4 Capital Budgeting 1

1

VI. Capital Budgeting Under Certainty

Professors Simon Pak and John Zdanowicz

Textbook Chapters 5 & 6

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Outline Capital Budgeting Process Estimation of Cash Flows

Accounting Income versus Cash Flow Incremental Analysis: Incremental After Tax Net Cash Flows

Evaluation Criterior Investment Characteristics Method of Evaluation: ARR, PB, DCF - NPV, PI, IRR

Comparison of Methods of Evaluation Average Rate of Return, Payback Period NPV vs IRR

• Independent Projects• Mutually Exclusive Projects• Independent Projects - Non-conventional CF’s

NPV vs PI PROBLEM SOLVING

P&Z Electronics P&Z Machine Tool Co. Concrete Mixer Truck

Long- And Short-lived Equipment: Equivalent Annual Cost (EAC) Inflation and DCF Analysis Capital Rationing Appendix A - More on IRR

© Simon Pak & John Zdanowicz 2000

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1. Capital Budgeting Process

Asset Management: Short-term: Working Capital Management Long-term: Capital Budgeting or Capital Investment

Steps in Capital Budgeting1. Generate investment proposal

• new products or expansion of existing products• replacement of equipment or building• R & D• other - education of management and/or employees

2. Estimate cash flows from the proposed investment3. Evaluate the cash flows: Accept or Reject

Most firms stops here.4. Continual Reevaluation:

• A rejected project may become acceptable:– As the discount rate goes down, the NPV goes up.

• Cut the losses - develop abandonment criterior in advance– Sunk costs are irrelevant in decision making– Personal ego to push for project is not value maximizing behavior.


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2. Estimation of Cash Flows Most difficult and most important in a capital budgeting process To estimate cash flows from a proposed project:

Distinguish between Accounting Income and Cash Flows Use only Incremental After Tax Net Cash Flows

• Initial Cash Flows• Future Cash Flows


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2.1 Accounting Income vs. Cash Flows

Future Income IS NOT EQUAL Future Cash Flow In Finance: focus is on cash

Invest it ; Receive it ; Consume it In Accounting, objectives are different:

Matching revenues and expenses Other issues:

• historical cost: depreciation methods• inventory valuation - LIFO or FIFO

Cash Flow versus Accounting Income

Project Income StatementCash Flow = PNI + NoncashExpenses

Revenues (R) $1,000 = PNI + DepreciationDepreciation (D) $150 = $270 + $150 = $420All other costs (OC) $400 Alternatively

NIBT $450 Cash Flow = (R - OC - D) x (1 - T) + DTaxes (T=40%) $180 = (R - OC) x (1 - T) + T x DProject Net Income (PNI) $270 = (1000 - 400) x 0.6 + 0.4 x 150( = Accounting Income) = $420


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2.2 Incremental Analysis: Incremental After Tax Net Cash Flows

“Incremental” = Change in CF due to the proposed project Sales of a new product may be partially offset by a decrease in the sales

of the existing product. Equipment Replacement:

• gains depreciation of the new equipment but loses the depreciation of the old equipment

• (cost of the new equipment) - (salvage value of the old) Increase In Net Working Capital

• WorkingCapital = ShortTermAssets - ShortTermLiabilities• Short-term Assets = Cash + Accounts receivable +Inventories of raw

materials and finished goods• Short-term Liabilities = Accounts Payable + Notes payable + Accruals• Include working capital effects in the early stages of the project• Adjust for changes in net working capital during the life of the project• Include recovery of net working capital at the end of the project


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2.2.1 Incremental Analysis - continued

“After tax” : Only after-tax cash flow can be consumed

Cash Flow: positive if cash inflow or cash outflow negative if cash inflow or cash outflow

Net CF: Net out all +’s and -’s for each time period Time frame:

t = 0 : Nowt = 1, 2, … , n where n = number of years of life of the project

Conclusion: Necessary to obtain Incremental After Tax Net Cash Flow for each t = 0, 1, 2, … , n Important to have a good tax accountant!

FORGET SUNK COST! Any cost already paid or obligated to be paid in the future Not affected by decision to accept or reject project


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2.2.2 Initial Cash Flows

CF0 = - Cost of new investment- Cost of installation+ Sale of existing assets if replacement+ or - Tax effect of sale of existing assets

If SalePrice < BookValue, tax ( + )If SalePrice = BookValue, no tax effect ( 0 )If SalePrice > BookValue, tax ( - )

+ Investment tax credit

Note: Initial investment costs may be spread out over several years.


