chapter 10. cash flows and other topics in capital budgeting

Chapter 10

Cash Flows and Other Topics in Capital Budgeting

NET PRESENT VALUE (NPV)INTERNAL RATE OF RETURN (IRR)

NPVNPV = - IO = - IO ACFACFtt

(1 + k)(1 + k) tt

nn

t=1t=1

n

t=1IRR: = IO

ACFt

(1 + IRR) t

Capital Budgeting: the process of planning for purchases of long-term assets.

exampleexample: :

Our firm must decide whether to purchase a Our firm must decide whether to purchase a new plastic molding machine for new plastic molding machine for $127,000$127,000. . How do we decide?How do we decide?

Will the machine be Will the machine be profitableprofitable?? Will our firm earn a Will our firm earn a high rate of returnhigh rate of return on on

the investment?the investment? The relevant project information follows:The relevant project information follows:

The cost of the new machine is The cost of the new machine is $127,000$127,000. . Installation will cost Installation will cost $20,000$20,000.. $4,000$4,000 in net working capital will be needed in net working capital will be needed

at the time of installation.at the time of installation. The project will increase revenues by The project will increase revenues by

$85,000$85,000 per year, but operating costs will per year, but operating costs will increase by increase by 35%35% of the revenue increase. of the revenue increase.

Simplified straight line depreciation is used.Simplified straight line depreciation is used. Class life is Class life is 55 years, and the firm is planning years, and the firm is planning

to keep the project for to keep the project for 55 years. years. Salvage value at year 5 will be Salvage value at year 5 will be $50,000$50,000.. 14%14% cost of capital; cost of capital; 34%34% marginal tax rate. marginal tax rate.

CAPITAL BUDGETING STEPS

1.1. EVALUATE CASH FLOWSEVALUATE CASH FLOWS

2.2. DETERMINE RISK (DISCOUNT %)DETERMINE RISK (DISCOUNT %)

3.3. MAKE ACCEPT/REJECT DECISIONMAKE ACCEPT/REJECT DECISION

Capital Budgeting Steps

1) 1) Evaluate Cash FlowsEvaluate Cash Flows

Look at all incremental cash flows Look at all incremental cash flows occurring as a result of the project.occurring as a result of the project.

Initial outlayInitial outlay Differential Cash FlowsDifferential Cash Flows over the life over the life

of the project (also referred to as of the project (also referred to as annual cash flows).annual cash flows).

Terminal Cash FlowsTerminal Cash Flows

Capital Budgeting Steps

1) 1) Evaluate Cash FlowsEvaluate Cash Flows

0 1 2 3 4 5 n6 . . .

TerminalTerminalCash flowCash flow

Annual Cash FlowsAnnual Cash Flows

InitialInitialoutlayoutlay

2) 2) Evaluate the risk of the projectEvaluate the risk of the project.. We’ll get to this at the end of this chapter.We’ll get to this at the end of this chapter. For now, we’ll assume that the For now, we’ll assume that the risk of the risk of the

projectproject is the same as the is the same as the risk of the risk of the overall firm.overall firm.

If we do this, we can use the firm’s If we do this, we can use the firm’s cost of cost of capitalcapital as the discount rate for capital as the discount rate for capital investment projects.investment projects.

Capital Budgeting StepsCapital Budgeting Steps

3) 3) Accept or Reject the ProjectAccept or Reject the Project..

Capital Budgeting StepsCapital Budgeting Steps

Step 1: Evaluate Cash Flows

a) a) Initial OutlayInitial Outlay:: What is the cash flow What is the cash flow at “time 0?”at “time 0?”

(Purchase price of the asset)(Purchase price of the asset)

+ (+ (shipping and installation costs)shipping and installation costs)

(Depreciable asset)(Depreciable asset)

+ (Investment in working capital)+ (Investment in working capital)

+ + After-tax proceeds from sale of old assetAfter-tax proceeds from sale of old asset

Net Initial OutlayNet Initial Outlay



(127,000)(127,000)

+ (+ (shipping and installation costs)shipping and installation costs)






a) a) Initial OutlayInitial Outlay:: What is the cash flow at What is the cash flow at “time 0?”“time 0?”

