Capital Budgeting: Decision Criteria and Real Option Considerations

Copyright ©2003 South-Western/Thomson Learning

Chapter 9Capital Budgeting: Decision

Criteria and Real Option Considerations

Introduction

• This chapter looks at capital budgeting decision models.

• It discusses and illustrates their relative strengths and weaknesses.

• It examines project review and post-audit procedures, and traces a sample project through the capital budgeting process.

Capital Budgeting Criteria

• Net present value (NPV)

• Internal rate of return (IRR)

• Profitability index (PI)

• Payback period (PB)

Net Present Value

• The net present value—that is, the present value (PV) of the expected future cash flows minus the initial outlay—of an investment made by a firm represents the contribution of that investment to the value of the firm, and accordingly, to the wealth of the firm’s shareholders.

Net Present Value

• The net present value (NPV) of a capital expenditure project is defined as the present value of the stream of net (operating) cash flows from the project minus the project’s net investment.

Net Present Value

• The net present value method is also sometimes called the discounted cash flow (DFC) technique. The cash flows are discounted at the firm’s required rate of return; that is, its cost of capital.

• A firm’s cost of capital is defined as its minimum acceptable rate of return for projects of average risk.

Net Present Value

• The net present value of a project may be expressed as follows:

NPV = PVNCF – NINV

where NPV is the net present value, PVNCF is the present value of net (operating) cash flows, and NINV is the net investment.

Net Present Value

• In general, the net present value of a project can be defined as follows:

where k is the cost of capital, n is the expected project life, and is the arithmetic sum of the discounted net cash flows for each year t over the life of the project (n years); that is, the present value of the net cash flows.

NCF

11

,1

NPV NINV

NCF PVIF NINV

tt

n

kt

n

t k tt

[NCF /(1 ) ]tt k

Net Present Value: Example

TABLE 9.1 Sample Project Cash Flows Year Project A Net Cash Flow After

Taxes Project B Net Cash Flow After

Taxes 1 $12,500 $5,000 2 12,500 10,000 3 12,500 15,000 4 12,500 15,000 5 12,500 25,000 6 12,500 30,000

Net Investment $50,000 $50,000


TABLE 9.2 Sample Net Present Value Calculations: Project A

Present value of an annuity of $12,500 for 6 years at 14 percent:

PV of NCF = $12,500(PVIFA0.14, 6) = $12,500(3.889) = $48,613

Less Net investment $50,000

Net present value $-1,387


TABLE 9.2 Sample Net Present Value Calculations: Project B Year

NCF PVIF0.14, t PV of NCF

1 $5,000 0.877 $4,385 2 10,000 0.769 7,690 3 15,000 0.675 10,125 4 15,000 0.592 8,880 5 25,000 0.519 12,975 6 30,000 0.456 13,680 57,735

Less Net investment 50,000 Net present value $7,735

NPV Characteristics

• Decision Rule: NPV > 0 acceptable above-normal profits

• Considers the time value of money• Absolute measure of wealth

– Positive NPVs increase owner’s wealth– Negative NPVs decrease owner’s wealth

• CFs over the project’s life reinvested at k• If two or more mutually exclusive

investments have positive net present values, the project having the largest net present value is the one selected.

Conditions Allowing Above-Normal Profits

• Buyers preferences for established brand names

• Ownership or control of distribution systems

• Patent control of superior product designs or production systems

• Exclusive ownership of superior natural resources


• Inability of new firms to acquire factors of production (management, labor, equipment)

• Superior access to financial resources at lower costs (economies of scale in attracting capital)

• Economies of large-scale production and distribution

• Access to superior labor or managerial talents at costs that are not fully reflective of their value


• The net present value of a project can be thought of as the contribution to the value of a firm resulting from undertaking that particular project.

• If a firm identifies projects having expected positive net present values, efficient capital markets can quickly reflect these positive net present value projects in the market value of the firm’s securities.