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2.2.3 Future Cash Flows: CF1, CF2, . . . , CF(n-1), CFn

CFt = + Increase in Revenue (sales)+ Decrease in Expense Operating expenses, labor, raw material, etc. Administrative expenses+ or - Impact of changes in depreciation expenses

Non cash charges Depreciation expenses means tax shield Must net lost depreciation in a replacement project- Change in working capital requirements

in the particular year- Change in taxes

CFn = Same as above+ Salvage value of assets- Removal cost (environmental issue, cleaning up sites)

* Depending upon specific project, many other CF’s may need to be considered.


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3. Evaluation Criterior Once CF’s, incremental after tax net CF, are determined, an

investment project can be evaluated.

Investment Characteristics will be important in later discussions. Cash flow characteristics: Pattern of positive CFs and negative CFs

• Conventional case: . . . • Non-conventional case: . . .

change in signs of CFs over time - complicates analysis

Types of Investment• Independent projects: The evaluation of a project is independent of

any other projects, i.e., A or B or Both in accept-reject decision• Mutually exclusive projects:

– Only one project can be accepted, i.e., A or B, but not Both: • gas heater or oil heater

– Capital Constraint: • Example: Up to $1 million available for investment. This means

that not all the good projects can be accepted.


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3.1. Methods of Evaluation Five methods of evaluation:

Average Rate of Return (ARR) Payback Period (PB) Net Present Value (NPV) Profitability Index (PI) Internal Rate of Return (IRR)

NPV, PI, and IRR use Discount Cash Flow (DCF) technique.

For each one of the five methods, we will discuss: The way each measure is calculated The way each measure is used Advantages Disadvantages


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3.2. Average Rate of Return (ARR), Book R of R

2. How to Apply: Establish a Required ARR. Rank, Accept or Reject a project by comparing to the req’d ARR

3. Advantage: Simple to calculate based on accounting income (readily available information)

4. Disadvantages:Ignores Cash Flows by using Accounting incomeIgnores Time Value of Money by using Average Income

InvestmentAverageTaxAfterProfitAnnualAverage

ARR1.

Project A Project BPeriod Net Income Net CF Net Income Net CF

1 $3,000 $6,000 $1,000 $4,0002 $2,000 $5,000 $2,000 $5,0003 $1,000 $4,000 $3,000 $6,000

AvgInv = (9000+6000+3000+0)/4 = 4500ARRA = ARRB = 2000/4500 = 44.44%However, A is preferable B because PV(CFA) > PVCFB)

Example 1: Projects A and B both cost $9,000 and have a 3 year project life. Compare the two project using ARR criterior.


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3.3. Payback Period (PB)

1. PB = number of years required to recover the initial investmentExample: Uneven Cash flows Even Cash Flows

CF0 = - 10,000 ( - 10,000) CF0 = - 18,000CF1 = + 4,000 ( - 6,000) CF1 ~ CF5 = + 5,600CF2 = + 5,000 ( - 1,000) PB = 18,000/ 5,600 = 3.2

yearsCF3 = + 4,000 ( + 3,000)PB = 2 years + 1,000/4,000 = 2.25 years

2. How to Apply: Establish a maximum acceptable payback period. Rank by payback period. Accept (or Reject) a project with a PB shorter(or longer) than the maximum acceptable PB

3. Advantage: Simple to calculateUses CFsMaybe useful if liquidity is a problemMaybe useful as supplement to other evaluation methods© Simon Pak & John Zdanowicz 2000

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3.3.1. Payback Period (PB) - continued

4. Disadvantages: (i) Ignores CF’s after the PB period.

(ii) Does not take into account time value of money

Project Cost = $10,000Period CFA CFB

1 $5,000 $5,0002 $3,000 $3,0003 $2,000 $2,0004 $1,000 $1,000,0005 $0 $2,000

PBA = PBB = 3 yrs. However, CFB isbetter than CFA

Project Cost = $10,000Period CFA CFB

1 $5,000 $2,0002 $3,000 $3,0003 $2,000 $5,0004 $2,000 $2,000

PBA = PBB = 3 yrs. However, CFA isbetter than CFB

Payback period: may be viewed as a constraint to be satisfied, rather than a measure of profitability to be maximized.


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3.4. Discount Cash Flow Techniques

The remaining three method of evaluation uses DCF techniques Net Present Value (NPV) Profitability Index (PI) Internal Rate of Return (IRR)

All three methods require a discount rate, k = i + Discount rate, k, may be determined centrally in an organization Different division within a same organization may use different discount

rate depending upon the level of risk (Risk Premium: ). In this section the following project example will be used:

Discount rate = 10%CF0 = - $18,000

CF1, CF2, . . . , CF5 = $5,600


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3.4.1. Net Present Value (NPV) Method

Calculate NPV of a project NPV = PV (CF’s from t= 0 to N)

Often: NPV = PV (CF’s from t= 1 to N) - Cost(t=0) How to use NPV?

