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The Basics of Capital Budgeting

Should we build this

plant?

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Learning Outcomes•Explain the capital budgeting process.•Learn different methods of capital

budgeting (NPV, IRR, MIRR, Payback period, Discounted Payback & Profitability index.

•Difference between independent project and Mutually exclusive project.

•Conflict between IRR and NPV decision.•Multiple IRR problem (mutually exclusive

project with different cash flow pattern/ projects of different scale)

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What is capital budgeting?•Analysis of potential additions to

fixed assets.•Long-term decisions; involve large

expenditures.•Very important to firm’s future.

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Steps to capital budgeting

1. Estimate CFs (inflows & outflows).2. Assess riskiness of CFs.3. Determine the appropriate cost of

capital.4. Find NPV and/or IRR.5. Accept if NPV > 0 and/or IRR > WACC.

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Investment Decision Criteria•Analyst use several important criteria to

evaluate capital investments. •Two most comprehensive measures are:

▫ Net Present Value (NPV) and▫ Internal Rate of Return (IRR)

•Four other criteria that are frequently used are: ▫Payback Period▫Discounted Payback Period▫Modified Internal Rate of Return (MIRR)▫Profitability Index

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What is the difference between independent and mutually exclusive projects?•Independent projects – if the cash

flows of one are unaffected by the acceptance of the other.

•Mutually exclusive projects – if the cash flows of one can be adversely impacted by the acceptance of the other.

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Payback Period

•The payback period is the number of years required to recover the original investment in a project. The payback period is based on cash flows.Payback Period: Years before full recovery + Unrecovered cost at start of year

Cash flow during the year

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Calculating payback

PaybackL = 2 + / = 2.375 years

CFt -100 10 60 100Cumulative -100 -90 0 50

0 1 2 3

=

2.4

30 80

80

-30

Project L

PaybackS = 1 + / = 1.6 years

CFt -100 70 100 20Cumulative -100 0 20 40

0 1 2 3

=

1.6

30 50

50-30

Project S

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Discounted payback period

•Uses discounted cash flows rather than raw CFs.

Disc PaybackL = 2 + / = 2.7 years

CFt -100 10 60 80

Cumulative -100 -90.91 18.79

0 1 2 3

=

2.7

60.11

-41.32

PV of CFt -100 9.09 49.59

41.32 60.11

10%

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Self Test

• Which of the following statements about the payback period is NOT correct?A) The payback method considers all cash flows throughout the entire life of a project.B) The payback period provides a rough measure of a project's liquidity and risk.C) The payback period is the number of years it takes to recover the original cost of the investment.

The correct answer is A.• The payback period does not take any cash

flows after the payback point into consideration

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Self Test• A company is considering the purchase of a copier that

costs $5,000. Assume a cost of capital of 10 percent and the following cash flow schedule:Year 1: $3,000 Year 2: $2,000 Year 3: $2,000 Determine the project's payback period and discounted payback period. Payback Period Discounted Payback PeriodA) 2.0 years 1.6 yearsB) 2.0 years 2.4 yearsC) 2.4 years 1.6 years

The correct answer is B

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Net Present Value (NPV)

•Sum of the PVs of all cash inflows and outflows of a project:

n

0tt

t

) k 1 (CF

NPV

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What is Project L’s NPV?

Year CFt PV of CFt

0 -100 -$100 1 10 9.09 2 60 49.59 3 80 60.11

NPVL = $18.79

NPVS = $19.98

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Rationale for the NPV methodNPV= PV of inflows – Cost

= Net gain in wealth•If projects are independent, accept if

the project NPV > 0.•If projects are mutually exclusive,

accept projects with the highest positive NPV, those that add the most value.

•In this example, would accept S if mutually exclusive (NPVs > NPVL), and would accept both if independent.

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Self Test• A firm is reviewing an investment opportunity that

requires an initial cash outlay of $336,875 and promises to return the following irregular payments: Year 1: $100,000, Year 2: $82,000, Year 3: $76,000Year 4: $111,000, & Year 5: $142,000If the required rate of return for the firm is 8%, what is the net present value of the investment? A) $99,860.B) $86,133.C) $64,582.The correct answer is C) $64,582. In order to determine the net present value of the investment, given the required rate of return; we can discount each cash flow to its present value, sum the present value, and subtract the required investment.

