept the other, in other words, all can be accepted.
Accounting
Income vs Cash flows
Net Income is not a good decision variable in Finance. The reason for
this is that Net Income is the figment of a creative accountant’s mind, and
therefore very subjective. The
variable of importance is called cash flows, which is concerned with the cash
flowing in and out of the company.
Capital
Rationing
Capital Rationing is the process of deliberately limiting the funds available for capital investment. By so doing the firm with a number of acceptable projects may have to forego some, as available funding does not allow investing in all the good projects. The main reason for this is the reluctance of the company to use external sources of funding. Capital rationing therefore does not maximize the value of the company. Nevertheless, the Profitability Index (see below) is the criteria which is often used to rank projects when Capital Rationing exists. The Profitability Index is not a full proof method as there are occasions when its use does not accurately reflects the proper ranking.
Project
Selection Methods
There
are two basic categories:
| 1. Non-discounting* | 2.
Discounted Cash
Flows |
|
(a) Payback Period |
(b) Discounted Payback period |
| (c)
Net Present
Value (NPV) |
|
| (d)
Profitability
Index (PI) |
|
| (e)
Internal rate
of Return (IRR) |
|
| (f) Modified Internal Rate of Return (MIRR) |
* - Another selection method is the Accountant's Rate of Return (ARR). It is not discussed here because it utilises net profit which by itself has inherent limitations due to its subjectivity.
|
|
Project A |
Project B |
|
Period |
After-tax Cash Flows | After-tax Cash Flows |
|
0 |
(5,000) |
(5,000) |
|
1 |
3,000 |
1,000 |
|
2 |
2,500 |
2,200 |
|
3 |
1,700 |
4,700 |
|
4 |
800 |
3,000 |
The
table above lists after-tax cash flows over four periods
for two mutually exclusive projects of Company X which has a cost of capital of 10%. (Time period 0 is
now).
We will now use the above techniques to evaluate these projects:
(a)
Payback Period
This technique calculates the number of years in which it takes a company to recover its initial investment.
Project A
|
Year |
Amount to be recovered | Amount Recovered | Amount Outstanding |
| 1 | 5,000 | 3,000 | 2,000 |
| 2 | 2,000 | 2,500 | |
| Answer = 1 year and 2,000/2,500 = 1.8 years | |||
Project B
|
Year |
Amount to be recovered | Amount Recovered | Amount Outstanding |
| 1 | 5,000 | 1,000 | 4,000 |
| 2 | 4,000 | 2,200 | 1,800 |
| 3 | 1,800 | 4,700 | |
| Answer = 2 years and 1,800/4,700 = 2.38 years | |||
Decision Rule
For independent projects, a project should be selected if its PP is less than or equal to the company's standard PP. For mutually exclusive projects, select the project which has the shortest PP. In this case, Project A should be selected.
Pros and Cons
Pros -(1) Simple to calculate (2) Indicates the project's liquidity (3) It gives some sort of measure of risk, in that shorter recovery periods means that funds are tied up for shorter periods (4) It can be used to supplement other methods
Cons -(1) does not factor in cash flows which occur beyond the pay back period (2) It does not factor in the time value of money (3) It does not indicate to shareholders any change in their wealth position.
(b)
Discounted Payback Period
This is a modification of the method in part (a) above. As the name suggests, this method factors in the time value of money by first discounting the relevant cash flows using the project's/company's cost of capital..
Project A
|
Year |
Amount to be recovered | Discounted Amount Recovered | Amount Outstanding |
|
1 |
5,000 | 3000(PVIF10%1) = 3000(0.9091) = 2,727.30 | 2,272.70 |
| 2 | 2,272.70 | 2500(PVIF10%2) = 2500(0.8264) = 2,066.00 | 206.70 |
| 3 | 206.70 | 1700(PVIF10%3) = 1700(0.7513) = 1,277.21 | |
| Answer = 2 years and 206.70/1,277.21 = 2.16 years | |||
Project B
|
Year |
Amount to be recovered | Discounted Amount Recovered | Amount Outstanding |
|
1 |
5,000 | 1000(PVIF10%1) = 1000(0.9091) = 909.10 | 4,090.90 |
| 2 | 4,090.90 | 2200(PVIF10%2) = 2200(0.8264) = 1,818.08 | 2,272.82 |
| 3 | 2,272.80 | 4700(PVIF10%3) = 4700(0.7513) = 3,531.11 | |
| Answer = 2 years and 2,272.82/3,531.11 = 2.64 years | |||
Decision Rule
For independent projects, a project should be selected if its DPP is less than or equal to the company's standard D PP. For mutually exclusive projects, select the project which has the shortest D PP. In this case, Project A should be selected.