Accept the project if NPV > 0, reject if NPV < 0 If NPV = 0, the project earns “k” on the investment Projects can be ranked by NPV

Example:

Nt

tt

tN

N

kCF

kCF

kCF

kCF

NPV0

10

0

)1()1()1()1(

discount rate k=10%t CFt PVIF PV0 -$18,000 1 -$18,000

1 ~ 5 $5,600 3.7908 $21,228NPV = $3,228

Accept the project since NPV > 0


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3.4.2. Profitability Index (PI)

How to use PI: Accept a project if PI > 1 Accept a project if PI = 1 (makes required return) Reject a project if PI < 1

Example:CF0 = - $18,000PV(CF1 ~ CF5) = $21,228Therefore, PI = 21,228 / 18,000 = 1.18

Note: PI is also called Benefit-Cost Ratio When costs are spread over for more than one period, then the cost is

the PV of all cash outflows. PI may alternatively defined as (NPV/Cost). In this case, PI will simply be

reduced by 1.

CostBenefitsFutureofPV

CFPV

PI 0


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3.4.3. Internal Rate of Return (IRR)

IRR = The discount rate that makes NPV = 0.Can not be calculated directly. Only by trial and error.

Example 1:Try k= 15%

t CFt PVIF PV0 -$18,000 1 -$18,000

1 ~ 5 $5,600 3.3522 $18,772NPV = $772

Try k= 20%t CFt PVIF PV0 -$18,000 1 -$18,000

1 ~ 5 $5,600 2.9906 $16,747NPV = -$1,253

Try k= 17%t CFt PVIF PV0 -$18,000 1 -$18,000

1 ~ 5 $5,600 3.1993 $17,916NPV = -$84

trial k NPV1 10% + $ 3,2282 15% + $ 7723 20% - $1,2534 17% - $ 84… … …..N ? 0

IRR must be between 16% and 17%The true value is 16.80% when calculated with a calculator


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3.4.3a. IRR Calculation with TI BA-II Plus

Example1: IRR ComputationCF0 = 18000, CF1 ~ CF5 = 5,600

CF CF0 = No. in mem Start CF worksheet

2nd [CLR Work] CF0 = 0.00 Clear CF memory

18000 +/- CF0 -18,000

[ENTER] CF0 = -18,000 CF(t=0 ) = - 18,000

x C01 0.00

5600 [ENTER] C01 = 5,600.00 CF(t=1 ) = 5,600

x F01 = 1.00

5 [ENTER] F01 = 5.00 CF repeats 5 times

IRR IRR= 0.00CPT IRR= 16.80 Answer

2nd [QUIT] 0.00 exit CF worksheet


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3.4.3b. IRR Calculation with TI BA-II Plus

Example 2. Calculate IRR.A project has the following CF’s:CF0 = -$10 million; CF1 = $2 m; CF2 = $ 4 m; CF3 - CF6 = $ 3 m; CF7 = $ 2 m; CF8 = $ 4 m

Calculate IRR.

Answer using TI II Plus calculator CF, 2nd, CLR Work,10000000, +/-, ENTER, , 2000000, ENTER, , , 4000000, ENTER, , , 3000000, ENTER, , 4, ENTER, , 2000000, ENTER, , , 4000000, ENTER, IRR, CPT

Ans: IRR= 24.23%. © Simon Pak & John Zdanowicz 2000

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3.4.3b. How to Use IRR

USE OF IRR METHOD Accept if IRR >= k, (cost of capital) Reject if IRR < k, (cost of capital) Rank by IRR

k, risk adjusted cost of capital: No clear cut way of determination. Risk is estimated.

B

A

Risk

Dis

coun

t Rat

e, k

k=10%

Assuming the required rate, or discount rate adjusted for the risk level of projects A and B is 10%:

Accept the project A : IRRA > k =10%

Reject the project B : IRRB < k =10%


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4. Comparison: ARR and PB Period

Average Rate of Return and Payback Period Often used due to simplicity Poor measure of profitability because CF’s and TVM are not employed

• ARR - Accounting income is used, not CF’s• PB - Ignores CF’s after the payback period

Can be used as back up if other methods rank similarly• Accuracy of NPV calculation of a project depends upon the accuracy

of CF forecast.• A project with NPV > 0 is more easily acceptable if it has a shorter PB

period.


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4.1. NPV vs IRR - Independent Projects

Both NPV and IRR give the same answer when evaluating an independent project.

Sum of all CF’s

IRR1

ACCEPT:Positive NPVfor k < IRR1

REJECT:Negative NPV

for k > IRR1

discount rate k (%)opportunity cost of capital

NPV

($)

k1

NPV1

NPV Profile of a project as a function of k

IRR1 >= k1 : AcceptNPV1 > 0 : Accept


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4.1.1. NPV vs IRR: Mutually Exclusive Projects

NPV and IRR can give a conflicting choice.NPV is more realistic given opportunity

cost of capital.

