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Chapter 10

The Basics of Capital Budgeting

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Topics Methods

NPV IRR, MIRR Payback, discounted payback EAS (EAA)

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What is capital budgeting? Analysis of potential projects. Long-term decisions; involve large

expenditures.

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Steps in Capital Budgeting Estimate cash flows (inflows &

outflows). Determine r = WACC for project. Evaluate

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Capital Budgeting Project Categories

1. Replacement to continue profitable operations

2. Replacement to reduce costs3. Expansion of existing products or

markets4. Expansion into new

products/markets5. Contraction decisions6. Safety and/or environmental projects7. Mergers8. Other

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Independent versus Mutually Exclusive Projects Projects are:

independent, if the cash flows of one are unaffected by the acceptance of the other.

mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.

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Net present value (NPV) rule

Accept project if

Net present value > 0

What is Net present value?

Net present value = Benefits minus Costs

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How do we measure benefits & costs?

NPV = B – C =

N

ttt

N

ttt

r

COF

r

CIF

00 11

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NPV: Sum of the PVs of All Cash Flows

Cost often is CF0 and is negative.

NPV = ΣN

t = 0

CFt

(1 + r)t

NPV = ΣN

t = 1

CFt

(1 + r)t– CF0

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Cash Flows for Franchises

L and S

10 8060

0 1 2 310%L’s CFs:

-100.00

70 2050

0 1 2 310%S’s CFs:

-100.00

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What’s Franchise L’s NPV?

10 8060

0 1 2 310%L’s CFs:

-100.00

9.09

49.59

60.1118.79 = NPVL NPVS = $19.98.

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Calculator Solution: Enter Values in CF Register for L

-100

10

60

80

10

CF0

CF1

NPV

CF2

CF3

I = 18.78 = NPVL

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Rationale for the NPV Method NPV = PV inflows – Cost

This is net gain in wealth, so accept project if NPV > 0.

Choose between mutually exclusive projects on basis of higher positive NPV. Adds most value.

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Using NPV method, which franchise(s) should be accepted?

If Franchises S and L are mutually exclusive, accept S because NPVs > NPVL.

If S & L are independent, accept both; NPV > 0.

NPV is dependent on cost of capital.

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Internal Rate of Return: IRR

0 1 2 3

CF0 CF1 CF2 CF3

Cost Inflows

IRR is the discount rate that forcesPV inflows = cost. This is the sameas forcing NPV = 0.

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NPV: Enter r, Solve for NPV

= NPV ΣN

t = 0

CFt

(1 + r)t

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IRR: Enter NPV = 0, Solve for IRR

= 0 ΣN

t = 0

CFt

(1 + IRR)t

IRR is an estimate of the project’s rate of return, so it is comparable to the YTM on a bond.

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What’s Franchise L’s IRR?

10 8060

0 1 2 3IRR = ?

-100.00

PV3

PV2

PV1

0 = NPV Enter CFs, then press IRR: IRRL = 18.13%. IRRS = 23.56%.

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Rationale for the IRR Method If IRR > WACC, then the project’s

rate of return is greater than its cost-- some return is left over to boost stockholders’ returns.

Example:WACC = 10%, IRR = 15%.

So this project adds extra return to shareholders.

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Decisions on Franchises S and L per IRR

If S and L are independent, accept both: IRRS > r and IRRL > r.

If S and L are mutually exclusive, accept S because IRRS > IRRL.

IRR is not dependent on the cost of capital used.

r > IRRand NPV < 0.

Reject.

NPV ($)

r (%)IRR

IRR > rand NPV > 0

Accept.

NPV and IRR: No conflict for independent projects.

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Reinvestment Rate Assumptions

NPV assumes reinvest at r (opportunity cost of capital).

IRR assumes reinvest at IRR. Reinvest at opportunity cost, r, is

more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.

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Modified Internal Rate of Return (MIRR)

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 all inflows at WACC.

Thus, MIRR assumes cash inflows are reinvested at WACC.

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10.0 80.060.0

0 1 2 310%

66.0 12.1

158.1

-100.010%

10%

TV inflows

-100.0PV outflows

MIRR for Franchise L: First, Find PV and TV (r = 10%)

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MIRR = 16.5% 158.1

0 1 2 3

-100.0

TV inflowsPV outflows

MIRRL = 16.5%

$100 =

$158.1(1+MIRRL)3

Second, Find Discount Rate that Equates PV and TV

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BAII: Step 1, Find PV of Inflows First, enter cash inflows in CF register:

CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80

Second, enter I = 10.

Third, find PV of inflows:Press NPV = 118.78

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Step 2, Find TV of Inflows

Enter PV = -118.78, N = 3, I/YR = 10, PMT = 0.

Press FV = 158.10 = FV of inflows.

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Step 3, Find PV of Outflows

For this problem, there is only one outflow, CF0 = -100, so the PV of outflows is -100.