Pros and Cons
Pros -(1) Simple to calculate (2) It considers the time value of money (3) Indicates the project's liquidity (4) It gives some sort of measure of risk, in that shorter recovery periods means that funds are tied up for shorter periods (5) It can be used to supplement other methods
Cons -(1) does not factor in cash flows which occur beyond the pay back period (2) It does not indicate to shareholders any change in their wealth position.
(c)
Net Present
Value (NPV)
In this technique, all the cash flows associated with the project (including the initial investment) are discounted using the project's/company's cost of capital to arrive at a net present value.
Project A
|
|
Project B
|
|
Note - The NPV method assumes that cash flows are reinvested at the cost of capital rate.
Decision Rule
For independent projects select those whose NPV is equal to or greater than zero (0). For mutually exclusive projects select the one with the highest NPV (assuming it is positive). In this case, project B should be selected.
Pros and Cons
Pros -(1) It considers the time value of money (2) Indicates how much each project will cause the shareholders' wealth to increase/decrease by (In conjunction with the goal of financial management).
Cons-(1) May be difficult to explain to a non-finance person (2) The cost of capital for a particular project may be difficult to estimate
(d)
Profitability
Index (PI)
This approach expresses the viability of a project in terms of a single ratio. This ratio, the PI, is computed by dividing the present value of all the annual cash flows from a project (excluding the initial investment but including the terminal cash flow) by the project's initial investment. The formula is as follows:
|
PV of all annual cash flows Initial investment
|
Project A
|
|
Project B
|
|
Decision Rule
For independent projects select those whose PI is equal to or greater than one (1). For mutually exclusive projects select the one with the highest PI (assuming it exceeds one). In this case, project B should be selected.
Pros and Cons
Pros -(1) Useful in selecting projects whenever there is a limitation of funds (2). It considers the time value of money
Cons-The same as for NPV( above)
(e)
Internal Rate
of Return (IRR)
This method determines that particular rate of return that equates the present value of all the cash flows that are derived from a project to its initial investment. In other words, it is that rate of return that causes the NPV = 0 or that rate of return that causes the project to 'breakeven' . It is determined in the most part by trial and error as follows:
|
First, determine two NPVs, one positive and one negative, along with their corresponding costs of capital, k%. Secondly, apply linear interpolation to find the IRR. |
Project A
|
We already have a positive NPV: $1,616.91, at 10%. We therefore need a negative NPV: Trying 32% we have: |
|
|
Project B
|
We already have a positive NPV: $3,307.29, at 10%. We therefore need a negative NPV: Trying 36% we have: |
 |
|
|
Note - The IRR method assumes that cash flows are reinvested at the IRR.
Decision Rule
For independent projects select those whose IRR is equal to or greater than the company's cost of capital. For some companies, there may be a 'hurdle rate' in place and projects whose IRR exceed this 'hurdle rate' would be taken on. For mutually exclusive projects select the one with the highest IRR. In this case, project B should be selected.
Pros and Cons
Pros - (1) It is relatively easy to understand and use because it incorporates the notion of 'breakeven'. (2) It considers the time value of money (3) Indirectly, it indicates movement in shareholder's wealth.
Cons: (1) Whenever, there is a series of positive annual cash flows followed by a series of negative annual cash flows, the following may occur:
(a) The IRR method may arrive at the wrong accept -reject decision e.g.
| Year | 0 | 1 | 2 | 3 | 4 |
| Cash Flow($) | (1,500) | 2,600 | 3,000 | (4,000) | (1,500) |
Cost of Capital = 14%, NPV = -$498.90 and IRR = 35.50% . In this case NPV says No, while IRR says Yes. ( Note - when this conflict exists, use the NPV as the deciding criteria i.e. reject project in this case.
(b) There may be multiple IRRs e.g.
| Year | 0 | 1 | 2 |
| Cash Flow($) | (1,600) | 10,000 | (10,000) |
Cost of Capital = 30%, NPV = $175.15 and IRR = 25% and 400%.
(c) There may be no IRR. e.g.
| Year | 0 | 1 | 2 |
| Cash Flow($) | (1,600) | 1,000 | (1,000) |
Cost of Capital = 30%, NPV = -$1,422.49 and IRR = ?