Mutually Exclusive Projects: C and D

discount rate k=8% (opportunity cost of capital)

Project C Project Dt CFt PVIF PV t CFt PVIF PV0 -$155.22 1.0000 -$155.22 0 -$155.22 1.0000 -$155.221 $100.00 0.9259 $92.59 1 $0.00 0.9259 $0.002 $0.00 0.8573 $0.00 2 $0.00 0.8573 $0.003 $100.00 0.7938 $79.38 3 $221.00 0.7938 $175.44

NPV = $16.76 NPV = $20.22IRR = 14.00% IRR = 12.50%

NPV method: Pick the project D since NPVD > NPVC

I RR method: Pick the project C since I RRC > I RRD

discount rate k (%)

NPV

($)

Project DProject C

8% 12.5%

IRR C

NPVD

NPVC

14%

IRR D

NPVD> NPVC NPVC> NPVD


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4.1.2. NPV vs IRR Non-conventional Cash Flows Independent Projects

Non-conventional cash flows: Conventional case: . . . Non-conventional case: . . .

• Change in signs of CFs over time - complicates analysis Non-conventional CF’s can result in multiple IRR values.

For more details, see Appendix A

Example: Should you accept a project with the following cash flows? CF0= -1,600, CF1= +10,000, CF2= -10,000 ? Assume k=20%

ANS: With trial and error method, we find IRR = 25% and 400% . Since both IRR > k, the project should be accepted. But wrong. NPV = - 211.11, at k = 20% . Therefore, the NPV rule indicates rejecting the project.

Given k=20%, borrow $1,600 at t=0 for one year and invest the amount.At t=1, your net CF = 10,000 - 1,600 x (1+0.2) = + $8,080Deposit $8,080 at t=1 for one year @20%At t=2, your net CF= 8,080 x (1+0.2) - 10,000 = - $304 [ = FV(NPV), net loss!]


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CONCLUSION on NPV vs IRR: IRR can lead you into a wrong decision for

• Projects with non-conventional CF’s• Mutually exclusive projects

At the end of the day, we are interested • In a dollar measure of profitability• Not in the profitability per dollar of investment

4.1.2. Conclusion on NPV vs IRR


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4.2. NPV vs PI

On Accept/Reject decision for Independent Projects: Both NPV and PI give same answer.

For Mutually Exclusive Projects:

NPV: Choose A (absolute $ amount)PI: Choose B (relative measure)

NPV is better than PI for share holder wealth maximization

Mutually Exclusive ProjectsProj. A Proj. B

PV $20,000 $8,000CF0 $15,000 $5,000NPV $5,000 $3,000PI = PV/CF0 1.33 1.60


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5. P&Z Electronics

P&Z Electronics has two mutually exclusive investments under consideration. Each project is to produce incremental cost savings for 7 years. The required rate of return for P&Z is 14% .

Determine for each project:(1) the payback period(2) the net present value.

Which project should you choose and why?

Assume the accelerated cost recovery system (ACRS) for depreciation for a 5-year property class. The corporate tax rate is 40%.

P&Z ElectronicsInvestment

Project A $28,000

Project B $20,000

Cost SavingsPeriod Project A Project B

1 $8,000 $5,0002 $8,000 $5,0003 $8,000 $6,0004 $8,000 $6,0005 $8,000 $7,0006 $8,000 $7,0007 $8,000 $7,000


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5a. Projects A & B - Cash FlowsInvestment $28,000 Project A Cash Flows

YearSavings

(1)Deprec

(2)Taxable

Income (3) Tax (4)

Cash Flow (1) - (4)

Year Rate Deprec 0 -$28,000 -$28,0001 20.00% $5,600 1 $8,000 $5,600 $2,400 $960 $7,0402 32.00% $8,960 2 $8,000 $8,960 -$960 -$384 $8,3843 19.20% $5,376 3 $8,000 $5,376 $2,624 $1,050 $6,9504 11.52% $3,226 4 $8,000 $3,226 $4,774 $1,910 $6,0905 11.52% $3,226 5 $8,000 $3,226 $4,774 $1,910 $6,0906 5.76% $1,613 6 $8,000 $1,613 $6,387 $2,555 $5,445

100% $28,000 7 $8,000 $0 $8,000 $3,200 $4,800

5-year Depreciation Schedule

Investment $20,000 Project B Cash Flows

YearSavings

(1)Deprec

(2)Taxable

Income (3) Tax (4)

Cash Flow (1) - (4)