For other problems there may be negative cash flows for several years, and you must find the present value for all negative cash flows.

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Step 4, Find “IRR” of TV of Inflows and PV of Outflows

Enter FV = 158.10, PV = -100, PMT = 0, N = 3.

Press I/YR = 16.50% = MIRR.

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Why use MIRR versus IRR?

MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs.

Managers like rate of return comparisons, and MIRR is better for this than IRR.

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Apply NPV, IRR Assume a discount rate of 11%. Compute

the NPV, IRR and decide whether the project should be accepted or rejected.

Project

C0 C1 C2 C3 C4 C5

T=0 T=1 T=2 T=3 T=4 T=5

A -1000 400 400 400 500 500

Verify that NPV = 603.58, IRR = 31.79%,

Since NPV>0, IRR>11%, accept the project

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Conceptual problem: NPV and IRR Consider a project with an initial outflow at

time 0 and positive cash flows in all subsequent years. As the discount rate is decreased the _____________.

A. IRR remains constant while the NPV increases.B. IRR decreases while the NPV remains constant.C. IRR increases while the NPV remains constant.D. IRR remains constant while the NPV decreases.E. IRR decreases while the NPV decreases.

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Computational problem: NPV and IRR

You are attempting to reconstruct a project analysis of a co-worker who was fired. You have found the following information:

The IRR is 12%. The project life is 4 years. The initial cost is $20,000. In years 1, 3 and 4 you will receive cash

inflows of $6,000. You know there will be a cash flow in year 2,

but the amount is not in the file. The appropriate discount rate is 10%. What is the NPV of the project?

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Condition 1: Cash inflows occur before cash outflows

Thus far, we have considered projects with normal cash flows, (i.e., a single cash outflow in year 0 followed by cash inflows in all future years).

With normal cash flows, IRR works fine. However, if you have cash inflow first,

followed by cash outflow, then IRR will be negative.

Result: You cannot use IRR to make the accept/reject decision.

Use NPV to get the correct decision.

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Condition 2: Cash flows change signs more than once

Consider the following project cash flows: t = 0, -$400, t = 1, $2,500, t = 2, -$3,000. Suppose that the company’s cost of capital is 70 percent.

NPV = $32.53. The project is, acceptable. There are two IRR’s for this project: 61.98%,

363%. Look at the NPV profile (next slide). When there are multiple IRRs, the IRR

method loses meaning and is NOT appropriate.

However, the NPV method still gives the correct accept/reject decision.

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What is the payback period?

The number of years required to recover a project’s cost,

or how long does it take to get the business’s money back?

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Payback for Franchise L

10 8060

0 1 2 3

-100

=

CFt

Cumulative -100 -90 -30 50

PaybackL 2 + $30/$80 = 2.375 years

0

2.4

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Payback for Franchise S

70 2050

0 1 2 3

-100CFt

Cumulative -100 -30 20 40

PaybackS 1 + $30/$50 = 1.6 years

0

1.6

=

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Applying the PBP criterion

Compute the payback periods for the following two projects.

Project C0 C1 C2 C3 C4 C5

A -9000 2000 3000 4000 5000 6000

B -11000 2000 3000 4000 5000 6000

Verify that PBP for A = 3 years, PBP for B = 3.4 years (assume cash flows occur evenly throughout the year)

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NPV + PBP Problem Bantam Industries is considering a project

which has the following cash flows:Year Cash flow

0 ? 1 $2,000 2 $3,000 3 $3,000 4 $1,500

The project has a payback period of 2 years. The firm's cost of capital is 12%.

What is the project's net present value?Verify that NPV = 2,265.91

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Strengths and Weaknesses of Payback Strengths:

Provides an indication of a project’s risk.

Easy to calculate and understand. Weaknesses:

Ignores the TVM. Ignores CFs occurring after the

payback period.

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PBP does not consider cash flows after the critical number

Project C0 C1 C2 C3

A -1000 500 510 10

B -1000 0 0 99,000,000

A firm uses two years as the critical number for the payback period.

This firm is faced with two projects whose cash flows are:

According to the payback rule, project A will be accepted and B will be rejected.

But, if you consider all cash flows, including those after 2 years, then project B is more attractive.

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10 8060

0 1 2 3

CFt

Cumulative -100 -90.91 -41.32 18.79

Discountedpayback 2 + $41.32/$60.11 = 2.7 yrs

PVCFt -100

-100

10%

9.09 49.59 60.11

=

Recover investment + capital costs in 2.7 yrs.

Discounted Payback: Uses Discounted CFs

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Example of discounted payback period criterion Example: Suppose that the discount rate is 10

percent. Project A has the following cash flows and discounted cash flows. Find A’s discounted PBP.

Project A C0 C1 C2 C3

Cash flow -9000 3000 6000 9000

Discounted cash flow 2727 4959 6762

Verify that discounted payback period = 2.194 years

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Normal vs. Nonnormal Cash Flows Normal Cash Flow Project:

Cost (negative CF) followed by a series of positive cash inflows.