(127,000)(127,000)

+ (+ ( 20,000 20,000))







(127,000)(127,000)

+ (+ ( 20,000 20,000))

(147,000)(147,000)






(127,000)(127,000)

+ (+ ( 20,000 20,000))

(147,000)(147,000)

+ ( 4,000)+ ( 4,000)





(127,000)(127,000)

+ (+ ( 20,000 20,000))

(147,000)(147,000)

+ ( 4,000)+ ( 4,000)

+ + 0 0




(127,000)(127,000) Purchase price of asset Purchase price of asset

+ (+ ( 20,000 20,000)) shipping and installation shipping and installation

(147,000)(147,000) depreciable asset depreciable asset

+ ( 4,000)+ ( 4,000) net working capital net working capital

+ + 0 0 proceeds from sale of old asset proceeds from sale of old asset

($151,000) net initial outlay($151,000) net initial outlay


b) b) Annual Cash FlowsAnnual Cash Flows:: What What incremental cash flows occur over the incremental cash flows occur over the life of the project?life of the project?

Incremental revenueIncremental revenue

- Incremental costs- Incremental costs

- - Depreciation on project Depreciation on project

Incremental earnings before taxesIncremental earnings before taxes

- - Tax on incremental EBTTax on incremental EBT

Incremental earnings after taxesIncremental earnings after taxes

+ + Depreciation reversalDepreciation reversal

Annual Cash Flow Annual Cash Flow

For Each Year, Calculate:

Incremental revenueIncremental revenue








For Years 1 - 5:

85,00085,000








For Years 1 - 5:

85,00085,000

(29,750)(29,750)






Annual Cash FlowAnnual Cash Flow

For Years 1 - 5:

85,00085,000

(29,750)(29,750)

(29,400)(29,400)






For Years 1 - 5:

85,00085,000

(29,750)(29,750)

(29,400) (29,400)

25,85025,850





For Years 1 - 5:

85,00085,000

(29,750)(29,750)

(29,400) (29,400)

25,85025,850

(8,789)(8,789)




For Years 1 - 5:

85,00085,000

(29,750)(29,750)

(29,400) (29,400)

25,85025,850

(8,789)(8,789)

17,06117,061



For Years 1 - 5:

85,00085,000

(29,750)(29,750)

(29,400) (29,400)

25,85025,850

(8,789)(8,789)

17,06117,061

29,40029,400


For Years 1 - 5:

85,00085,000 RevenueRevenue

(29,750)(29,750) CostsCosts

(29,400) (29,400) Depreciation Depreciation

25,85025,850 EBTEBT

(8,789)(8,789) TaxesTaxes

17,06117,061 EATEAT

29,40029,400 Depreciation Depreciation reversalreversal

46,46146,461 = = Annual Cash FlowAnnual Cash Flow

For Years 1 - 5:


c) c) Terminal Cash FlowTerminal Cash Flow:: What is the cash What is the cash flow at the end of the project’s life?flow at the end of the project’s life?

Salvage valueSalvage value

+/- Tax effects of capital gain/loss+/- Tax effects of capital gain/loss

+ + Recapture of net working capitalRecapture of net working capital

Terminal Cash FlowTerminal Cash Flow



50,00050,000 Salvage value Salvage value




Tax Effects of Sale of Asset:

Salvage value = Salvage value = $50,000$50,000 Book value = depreciable asset - total Book value = depreciable asset - total

amount depreciated.amount depreciated. Book value = $147,000 - $147,000Book value = $147,000 - $147,000

= $0.= $0. Capital gain = SV - BVCapital gain = SV - BV

= 50,000 - 0 = $50,000= 50,000 - 0 = $50,000 Tax payment = 50,000 x .34 = Tax payment = 50,000 x .34 = ($17,000)($17,000)




(17,000)(17,000) Tax on capital gain Tax on capital gain

Recapture of NWCRecapture of NWC






4,0004,000 Recapture of NWCRecapture of NWC






4,0004,000 Recapture of NWC Recapture of NWC

37,00037,000 Terminal Cash Flow Terminal Cash Flow

Project NPV:

CF(0) = CF(0) = -151,000-151,000 CF(1 - 4) = CF(1 - 4) = 46,46146,461 CF(5) = 46,461 + 37,000 = CF(5) = 46,461 + 37,000 = 83,46183,461 Discount rate = Discount rate = 14%14% NPV = NPV = $27,721$27,721 IRR = IRR = 21%21% We would We would acceptaccept the project.the project.