Year Rate Deprec 0 -$20,000 -$20,0001 20.00% $4,000 1 $5,000 $4,000 $1,000 $400 $4,6002 32.00% $6,400 2 $5,000 $6,400 -$1,400 -$560 $5,5603 19.20% $3,840 3 $6,000 $3,840 $2,160 $864 $5,1364 11.52% $2,304 4 $6,000 $2,304 $3,696 $1,478 $4,5225 11.52% $2,304 5 $7,000 $2,304 $4,696 $1,878 $5,1226 5.76% $1,152 6 $7,000 $1,152 $5,848 $2,339 $4,661

100% $20,000 7 $7,000 $0 $7,000 $2,800 $4,200

5-year Depreciation Schedule


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5b. Projects A & B - Payback PeriodsPayback Periods

Year CF for AAmount

NotPaidBackCF for B

Amount NotPaidBack

0 -$28,000 -$28,000 -$20,000 -$20,0001 $7,040 -$20,960 $4,600 -$15,4002 $8,384 -$12,576 $5,560 -$9,8403 $6,950 -$5,626 $5,136 -$4,7044 $6,090 $465 $4,522 -$1825 $6,090 $5,122 $4,9396 $5,445 $4,6617 $4,800 $4,200

PB Period A = 3 + 5626 / 6090= 3.92 yrsPB Period B = 4 + 182 / 5122= 4.04 yrs


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5c. Projects A & B - NPVNet Present Value k= 14%Year PVIF CF for A PVA CF for B NPVB

0 1.0000 -$28,000 -$28,000 -$20,000 -$20,0001 0.8772 $7,040 $6,175 $4,600 $4,0352 0.7695 $8,384 $6,451 $5,560 $4,2783 0.6750 $6,950 $4,691 $5,136 $3,4674 0.5921 $6,090 $3,606 $4,522 $2,6775 0.5194 $6,090 $3,163 $5,122 $2,6606 0.4556 $5,445 $2,481 $4,661 $2,1237 0.3996 $4,800 $1,918 $4,200 $1,678

NPVA $486 NPVB $919

NPV Payback Project A $486 3.92 yrsProject B $919 4.04 yrsNPV rule: Choose BPB rule: Choose AWhich one?


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6. P&Z Machine Tool Co.

P&Z Machine Tool Co. is considering the purchase of a new drill press to replace the one currently being used. The present machine is expected to last another seven years and have no salvage value. The drill press in current use as a book value of $7,000 and can be sold today for $4,000. P&Z pays $5,000 a year maintenance on the press.

The new drill press will cost $15,000; is expected to last 7 years at which time it will be sold for $1,000. The maintenance cost on the new machine is expected to be $1,500 a year. P&Z depreciate its assets on the straight line basis and pays taxes at the rate of 40%.

1) What is the initial cash outlay associated with the new machine?2) What is the additional cash flow expected to be produced by the new machine for the

years 1-7 ?3) What is the average rate of return?4) What is the payback period?5) What the the NPV assuming a discount rate of 20% ?6) What is the profitability index assuming a discount rate of 20% ?7) What is the internal rate of return?


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1) CF0 = Cost + Salvage + TaxSavingTaxSaving = (BookValue - SalePrice) x TaxRate

= (7,000 - 4,000) x 0.4 = 1,200Thus, CF0 = - 15,000 + 4,000 + 1,200 = - 9.800

2) Cash Flows Year 1 thru Year 7: Changes in Depreciation & IncomeDepreciation on New Machine = (15,000 - 1,000) / 7 = $2,000/yrDepreciation on Old Machine = (7,000 - 0) / 7 = $1,000/yrChange in Depreciation = $1,000/yr

Year 1 thru Year 6Cash savings: Maintenance on Old - New = 5,000 - 1,500 = 3,500Change in depreciation expense = - 1,000Change in taxable income = 2,500Change in tax @40% = - 1,000Change in net income = 1,500Change in CF (add back Change in depreciation, 1,000) = + 2,500Year 7Change in CF + Salvage Value = 2,500 + 1,000 = + 3,500

6a P&Z Machine Tool Co. - solution


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6b P&Z Machine Tool Co. - Solution

3) Average Rate of Return:ARR = (AverageAnnualChangeInNetIncome) / (AverageInvestment) = 1,500/ ((15,000+1,000)/2) = 1,500 / 8,000 = 18.75%

4) Payback period:Year 1: 9,800 - 2,500 = 7,300Year 2: 7,300 - 2,500 = 4,800Year 3: 4,800 - 2,500 = 2,300Year 4: 2,300 / 2,500 = 0.92 yrs.Payback period = 3 + 0.92 = 3.92 years

5) NPV = - $ 509 : The project should be rejected!