One change of signs. Nonnormal Cash Flow Project:

Two or more changes of signs. Most common: Cost (negative CF), then

string of positive CFs, then cost to close project.

For example, nuclear power plant or strip mine.

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0 1 2

-800,000 5,000,000 -5,000,000

PV outflows @ 10% = -4,932,231.40.

TV inflows @ 10% = 5,500,000.00.

MIRR = 5.6%

When There are Nonnormal CFs and More than One IRR, Use MIRR

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If the two projects have different lifespan, then…

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S and L are Mutually Exclusive, r = 10%

0 1 2 3 4

S: -100

L: -100

60

33.5

60

33.5 33.5 33.5

Note: CFs shown in $ Thousands

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NPVL > NPVS, but is L better?

S LCF0 -100 -100

CF1 60 33.5

NJ 2 4

I/YR 10 10

NPV 4.132 6.190

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Method 1:mPut Projects on Common Basis Note that Franchise S could be

repeated after 2 years to generate additional profits.

Use replacement chain to put on common life.

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Replacement Chain Approach (000s)Franchise S with Replication

NPV = $7.547.

0 1 2 3 4

S: -100 60 -100 60

60-100 -40

6060

6060

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Method 2:Equivalent annual series (EAS) or Equivalent Annual Annuity (EAA)

When projects are mutually exclusive but have unequal lives

a. We construct the equivalent annual series (EAS) of each project and

b. We choose the project with the highest EAS A project’s EAS is the payment on an

annuity whose life is the same as that of the project and whose present value, using the discount rate of the project, is equal to the project’s NPV.

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Equivalent Annual Annuity Approach (EAA) Convert the PV into a stream of

annuity payments with the same PV.

S: N=2, I/YR=10, PV=-4.132, FV = 0. Solve for PMT = EAAS = $2.38.

L: N=4, I/YR=10, PV=-6.190, FV = 0. Solve for PMT = EAAL = $1.95.

S has higher EAA, so it is a better project.

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Calculating EAS

Consider Projects J & K, with the following cash flows. The discount rate is 10%.

Project C0 C1 C2 C3 C4

J -12000 6000 6000 6000

K -18000 7000 7000 7000 7000

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EAS for Project J To compute Project J’s EAS, do the following: Compute Project J’s NPV

• Verify that NPV(J) = $2,921.11 Find the payment on the 3-year (life of project J)

annuity whose PV is equal to $2,921.11. Enter the following values:N=3, I/Y=10, PV=-2921.11, FV=0, Then CPT, PMT.PMT = 1,174.62, which is Project J’s EAS. So, finding EAS is nothing more than finding the

payment of an annuity.

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EAS for Project K Verify that Project K’s NPV= $4,189.06 Find the payment on the 4-year (life of

project K) annuity whose PV is equal to $ 4,189.06.

Enter the following values:N=4, I/Y=10, PV=- 4,189.06, FV=0, Then CPT,

PMT.PMT = 1,321.53, which is Project K’s EAS. Recall that Project J’s EAS=1174.62 So, choose Project K since it has the higher

EAS.

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Another application of EAA

We can use the EAA concept to choose between two machines that do the same job but have different costs and lives.

Consider the following problem.

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Problem Suppose that your firm is trying to

decide between two machines, that will do the same job. Machine A costs $90,000, will last for ten years and will require operating costs of $5,000 per year. At the end of ten years it will be scrapped for $10,000. Machine B costs $60,000, will last for seven years and will require operating costs of $6,000 per year. At the end of seven years it will be scrapped for $5,000. Which is a better machine? (discount rate is 10 percent)

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Step 1: compute the PV of the costs of each machine

PV of costs (A) = $90,000 + PV of $5,000 annuity for ten

years - PV of the scrap (at t = 10) value of $10,000

= 90000 + 30722.84 – 3855.43 = $116,867.41

PV of costs (B)= $60,000 + PV of $6,000 annuity for seven

years - PV of the scrap (at t = 7) value of $5,000

= $60,000 + $29,210.51 - $2,565.79 =$86,644.72

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Step 2: compute equivalent annual cost (EAC) series of each machine

The equivalent annual cost series is the payment of an annuity that has the same present value as the PV of the machine’s cost.

EAC of machine A, EAC(A): N = 10, I/Y = 10, PV = -116867.41, FV = 0. Then

CPT, PMT. This yields EAC(A) = $19,019.63. EAC of machine B, EAC(B): N = 7, I/Y = 10, PV = -86644.72, FV = 0. Then

CPT, PMT. This yields EAC(B) = $17,797.30. Choose machine B because it has the lower cost.

Homework Assignment

Problems: 1,2,3,4,5,6,7,9,11,13(a,b,c),16,17,21(a,b,c,d)

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