NPV: Advantage

• The net present value of a project is the expected number of dollars by which the present value of the firm is increased as a result of adopting the project. The NPV method is consistent with the goal of shareholder wealth maximization.

• The NPV approach considers both the magnitude and the timing of cash flows over a project’s entire expected life.

NPV: Advantage

• A firm can be thought of as a series of projects, and the firm’s total value is the sum of the net present values of all the independent projects that make it up. Therefore, when the firm undertakes a new project, the firm’s value is increased by the (positive) net present value of the new project. The additivity of net present values of independent projects is referred to in finance as the value additivity principle.

NPV: Advantage

• The net present value approach also indicates whether a proposed project will yield the rate of return required by the firm’s investors. The cost of capital represents this rate of return; when a project’s net present value is greater than or equal to zero, the firm’s investors can expect to earn at least their required rate of return.

NPV: Disadvantage

• The net present value criterion has a weakness in that many people find it difficult to work with a present value dollar return rather than a percentage return. As a result, many firms use another present value-based method that is interpreted more easily: the internal rate of return method.

Internal Rate of Return

• The internal rate of return is defined as the discount rate that equates the PV of net cash flows of a project with the PV of the NINV.

• It is the discount rate that causes a project’s net present value to equal zero.

• The internal rate of return for a capital expenditure project is identical to the yield to maturity for a bond investment.


• A project’s internal rate of return (IRR) can be determined by means of the following equation:

where NCFt /(1 + r)t is the present value of net (operating) cash flows in period t discounted at the rate r, NINV is the net investment in the project, and r is the internal rate of return.

1 1

NCF NCFNINV NINV 0

(1 ) (1 )

n nt tt t

t tr r


• NPV versus IRR: The only difference is that in the NPV approach a discount rate, k, is pre-specified and the net present value is computed, whereas in the IRR method the discount rate, r, which causes the project net present value to equal to, is the unknown.


• Figure 9.1 illustrates the relationship between NPV and IRR. The figure plots the net present value of Project B (from Table 9.1) against the discount rate used to evaluate its cash flows. Note that at a 14% cost of capital, the net present value of Project B is $7,735. The internal rate of return for Project B is approximately equal to 18.2%. Thus, the internal rate of return is a special case of the net present value computation.

Internal Rate of Return: Project A

• The internal rate of return for Projects A and B can now be calculated. Because Project A is an annuity of $12,500 for six years requiring a net investment of $50,000, its internal rate of return may be computed directly with the aid of a PVIFA table, such as Table IV, or with a financial calculator.


• In this case, the present value of the annuity, PVAN0, $50,000, the annuity payment, PMT, is $12,500, and n = 6 years. The following equation,

PVAN0 = PMT(PVIFAr,n)

can be rewritten to solve for the PVIFA:

PVIFAr,n = PVAN0 PMT


• In this case, PVIFA = $50,000/$12,500 = 4.000. Referring to Table IV and reading across the table for n = 6, it can be seen that the interest factor of 4.000 occurs near 13 percent, where it is 3.998. Thus, the internal rate of return fro Project A is about 13 percent.


• 6 → N

-50,000 → PV

12,500 → PMT

0 → FV (You can skip this step.)

Compute

i% (= 12.98)

Internal Rate of Return: Project B

• -50,000 → CF0

5,000 → CF1

10,000 → CF2

15,000 → CF3

15,000 → CF4

25,000 → CF5

30,000 → CF6

ComputeIRR (= 18.19)

IRR Characteristics

• Decision Rule: IRR > k acceptable• Generally, the internal rate of return

method indicates that a project whose internal rate of return is greater than or equal to the firm’s cost of capital should be acceptable, whereas a project whose internal rate of return is less than the firm’s cost of capital should be rejected.

• IRR assumes CF is reinvested at IRR.

IRR: Advantage

• The internal rate of return technique takes into account both the magnitude and the timing of cash flows over the entire life of a project in measuring the project’s economic desirability.

• The greater popularity of the internal rate of return method may be due to the fact that some people feel more comfortable dealing with the concept of a project’s percentage rate of return than with its dollar amount of net present value.