Discount Rate 20%Year CFs PVIF PV

0 -$9,800 1.0000 -$9,8001-6 $2,500 3.3255 $8,314

7 $3,500 0.2791 $977NPV = -$509


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6c P&Z Machine Tool Co. - Solution

6) Profitability Index:CF0 = - $9.800PV(CF1, CF2, . . . , CF7) = 8,314 + 977 = $ 9,291PI = PV(CF1, CF2, . . . , CF7 / CF0 = 9291/9800 = 0.95Since PI < 1, the project should be REJECTED!

7) IRR

Answer using TI BA-II Plus calculator CF, 2nd, CLR Work,9800, +/-, ENTER, , 2500, ENTER, , 6, ENTER,, 3500, ENTER, IRR, CPT

Ans: IRR= 18.15%.

Since IRR = 18.15% is less than the discount rate of 20%, the projectshould be rejected !


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7. Concrete Mixer Truck

The City of Miami must replace a number of its concrete mixer trucks with new trucks. It has received several bids and has evaluated closely the performance characteristics of the various trucks. The Patterbilt truck, which costs $74,000 is top-of-the-line equipment. It has a life of 8 years assuming that the engine is rebuilt in the fifth year. Maintenance costs of $2,000 a year are expected in the first 4 years, followed by total maintenance and rebuilding costs of $13,000 in the fifth year. During the last 3 years, maintenance costs are expected to be $4,000 a year. At the end of 8 years, the truck will have an estimated scrap value of $9,000.

A bid from Bulldog Trucks, Inc., is for $59,000 a truck. The maintenance costs are expected to be $3,000 in year 1. This amount is expected to increase by $1,500 a year through the eighth year. In year 4 the engine will need to be rebuilt, and this will cost the city $15,000 in addition to maintenance costs in that year. At the end of 8 years the Bulldog truck will have an estimated scrap value of $5,000.

continued . . .


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7. Concrete Mixer Truck … continued

The last bidder, Best Tractor and Trailer Company, has agreed to sell trucks at $44,000 each. Maintenance costs in the first 4 years are expected to be $4,000 the first year and to increase by $1,000 a year. For the city’s purpose, the truck has a life of only 4 years. At that time, it can be traded in for a new Best Truck, which is expected to cost $52,000. The likely trade-in value of the old truck is $15,000. During years 5 through 7 the second truck is expected to have maintenance costs of $5,000 in year 5, and these are expected to increase by $1,000 each year. At the end of 8 years, the second truck is expected to have a resale value or salvage value of $18,000.

1) If the opportunity cost of funds for the city is 8%, which bid should the city accept? Ignore tax considerations, as the city pays no taxes.

2) If its opportunity cost were 15%, would your answer change?


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7a Concrete Mixer Truck with k = 8%

k = 8%Patterbilt Bulldog Best

Time PVIF CF PV CF PV CF PV0 1.0000 -$74,000 -$74,000 -$59,000 -$59,000 -$44,000 -$44,0001 0.9259 -$2,000 -$1,852 -$3,000 -$2,778 -$4,000 -$3,7042 0.8573 -$2,000 -$1,715 -$4,500 -$3,858 -$5,000 -$4,2873 0.7938 -$2,000 -$1,588 -$6,000 -$4,763 -$6,000 -$4,7634 0.7350 -$2,000 -$1,470 -$22,500 -$16,538 -$44,000 -$32,3415 0.6806 -$13,000 -$8,848 -$9,000 -$6,125 -$5,000 -$3,4036 0.6302 -$4,000 -$2,521 -$10,500 -$6,617 -$6,000 -$3,7817 0.5835 -$4,000 -$2,334 -$12,000 -$7,002 -$7,000 -$4,0848 0.5403 $5,000 $2,701 -$8,500 -$4,592 $10,000 $5,403

Present Value -$91,625 -$111,273 -$94,960CF8 = -4,000+9,000=5,000 CF4 = -7,500 - 15,000 CF4 = - 52K + 15K - 7K = - 44,000

CF8 = -13,500 + 5,000 CF8 = - 8K + 18K = 10,000


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7b Concrete Mixer Truck with k = 15%

k = 15%Patterbilt Bulldog Best

Time PVIF CF PV CF PV CF PV0 1.0000 -$74,000 -$74,000 -$59,000 -$59,000 -$44,000 -$44,0001 0.8696 -$2,000 -$1,739 -$3,000 -$2,609 -$4,000 -$3,4782 0.7561 -$2,000 -$1,512 -$4,500 -$3,403 -$5,000 -$3,7813 0.6575 -$2,000 -$1,315 -$6,000 -$3,945 -$6,000 -$3,9454 0.5718 -$2,000 -$1,144 -$22,500 -$12,864 -$44,000 -$25,1575 0.4972 -$13,000 -$6,463 -$9,000 -$4,475 -$5,000 -$2,4866 0.4323 -$4,000 -$1,729 -$10,500 -$4,539 -$6,000 -$2,5947 0.3759 -$4,000 -$1,504 -$12,000 -$4,511 -$7,000 -$2,6328 0.3269 $5,000 $1,635 -$8,500 -$2,779 $10,000 $3,269