Incorporating Risk into Capital Budgeting

Risk-Adjusted Discount RateRisk-Adjusted Discount Rate

How can we adjust this model to take risk into account?

NPV = - IO NPV = - IO ACFACFtt

(1 + k)(1 + k) tt

nn

t=1t=1

How can we adjust this model to take risk into account?

Adjust the discount rate (k).Adjust the discount rate (k).


(1 + k)(1 + k) tt

nn

t=1t=1

Risk-Adjusted Discount Rate

Simply Simply adjust the discount rate (k)adjust the discount rate (k) to to reflect higher risk.reflect higher risk.

Riskier projects will use Riskier projects will use higherhigher risk- risk-adjusted discount rates.adjusted discount rates.

Calculate NPV using the new risk-Calculate NPV using the new risk-adjusted discount rate.adjusted discount rate.

Risk-Adjusted Discount Rate


(1 + k*)(1 + k*)tt

nn

t=1t=1

Risk-Adjusted Discount Rates

How do we determine the How do we determine the appropriate risk-adjusted discount appropriate risk-adjusted discount rate rate (k*)(k*) to use? to use?

Many firms set up Many firms set up risk classesrisk classes to to categorize different types of categorize different types of projects.projects.

Risk Classes

Risk RADR Risk RADR

ClassClass (k*) (k*) Project Type Project Type

1 12% Replace equipment,1 12% Replace equipment,

Expand current businessExpand current business

2 14% Related new products 2 14% Related new products

3 16% Unrelated new products3 16% Unrelated new products

4 24% Research & Development4 24% Research & Development

Practice Problems:Cash Flows & Other Topics

in Capital Budgeting

Practice Problems:Cash Flows & Other Topics

in Capital Budgeting

Project InformationProject Information:: Cost of equipment = Cost of equipment = $400,000$400,000 Shipping & installation will be Shipping & installation will be $20,000$20,000 $25,000$25,000 in net working capital required at setup in net working capital required at setup 3-year project life, 5-year class life3-year project life, 5-year class life Simplified straight line depreciationSimplified straight line depreciation Revenues will increase by Revenues will increase by $220,000$220,000 per year per year Defects costs will fall by Defects costs will fall by $10,000$10,000 per year per year Operating costs will rise by Operating costs will rise by $30,000$30,000 per year per year Salvage value after year 3 is Salvage value after year 3 is $200,000$200,000 Cost of capital = Cost of capital = 12%,12%, marginal tax rate = marginal tax rate = 34%34%

Problem 1a

Problem 1a Initial OutlayInitial Outlay::

(400,000)(400,000) Cost of assetCost of asset

+ (+ ( 20,000 20,000))Shipping & installationShipping & installation

(420,000)(420,000) Depreciable assetDepreciable asset

++ ( 25,000) ( 25,000)Investment in NWCInvestment in NWC

($445,000)($445,000) Net Initial OutlayNet Initial Outlay

220,000220,000 Increased revenueIncreased revenue

10,00010,000 Decreased defectsDecreased defects

(30,000)(30,000) Increased operating costsIncreased operating costs

(84,000) (84,000) Increased depreciation Increased depreciation

116,000116,000 EBTEBT

(39,440)(39,440) Taxes (34%)Taxes (34%)

76,56076,560 EATEAT

84,00084,000 Depreciation reversalDepreciation reversal

160,560 = 160,560 = Annual Cash Flow Annual Cash Flow

For Years 1 - 3: Problem 1aProblem 1a

Terminal Cash FlowTerminal Cash Flow::





Problem 1aProblem 1a

Terminal Cash FlowTerminal Cash Flow: :


amount depreciated.amount depreciated. Book value = $168,000.Book value = $168,000. Capital gain = SV - BV = $32,000Capital gain = SV - BV = $32,000 Tax payment = 32,000 x .34 = Tax payment = 32,000 x .34 = ($10,880)($10,880)



200,000 Salvage value200,000 Salvage value

(10,880) Tax on capital gain(10,880) Tax on capital gain

25,000 25,000 Recapture of NWC Recapture of NWC

214,120 Terminal Cash Flow214,120 Terminal Cash Flow


Problem 1a Solution:

NPV and IRR:NPV and IRR: CF(0) = -445,000CF(0) = -445,000 CF(1 ), (2), = 160,560CF(1 ), (2), = 160,560 CF(3 ) = 160,560 + 214,120 = 374,680CF(3 ) = 160,560 + 214,120 = 374,680 Discount rate = 12%Discount rate = 12% IRR = 22.1%IRR = 22.1% NPV = $93,044. Accept the project!NPV = $93,044. Accept the project!