IRR: Disadvantage

• If the pattern of cash flows over the project’s life contains more than one sign change (for example, - + + -.), it has multiple internal rates of return.

NPV versus IRR

• If the NPV and IRR criteria disagree, NPV is preferred.

• Always agree if NPV > 0, IRR > k; and if NPV < 0, IRR < k.

NPV versus IRR

• As was indicated, both the NPV and the IRR methods result in identical decisions to either accept or reject an independent project. This is true because the net present value is greater than (less than) zero if and only if the internal rate of return is greater than (less than) the required rate of return, k (or cost of capital).

NPV versus IRR

• In the case of mutually exclusive projects, however, the net present value and the internal rate of return methods may yield contradictory results; one project may have a higher internal rate of return than another and, at the same time, a lower net present value.

NPV versus IRR

• Consider, for example, mutually exclusive projects L and M described in the following table:

Project L Project M Net investment $1,000 $1,000 Net cash flows

Year 1 $667 $0 Year 2 $667 $1,400

Net present value at 5% $240 $270 Internal rate of return 21.5% 18.3%

NPV versus IRR

• The outcome depends on what assumptions the decision maker chooses to make about the implied reinvestment rate for the net cash flows generated from each projects. This can be seen in Figure 9.2.

NPV versus IRR

• For discount (reinvestment) rates below 10 percent, Project M has a higher net present value than Project L and therefore is preferred.

• For discount rates greater than 10 percent, Project L is preferred using both the present value and internal rate of return approaches.

• Hence, a conflict only occurs in this case for discount (cost-of-capital) rates below 10 percent.

NPV versus IRR

• The net present value method assumes that cash flows are reinvested at the firm’s cost of capital, whereas the internal rate of return method assumes that these cash flows are reinvested at the computed internal rate of return.

NPV versus IRR

• Generally, the cost of capital is considered to be a more realistic reinvestment rate than the computed internal rate of return because the cost of capital is the rate the next (marginal) investment project can be assumed to earn.

NPV versus IRR

• Consequently, in the absence of capital rationing, the net present value approach is normally superior to (both the profitability index and) the internal rate of return when choosing among mutually exclusive investment.

Profitability Index

• The profitability index (PI), or benefit-cost ratio, is the ratio of the present value of expected net cash flows over the life of a project to the net investment (NINV). It is expressed as follows:

1

NCF(1 )

PININV

nt

tt k

Profitability Index

• Assume a 14 percent cost of capital, k, and using the data from Table 9.2, the profitability index for Projects A and B can be calculated as follows:

PIA = $48,613/$50,000 = 0.97

PIB = $57,735/$50,000 = 1.15

Profitability Index

• The profitability index is interpreted as the present value return for each dollar of initial investment.

• In comparison, the net present value approach measures the total present value dollar return.

PI Characteristics

• Decision Rule: PI > 1 acceptable

• A project whose profitability index is greater than or equal to 1 is considered acceptable (+NPV), whereas a project having a profitability index less than 1 is considered unacceptable (-NPV).

• In the previous case, which project is acceptable?

• The profitability index considers the time value of money.

PI Characteristics

• When two or more independent projects with normal cash flows (for example, - + + + ….) are considered, the profitability index, net present value, and internal rate of return approaches all will yield identical accept-reject signals; this is true, for example, with Projects A and B in the previous case.

PI Characteristics

• When dealing with mutually exclusive investments, conflicts may arise between the net present value and the profitability index criteria. This is most likely to occur if the alternative projects require significantly different net investments.

PI Characteristics

• Consider, for example, the following information on Projects J and K.

• According to the net present value criterion, Project J would be preferred because of its larger net present value. According to the profitability index criterion, Project K would be preferred.