Present Value -$87,772 -$98,125 -$84,804CF8 = -4,000+9,000=5,000 CF4 = -7,500 - 15,000 CF4 = - 52K + 15K - 7K = - 44,000

CF8 = -13,500 + 5,000 CF8 = - 8K + 18K = 10,000


IV - 40

Two Machines Have Same Functionality Ignore Revenue Side Choose Between Them On the Basis Of Cost

Have To Be Replaced At the End Of Their Economic Life Machine A Has 3-year Life Machine B Has 2-year Life

Following Are Costs In Today’s Dollars Use Real Discount Rate Of 6%

Copyright 1996 by The McGraw-Hill Companies, Inc

8 Choosing Between Long- And Short-lived Equipment: Equivalent Annual Cost (EAC)

IV - 41

COSTS Year: 0 1 2 3 PV @ 6% A 15 5 5 5 28.37 B 10 6 6 21.00

Machine B Has Lower NPV But Shorter Life Has To Be Replaced one Year Earlier

Convert To Costs Per Year Fair Rental Payment Equivalent Annual Cost (EAC)

Equivalent annual cost of A =28.37/(3-year annuity factor)

= 28.37/2.673 = 10.61

Equivalent annual cost of B =21.00/(2-year annuity factor) = 21/1.834 = 11.45

Annual Cost Of A Is Less Than That Of B


8.2 Long- Versus Short-lived Equipment

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PV of Nominal cash flows Nominal CF’s discounted by nominal discount rates both nominal cash flows and nominal discount rates include expected

inflation

PV of Real cash flows Real CF’s discounted by real discount rates both cash flows and discount rates exclude inflation effects

Nominal cash flows discounted at the nominal rateare equal to

real cash flows discounted at the real ratebecause both methods measure $NOW

9 Inflation and DCF Analysis


IV - 44

9.1 Nominal vs. Real Cash Flows

NEXPECTED

NREAL

NNOMINAL )I(1)r(1r1

Periods N for Equation Fisher the Using

NREAL

REALN

EXPECTEDN

REAL

NEXPECTEDREAL

NNOMINAL

NOMINAL

)r(1C

)I(1)r)I(1C

)r(1C

(1

periods-N in )I(1CC

period one in )I(1CC

periods-N in Flow Cash Real :C

periods-N in Flow Cash Nominal :C

NEXPECTEDREALNOMINAL

EXPECTEDREALNOMINAL

REAL

NOMINAL


IV - 45

10. Capital Rationing

Shareholders are interested in the absolute amount of money. NPV rule is better than PI or IRR rules NPV rule often picks a larger investment project even though IRR or PI

may be lower. NPV rule assumes the firm can invest as much as it wants to.

Capital Rationing It occurs when the firm has a limitations on the capital it can invest

• Capital Rationing can be now and/or in the future It means not all the positive NPV projects will be undertaken

Under Capital Rationing What should be the investment decision rule?

• Maximize NPV subject to the capital constraint on all the investments

How to identify the investment projects?• Use Profitability Index with trial and error in simple cases• Use Linear Programming or Integer Programming in general

cases


IV - 46

0 1 2 NPV @ 10% A -10 +30 +5 21

B -5 +5 +20 16 C -5 +5 +15 12

Limited $10 million capital Firm can invest in project A or (projects B and C) Individually, B and C have lower NPV Taken together, B and C have higher NPV Choose projects that offer highest Benefits or NPV per dollar

invested


10.1 Example of Capital Rationing

IV - 47

Rank projects in terms of declining PIContinue making investments until capital exhaustedAccept projects B and C


10.2 Use Profitability Index in A Simple Case

Investment InitialBenefits of ValuePresent

Indexity Profitabil

Investment PV(CF1,CF2) PI NPV5 21 4.2 165 17 3.4 1210 31 3.1 21

IV - 48

Capital constraints in more than one periodExample: firm can raise $10 million in each of years 0 and 1


10.3 Limitations In Use Of Profitability Index

Project CF0 CF1 CF2 PV(benefits) PI NPV @10%A -10 30 5 31 3.1 21B -5 5 20 21 4.2 16C -5 5 15 17 3.4 12D 0 -40 60 50 1.4 13

If we accept projects B and C, based on PI, we cannot accept project D

Better to accept project A in period 0 Allows us to accept project D in period 1

IV - 49

PI cannot be used whenever there is any constraints in choice of projects, other than capital rationing in one period Capital rationing in multiple periods Mutually exclusive projects One project depends on another