(f) Modified Internal Rate of Return (MIRR)
This method seeks to eliminate the pitfalls which may be experience by the IRR method (above). In this approach, a rate of return is determined which equates the terminal (future) value of the annual cash flows at k% to the present value of the initial investment. The procedure is as follows:
|
Firstly, find the future value of the annual cash flows at k%, = FV Then, let the present value of the initial investment = PV and use either of the following equations to solve for the MIRR%: FV = PV (1 + MIRR)n or FV = PV(FVIFk% n) |
Project A
|
Firstly, the FV of the cash flows at 10%:
|
|
Secondly, using the equation FV = PV (FVIFk% n)
to solve for MIRR%:
|
Project B
|
Firstly, the FV of the cash flows at 10%:
|
|
Secondly, using the equation FV = PV (1 + MIRR)n
to solve for MIRR%:
|
Note - The MIRR method assumes that cash flows are reinvested at the cost of capital rate.
Decision Rule
Same as for IRR above.
Pros and Cons
Pros - (1) Avoids the problems of multiple IRRs, no IRRs and incorrect accept-reject decisions (see Cons at IRR above.) (2) Other Pros are similar to IRR above.
Cons - N/A
Note * The most common evaluation criteria are the NPV and the IRR.
Evaluation criteria and decision rule summary:
|
Criteria |
Accept | Reject | Indifferent (normally accept) |
| NPV | > 0 | < 0 | = 0 |
| IRR/MIRR | > k | < k | = k |
| PI | > 1 | <1 | = 1 |
| PP/DPP | < Company's standard | >Company's standard | = Company's standard |
Conflicts with evaluation criteria:
Normally for mutually exclusive projects, one should select the project which has the higher value for the criteria used e.g. the one with the greater NPV or the one with the greater IRR. However, there may be occasions when different evaluation criteria give contrasting results for the same project analysis. That is, one criteria says select project X, while the other criteria says select project Y. The conflict, which normally occurs between the NPV and the IRR (could also occur between the NPV and the PI) , is due to the following reasons:
Timing differences - e.g. the cash flows of project X may occur earlier than those of project Y.
|
Year |
0 | 1 | 2 | 3 | 4 | |
| Cash flows($) | X | (4,000) | 2,003 | 2,003 | 2,003 | 2,003 |
| Y | (4,000) | 0 | 0 | 0 | 10,736 | |
Cost of Capital = 14%, NPV for X = $1,836.17 and NPV for Y = $2,356.57. IRR for X = 35% and IRR for Y = 28%. In this case NPV prefers Y, while IRR prefers X.
Size (scale) differences - e.g. the size of project X's cash flows are extremely large relative to those of project Y.
|
Year |
0 | 1 | 2 | 3 | 4 | |
| Cash flows($) | X | (400,000) | 150,000 | 150,000 | 150,000 | 150,000 |
| Y | (2,000) | 1,000 | 1,000 | 1,000 | 1,000 | |
Cost of Capital = 14%, NPV for X = $37,056.85 and NPV for Y = $913.71. IRR for X = 18.45% and IRR for Y = 34.90%. In this case NPV selects X, while IRR selects Y.
Alternating signs of the cash flows - positive cash flows followed by negative cash flows.
|
Year |
0 | 1 | 2 | 3 | 4 | |
| Cash flows($) | X | (1,800) | 750 | 750 | 750 | 750 |
| Y | (1,500) | 2,600 | 3,000 | (4,000) | (1,500) | |
Cost of Capital = 14%, NPV for X = $385.28 and NPV for Y = -$498.90. IRR for X = 24.10% and IRR for Y = 35.50%. In this case NPV selects X, while IRR selects Y.
Note - in this example, Project Y's IRR and NPV conflict each other. [This is the same cash flow pattern that was used when we discussed the Cons of the IRR method - see Con (a) above]
Note - Whenever such a conflicts exist, the project that should be selected is the one with the higher NPV. This is the one that adds greater value to the shareholder's wealth.
NPV Profiles
A NPV profile is a graph showing the relationship between a project's NPV and varying costs of capital. The NPV profile of our two projects, A & B are shown below on one graph after computing the varying NPVs in the table immediately below:.
| Project A | Project B | |
| WACC | $1,617.03 | $3,307.49 |
| 0% | 3,000.00 | 5,900.00 |
| 10% | 1,617.03 | 3,307.49 |
| 20% | 605.71 | 1,527.78 |
| 30% | (159.13) | 260.67 |
| 40% | (753.85) | (669.51) |
| 50% | (1,227.16) | (1,370.37) |
| 60% | (1,611.33) | (1,910.40) |
| 70% | (1,928.44) | (2,334.68) |
| 80% | (2,194.03) | (2,673.75) |
|
|
The Post-audit
Firstly, the Post-audit is a process which involves (1) comparing actual results with expected results and (2) explaining why any differences occurred. The main purposes of this exercise is to improve forecasts and improve operations. See pages 411 - 412 for more.