Project J Project K Present value of net cash flows $25,000 $14,000 Less Net investment $20,000 $10,000 Net present value (NPV) $5,000 $4,000 PI 1.25 1.40

PI Characteristics

• When a conflict arises, the final decision must be made on the basis of other factors. For example, if a firm has no constraint on the funds available to it for capital investment—that is, no capital rationing—the net present value approach is preferred because it will select the projects that are expected to generate the largest total dollar increase in the firm’s wealth and, by extension, maximize shareholder wealth.

PI Characteristics

• If, however, the firm is in a capital rationing situation and capital budgeting is being done for only one period, the profitability index approach may be preferred because it will indicate which projects will maximize the returns per dollar of investment—an appropriate objective when a funds constraint exists.

Payback Period

• Number of years for the cumulative net cash flows from a project to equal the initial cash outlay

Net InvestmentAnnual net CF

PB =

When net CFs are unequal, When net CFs are unequal, interpolation is required.interpolation is required.

Payback Period

• The payback (PB) period of an investment is the period of time required for the cumulative cash inflows (net cash flows) from a project to equal the initial cash outlay (net investment).

Payback Period

• If the expected net cash inflows are equal each year, then the payback period is equal to the ratio of the net investment to the annual net cash inflows of the project:

When net CFs are unequal, When net CFs are unequal,

interpolation is required.interpolation is required.

Net InvestmentPB =

Annual net cash inflows

Payback Period

• When the annual cash inflows are not equal each year, the analyst must add up the yearly net cash flows until the cumulative total equals the net investment. The number of years it takes for this to occur is the project’s payback period.

Payback Period

• One can also compute a discounted payback period, where the net cash inflows are discounted at the firm’s cost of capital in determining the number of years required to recover the net investment in a project.

Payback Period

TABLE 9.3 Payback Period Calculations (NINV = $50,000) Project

A Undiscounted Discounted (at 14%)

Year (t) Cash Inflow

Cumulative Cash Inflow

Cash Inflow Cumulative Cash Inflow

1 $12,500 $12,500 $10,962.50 $10,962.50 2 12,500 25,000 9,612.50 20,575.00 3 12,500 37,500 8,437.50 29,012.50 4 12,500 50,000 7,400.00 36,412.50 5 12,500 62,500 6,487.50 42,900.00 6 12,500 75,000 5,700.00 48,600.00

Net Investment/Annual Cash Inflow

# of Years Before Full Recovery of Net Investment

+ (Unrecovered Initial Investment at Start of

Year)/(Discounted Cash Inflow During year)

PB

50,000/12,500 = 4.0 years Undefined

Payback Period

TABLE 9.3 Payback Period Calculations (NINV = $50,000) Project B Undiscounted Discounted (at 14%) Year (t) Cash

Inflow Cumulative Cash Inflow

Cash Inflow

Cumulative Cash Inflow

1 $5,000 $5,000 $4,385 $4,385 2 10,000 15,000 7,690 12,075 3 15,000 30,000 10,125 22,200 4 15,000 45,000 8,880 31,080 5 25,000 70,000 12,975 44,055 6 30,000 100,000 13,680 57,735



Year)/(Cash Inflow During year)



Year)/(Discounted Cash Inflow During year)

PB

4 + [(50,000 – 45,000)/25,000] = 4.2 years

5 + [(50,000 – 44,055)/13,680] = 5.43

years

Payback Period

• Table 9.3 illustrates the calculation of undiscounted and discounted (at a 14 percent required rate) payback periods for projects A and B, which were presented earlier in this section.

Payback Period

• In panel (a) of the table we see that the undiscounted PB period is 4.0 years for Project A and 4.2 years for Project B. In panel (b) we see that the discounted PB period for Project A is undefined. This occurs because the NPV of the project is negative, that is, the discounted cash inflows are less than the net investment. For Project B the discounted PB period is 5.43 years.

PB Characteristics

• Decision Rule: The decision criterion states that a project should be accepted if its payback period is less than or equal to a specified maximum period. Otherwise, it should be rejected.

Payback Period: Advantage

• The payback method gives some indication of a project’s desirability from a liquidity perspective because it measures the time required for a firm to recover its initial investment in a project. A company that is very concerned about the early recovery of investment funds might find this method useful.