Use of PI may be reasonable if we don’t have a good idea of future capital availability or investment opportunities

Alternatively, we may need linear programming or Integer Programming


10.4 Wrong Applications of PI

IV - 50

Soft Rationing: Internally Imposed Constraint Capital Rationing at the Division Level:

• To Force Divisions to Prioritize Among the Investment Opportunities Capital Rationing at the Corporate Level:

• to Limit Corporate Growth Due to Limited Management Resources

Hard Rationing: Externally Imposed Constraint Capital Markets Imperfections Shareholders may not want to Issue additional stocks to maintain the

control of the company Lenders may not provide funding for a new positive NPV Project Because

of Poor Financial Condition of Existing Projects of Firm

10.5 Types of Capital Rationing


IV - 51

11. Appendix A: More on IRR - A Positively Sloped NPV

Consider the following two Projects:

$200

- $4025%

IRR=20%

The Investing Project

Reject the projectbecause NPV<0

k > IRR

- $200

$40

25%

IRR=20%

The Borrowing Project

Accept the projectbecause NPV>0

k > IRR

Investing ProjectC0 = -$1,000C1 = $1,200

k NPV0% $2005% $142.86

10% $90.9115% $43.4820% $0.0025% -$40.00

NPV at various opportunity CC's

Borrowing ProjectC0 = $1,000C1 = -$1,200

k NPV0% -$2005% -$142.86

10% -$90.9115% -$43.4820% $0.0025% $40.00


IRR Rule: If NPV is downward sloping,

accept projects when k < IRR If NPV is upward sloping,

accept projects when k > IRR


IV - 52

11.1 Appendix A : More on IRR - Multiple IRR’s

Consider the following Project with CF’s changing signs:Project With Negative CF laterC0 = -$1,000

C1 = $1,200C2 = $1,500C3 = -$1,750 Clean-up Cost

k NPV0.0% -$505.0% -$8.316.4% $0.00

10.0% $15.7815.0% $27.0420.0% $28.9425.0% $24.0030.0% $14.1135.2% $0.0040.0% -$15.3145.0% -$33.01


IRR Rule: If DCF is positively sloping at IRR1,

accept the project when k > IRR1

If DCF is negatively sloping at IRR2, accept the project when k < IRR2

-$60

-$50

-$40

-$30

-$20

-$10

$0

$10

$20

$30

$40

10% 20% 30% 40% 50%

DCF: Net Present Value

IRR1IRR2

ACCEPT REJECTREJECT


IV - 53

11.2WARNING on IRR vs Opportunity Cost of Capital

Distinguish between IRR and opportunity cost of capital Both appear as discount rates in NPV formula.

IRR is a measure of profitability, depends on amount and timing of cash flows

Opportunity cost of capital measures what we could earn by investing in financial assets of similar risk Set by capital markets It is a cost of financing the project It provides us with a minimum acceptable level of profitability


IV - 54

11.3 Can IRR Rule be used for Mutually Exclusive Projects?

Project CF0 CF1 IRR(%) NPV@10% E -10,000 +20,000 +100 +8,182 F -20,000 +35,000 +75 +11,818

Project E manually controlled machine Project F computer controlled machine

HIGHER NPV PREFERRED MACHINE BUT LOWER IRR!

We can accept only one project We are choosing between alternative ways of doing the same thing We need one fork lift truck

What should be the criterion in choosing between alternative projects?

IRR rule can give wrong answer !


IV - 55

11.3a IRR Rule Vs. Mutually Exclusive Projects

Salvage IRR rule by considering IRR on the incremental project First analyze smaller project E

Accept project E IRR of 100% > 10% cost of capital At the least, project E is acceptable

Should I make the incremental investment to go from project E to project F?Incremental Cash Flows 0 1 IRR(%) NPV@10%

F-E -10,000 +15,000 +50 +3,636 Accept incremental project (F - E)

IRR of 50% > 10% cost of capital But we know that project E is acceptable Choose project F We could have chosen project F at the start by noting that it has

the higher NPVCopyright 1996 by The McGraw-Hill Companies, Inc

IV - 56

11.3b IRR rule vs. MUTUALLY EXCLUSIVE PROJECTS

A small project with a very high IRR

may have a smaller NPV

than a large project with a smaller IRR


IV - 57

11.4 DISCOUNTED PAYBACK RULE Calculate length of time until the sum of the discounted cash

flows is equal to the initial investment

Accept project if it is less than some cutoff value

Discounted-payback rule asks how long will it be until the project has a positive NPV

No longer gives equal weight to all cash flows before payback date

but still ignores cash flows after the cutoff date

Cannot be used for ranking projects


Documents

4 Capital Budgeting 1