Year Cash Flow PV of Cash flow at 8%0 -336,875.00 -336,875.001 100,000.00 92,592.592 82,000.00 70,301.783 76,000.00 60,331.254 111,000.00 81,588.315 142,000.00 96,642.81

Net Present Value 64,581.74

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Self Test• Tapley Acquisition, Inc., is considering the purchase

of Tangent Company. The acquisition would require an initial investment of $190,000, but Tapley's after-tax net cash flows would increase by $30,000 per year and remain at this new level forever. Assume a cost of capital of 15%. Should Tapley buy Tangent?A) No, because k > IRR.B) Yes, because the NPV = $30,000.C) Yes, because the NPV = $10,000.

The correct answer is C) Yes, because the NPV = $10,000. This is perpetuity.PV = PMT / I = 30,000 / 0.15 = 200,000200,000 − 190,000 = 10,000

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Self Test• An analyst has gathered the following data about a

company with a 12% cost of capital: Project A Project B

Cost $15,000 $25,000Life 5 Years 5 yearsCash Flows $5,000/Yr $7,500/YrProjects A and B are mutually exclusive. What should the company do? A) Reject A, Accept B.B) Accept A, Reject B.C) Reject A, Reject B.The correct answer is B) Accept A, Reject B.

• For mutually exclusive projects accept the project with the highest NPV. In this example the NPV for Project A (3,024) is higher than the NPV of Project B (2,036). Therefore accept Project A and reject Project B.

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Internal Rate of Return (IRR)•IRR is the discount rate that forces PV

of inflows equal to cost, and the NPV = 0:

n

0tt

t

) IRR 1 (CF

0

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Example: IRR

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How is a project’s IRR similar to a bond’s YTM?•They are the same thing.•Think of a bond as a project. The

YTM on the bond would be the IRR of the “bond” project.

•EXAMPLE: Suppose a 10-year bond with a 9% annual coupon sells for $1,134.20.▫Solve for IRR = YTM = 7.08%, the

annual return for this project/bond.

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Rationale for the IRR method•If IRR > WACC, the project’s rate of

return is greater than its costs. There is some return left over to boost stockholders’ returns.

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IRR Acceptance Criteria•If IRR > k, accept project.•If IRR < k, reject project.

•If projects are independent, accept both projects, as both IRR > k = 10%.

•If projects are mutually exclusive, accept S, because IRRs > IRRL.

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Self Test

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NPV Profiles•A graphical representation of project

NPVs at various different costs of capital.

k NPVL NPVS

0 $50 $40 5 33 2910 19 2015 7 1220 (4) 5

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Drawing NPV profiles

-10

0

10

20

30

40

50

60

5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

Crossover Point = 8.7%

SL

.

.

...

.

..

.

. .

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Comparing the NPV and IRR methods•If projects are independent, the two

methods always lead to the same accept/reject decisions.

•If projects are mutually exclusive …▫If k > crossover point, the two methods

lead to the same decision and there is no conflict.

▫If k < crossover point, the two methods lead to different accept/reject decisions.

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Reinvestment rate assumptions•NPV method assumes CFs are

reinvested at k, the opportunity cost of capital.

• IRR method assumes CFs are reinvested at IRR.

•Assuming CFs are reinvested at the opportunity cost of capital is more realistic, so NPV method is the best. NPV method should be used to choose between mutually exclusive projects.

•Perhaps a hybrid of the IRR that assumes cost of capital reinvestment is needed.

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Self Test• The underlying cause of ranking conflicts between the net

present value (NPV) and internal rate of return (IRR) methods is the underlying assumption related to the: A) initial cost.B) cash flow timing.C) reinvestment rate.

The correct answer is C) reinvestment rate. • The IRR method assumes all future cash flows can be

reinvested at the IRR. This may not be feasible because the IRR is not based on market rates. The NPV method uses the weighted average cost of capital (WACC) as the appropriate discount rate.

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Some managers prefer the IRR to the NPV method, is there a better IRR measure?•Yes, MIRR is the discount rate that causes

the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC.

•MIRR assumes cash flows are reinvested at the WACC.

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Calculating MIRR

66.0 12.1

10%

10%

-100.0 10.0 60.0 80.0

0 1 2 310%

PV outflows

-100.0 $100

MIRR = 16.5%158.1

TV inflows

MIRRL = 16.5%

$158.1

(1 + MIRRL)3=

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Profitability Index (PI)•The Profitability Index (PI) is the present

value of a project’s future cash flows divided by the initial investment. It can be expressed as:

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