Payback Period: Disadvantage

• First, the (undiscounted) payback method gives equal weight to all cash inflows within the payback period, regardless of when they occur during the period. In other words, the technique ignores the time value of money.


• Assume, for example, that a firm is considering two projects, E and F, each costing $10,000. – Project E is expected to yield cash flows

over a three-year period of $6,000 during the first year, $4,000 during the second year, and $3,000 during the third year.

– Project F is expected to yield cash flows of $4,000 during the first year, $6,000 during the second year, and $3,000 during the third year.


Viewed from the payback period perspective, these projects are equally attractive, yet the net present value technique clearly indicates that Project E increases the value of the firm more than Project F.


• Second, payback methods (both discount and undiscounted) essentially ignore cash flows occurring after the payback period. Thus, payback figures are biased against long-term projects and can be misleading.


• For example, suppose a firm is considering two projects, C and D, each costing $10,000. – It is expected that Project C will generate

net cash inflows of $5,000 per year for three years. The PB period for Project C is two years ($10,000/$5,000).

– It is expected that Project D will generate net cash inflows of $4,500 per year forever. The PB period for Project D is 2.2 years ($10,000/$4,500).


• If these projects were mutually exclusive, payback would favor Project C because it has the lower payback period. Yet Project D clearly has a higher net present value than Project C.


• Third, payback provides no objective criterion for decision making that is consistent with shareholder wealth maximization. The payback methods (both discounted and undiscounted) may reject projects with positive net present values.


The choice of an acceptable payback period is largely a subjective one, and different people using essentially identical data may make different accept-reject decisions about a project.


• The payback method is sometimes justified on the basis that it provides a measure of the risk associated with a project. Although it is true that less risk may be associated with a shorter payback period than with a longer one, risk is best thought of in terms of the variability of project returns. Because payback ignores this dimension, it is at best a crude tool for risk analysis.

Capital Budgeting Under Capital Rationing

• For each of the selection criteria previously discussed, the decision rule is to undertake all independent investment projects that meet the acceptance standard. This rule places no restrictions on the total amount of acceptable capital projects a company may undertake in any particular period.


• However, many firms do not have unlimited funds available for investment. Many companies choose to place an upper limit, or constraint, on the amount of funds allocated to capital investments. This constraint may be either self-imposed by the firm’s management or externally imposed by conditions in the capital markets.


• Step 1: Calculate the PI for projects

• Step 2: Order the projects from the highest to the lowest PI

• Step 3: Accept the projects with the highest PI until the entire capital budget is spent

What Happens When the Next Acceptable Project is too Large?

• Search for another combination of projects that increase the NPV

• Attempt to relax the funds constraint

• Excess funds – Invest in short-term securities– Reduce outstanding debt– C/S dividends

Example

• Suppose that management of the Old Mexico Tile Company has decided to limit next year’s capital expenditures to $550,000. Eight capital expenditure projects have been proposed—P, R, S, U, T, V, Q, and W—and ranked according to their profitability indexes, as shown in Table 9.5.

Example

TABLE 9.5 Sample Ranking of Proposed Projects According to Their Profitability Indexes Project

(1) Net

Investment (2)

Net Present Value

(3)

Present Value of

Net Cash Flows

(4)

Profitability Index

= (4)/(2)

Cumulative Net

Investment

Cumulative Net

Present Value

P $100,000 $25,000 $125,000 1.25 $100,000 $25,000 R 150,000 33,000 183,000 1.22 250,000 58,000 S 175,000 36,750 211,750 1.21 425,000 94,750 U 100,000 20,000 120,000 1.20 525,000 114,750 T 50,000 9,000 59,000 1.18 575,000 123,750 V 75,000 12,500 87,500 1.17 650,000 136,250 Q 200,000 30,000 230,000 1.15 850,000 166,250 W 50,000 -10,000 40,000 0.80 900,000 156,250

Example

• Given the $550,000 ceiling, the firm’s management proceeds down the list of projects, selecting P, R, S, and U, in that order. Project T cannot be accepted because this would require a capital outlay of $25,000 in excess of the $550,000 limit.