Project InformationProject Information:: For the same project, suppose we For the same project, suppose we

can only get $100,000 for the old can only get $100,000 for the old equipment after year 3, due to equipment after year 3, due to rapidly changing technology.rapidly changing technology.

Calculate the IRR and NPV for the Calculate the IRR and NPV for the project.project.

Is it still acceptable?Is it still acceptable?

Problem 1b






Problem 1bProblem 1b

Terminal Cash FlowTerminal Cash Flow: :


amount depreciated.amount depreciated. Book value = $168,000.Book value = $168,000. Capital loss = SV - BV = ($68,000)Capital loss = SV - BV = ($68,000) Tax refund = 68,000 x .34 = Tax refund = 68,000 x .34 = $23,120$23,120




23,120 Tax on capital gain23,120 Tax on capital gain




Problem 1b Solution

NPV and IRR: NPV and IRR: CF(0) = -445,000CF(0) = -445,000 CF(1 ), (2), = 160,560CF(1 ), (2), = 160,560 CF(3 ) = 160,560 + 148,120 = 308,680CF(3 ) = 160,560 + 148,120 = 308,680 Discount rate = 12%Discount rate = 12% IRR = 17.3%IRR = 17.3% NPV = $46,067. Accept the project!NPV = $46,067. Accept the project!

Automation ProjectAutomation Project:: Cost of equipment = Cost of equipment = $550,000$550,000 Shipping & installation will be Shipping & installation will be $25,000$25,000 $15,000$15,000 in net working capital required at setup in net working capital required at setup 8-year project life, 5-year class life8-year project life, 5-year class life Simplified straight line depreciationSimplified straight line depreciation Current operating expenses are Current operating expenses are $640,000$640,000 per yr. per yr. New operating expenses will be New operating expenses will be $400,000$400,000 per yr. per yr. Already paid consultant Already paid consultant $25,000$25,000 for analysis. for analysis. Salvage value after year 8 is Salvage value after year 8 is $40,000$40,000 Cost of capital = Cost of capital = 14%,14%, marginal tax rate = marginal tax rate = 34%34%

Problem 2

Problem 2 Initial OutlayInitial Outlay::

(550,000)(550,000) Cost of new machineCost of new machine

+ (+ (25,00025,000)) Shipping & Shipping & installationinstallation

(575,000)(575,000) Depreciable assetDepreciable asset

++ ( 15,000) ( 15,000) NWC investmentNWC investment

(590,000)(590,000) Net Initial OutlayNet Initial Outlay

240,000 240,000 Cost decreaseCost decrease

(115,000) (115,000) Depreciation increaseDepreciation increase

125,000125,000 EBITEBIT

(42,500)(42,500) Taxes (34%)Taxes (34%)

82,50082,500 EATEAT

115,000115,000 Depreciation reversalDepreciation reversal

197,500 = Annual Cash Flow 197,500 = Annual Cash Flow

For Years 1 - 5:Problem 2 Problem 2

240,000 240,000 Cost decreaseCost decrease

( 0) ( 0) Depreciation increaseDepreciation increase

240,000240,000 EBITEBIT

(81,600)(81,600) Taxes (34%)Taxes (34%)

158,400158,400 EATEAT

00 Depreciation reversalDepreciation reversal

158,400 = Annual Cash Flow 158,400 = Annual Cash Flow

For Years 6 - 8:Problem 2 Problem 2



(13,600) Tax on capital gain(13,600) Tax on capital gain



Problem 2 Problem 2

Problem 2 Solution:Problem 2 Solution:

NPV and IRR:NPV and IRR: CF(0) = -590,000CF(0) = -590,000 CF(1 - 5) = 197,500CF(1 - 5) = 197,500 CF(6 - 7) = 158,400CF(6 - 7) = 158,400 CF(10) = 158,400 + 41,400 = 199,800CF(10) = 158,400 + 41,400 = 199,800 Discount rate = 14%Discount rate = 14% IRR = 28.13% NPV = $293,543IRR = 28.13% NPV = $293,543 We would We would acceptaccept the project! the project!

chapter 10. cash flows and other topics in capital budgeting

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