Example

Projects P, R, S, and U together yield a net present value of $114,750 but require a total investment outlay of only $525,000, leaving $25,000 from the capital budget that is not invested in projects.

Example

• Management is considering the following three alternatives:

Alternative 1:

It could attempt to find another combination of projects, perhaps including some smaller ones, that would allow for a more complete utilization of available funds and increase the cumulative net present value.

Example

In this case, a likely combination would be Projects P, R, S, T, and V. This combination would fully use the $550,000 available and create a net present value of $116,250—an increase of $1,500 over the net present value of $114,750 from Projects P, R, S, and U.

Example

Alternative 2:

It could attempt to increase the capital budget by another $25,000 to allow Project T to be added to the list of adopted projects.

Example

Alternative 3:

It could merely accept the first four projects—P, R, S, and U—and invest the remaining $25,000 in a short-term security until the next period. This alternative would result in an NPV of $114,750, assuming that the risk-adjusted required return on the short-term security is equal to its yield.

Example

• In this case, Alternative 1 seems to be the most desirable of the three. In rearranging the capital budget, however, the firm should never accept a project, such as W, that does not meet the minimum acceptance criterion of a positive or zero net present value (i.e., a profitability index greater than or equal to 1).

Post-Auditing Implemented Projects

• Find systematic biases or errors of uncertain projected CFs.

• Decide whether to abandon or continue projects that have done poorly.

Incorporating Inflation into the Capital Budget

• Make sure the cost of capital takes account of inflationary expectations.

• Make sure that future CF estimates include expected price and cost increases.

Incorporating Inflation into the Capital Budget: Example

• Suppose that the Apple Manufacturing Company has an investment opportunity that is expected to generate 10 years of cash inflows of $300,000 per year. The net investment is $2,000,000. If the company’s cost of capital is relatively—say, 7 percent—the net present value is positive:



= $300,000(PVIFA0.07,10) – $2,000,000

= $300,000(7.024) – $2,000,000

= $107,200

According to the net present value decision rule, this project is acceptable.


• Suppose, however, that inflation expectations increase and the overall cost of the firm’s capital rises to say, 10 percent. The net present value of the project then would be negative:


= $300,000(PVIFA0.10,10) – $2,000,000

= $300,000(6.145) – $2,000,000

= -$156,500 reject

Real Options in Capital Projects

• Investment timing option– Evaluate additional

information

• Abandonment option– Reduce downside

risk

• Shutdown options– Temporarily

• Growth options– Research programs,

expand a small plant, or strategic acquisition

• Design-in options– Input/output

flexibility options or expansion options

Real Option Information on the Web

• http://www.mbs.umd.edu/finance/atriantis/RealOptions.html

• http://www.iur.ruhr-uni-bochum.de/forschung/real_options.html

• http://www.real-options.com/

How are Real Options Concepts Being Applied?

• Foundation level of use of real options concept– Increases awareness of value– Options can be created or destroyed– Think about risk and uncertainty– Value of acquiring additional information

• Analytical tool– Option pricing models

• Value the option characteristics of projects• Analyzing various project opportunities

International Capital Budgeting

• Find the PV of the foreign CFs denominated in the foreign currency and discounted by the foreign country’s cost of capital.

• Convert the PV of the CFs to the home country’s currency.

– multiplying by spot exchange rate

• Subtract the parent company’s NINV from the PVNCFh to get the NPV.

Amount and Timing of Foreign CFs

• Differential tax rates

• Legal and political constraints on CF

• Government-subsidized loans

Small Firms

• Should be the same as large firms

• Discrepancies– Lack experience to implement procedures– Expertise stretched too thin– Have cash shortages

• Focus on the PB

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Capital Budgeting: Decision Criteria and Real Option Considerations

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