Chapter 10: Cash Flows and Other Topics in Capital Budgeting

Chapter 10: Cash Flows and Other Topics in

Capital Budgeting

2002, Prentice Hall, Inc.

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

• example:

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

• Will the machine be profitable?

• Will our firm earn a high rate of return on the investment?

• The relevant project information follows:

• The cost of the new machine is $127,000.

• Installation will cost $20,000.

• $4,000 in net working capital will be needed at the time of installation.

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

• Simplified straight line depreciation is used.

• Class life is 5 years, and the firm is planning to keep the project for 5 years.

• Salvage value at the end of year 5 will be $50,000.

• 14% cost of capital; 34% marginal tax rate.

Capital Budgeting Steps

1) Evaluate Cash Flows

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

• Initial outlay

• Differential Cash Flows over the life of the project (also referred to as annual cash flows).

• Terminal Cash Flows



0 1 2 3 4 5 n6 . . .



0 1 2 3 4 5 n6 . . .

Initialoutlay



0 1 2 3 4 5 n6 . . .

Annual Cash Flows

Initialoutlay



0 1 2 3 4 5 n6 . . .

TerminalCash flow

Annual Cash Flows

Initialoutlay

2) Evaluate the risk of the project.

• We’ll get to this in the next chapter.

• For now, we’ll assume that the risk of the project is the same as the risk of the overall firm.

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


3) Accept or Reject the Project.


Step 1: Evaluate Cash Flows

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

(Purchase price of the asset)

+ (shipping and installation costs)

(Depreciable asset)

+ (Investment in working capital)

+ After-tax proceeds from sale of old asset

Net Initial Outlay



(127,000)

+ (shipping and installation costs)

(Depreciable asset)



Net Initial Outlay



(127,000)

+ ( 20,000)

(Depreciable asset)



Net Initial Outlay



(127,000)

+ ( 20,000)

(147,000)



Net Initial Outlay



(127,000)

+ ( 20,000)

(147,000)

+ ( 4,000)


Net Initial Outlay



(127,000)

+ ( 20,000)

(147,000)

+ ( 4,000)

+ 0

Net Initial Outlay



(127,000) Purchase price of asset

+ ( 20,000) shipping and installation

(147,000) depreciable asset

+ ( 4,000) net working capital

+ 0 proceeds from sale of old asset

($151,000) net initial outlay



(127,000) Purchase price of asset

+ ( 20,000) shipping and installation

(147,000) depreciable asset

+ ( 4,000) net working capital

+ 0 proceeds from sale of old asset

($151,000) net initial outlay


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

Incremental revenue

- Incremental costs

- Depreciation on project

Incremental earnings before taxes

- Tax on incremental EBT

Incremental earnings after taxes

+ Depreciation reversal

Annual Cash Flow

For Each Year, Calculate:

Incremental revenue

- Incremental costs






Annual Cash Flow

For Years 1 - 5:

85,000

- Incremental costs






Annual Cash Flow

For Years 1 - 5:

85,000

(29,750)






Annual Cash Flow

For Years 1 - 5:

85,000

(29,750)

(29,400)





Annual Cash Flow

For Years 1 - 5:

85,000

(29,750)

(29,400)

25,850




Annual Cash Flow

For Years 1 - 5:

85,000

(29,750)

(29,400)

25,850

(8,789)



Annual Cash Flow

For Years 1 - 5:

85,000

(29,750)

(29,400)

25,850

(8,789)

17,061


Annual Cash Flow

For Years 1 - 5:

85,000

(29,750)

(29,400)

25,850

(8,789)

17,061

29,400

Annual Cash Flow

For Years 1 - 5:

85,000 Revenue

(29,750) Costs

(29,400) Depreciation

25,850 EBT

(8,789) Taxes

17,061 EAT

29,400 Depreciation reversal

46,461 = Annual Cash Flow

For Years 1 - 5:


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

Salvage value

+/- Tax effects of capital gain/loss

+ Recapture of net working capital

Terminal Cash Flow



50,000 Salvage value



Terminal Cash Flow

Tax Effects of Sale of Asset:

• Salvage value = $50,000

• Book value = depreciable asset - total amount depreciated.

• Book value = $147,000 - $147,000

= $0.

• Capital gain = SV - BV

= 50,000 - 0 = $50,000

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




(17,000) Tax on capital gain

Recapture of NWC

Terminal Cash Flow





4,000 Recapture of NWC

Terminal Cash Flow






37,000 Terminal Cash Flow

Project NPV:

• CF(0) = -151,000

• CF(1 - 4) = 46,461

• CF(5) = 46,461 + 37,000 = 83,461

• Discount rate = 14%

• NPV = $27,721

• We would accept the project.

Capital Rationing

• Suppose that you have evaluated 5 capital investment projects for your company.

• Suppose that the VP of Finance has given you a limited capital budget.

• How do you decide which projects to select?

Capital Rationing

• You could rank the projects by IRR:

Capital Rationing

IRR

5%

10%

15%

20%

25%

$

11

• You could rank the projects by IRR:

Capital Rationing

• You could rank the projects by IRR:IRR

5%

10%

15%

20%

25%

$

11 22

Capital Rationing


5%

10%

15%

20%

25%

$

11 22 33

Capital Rationing


5%

10%

15%

20%

25%

$

11 22 33 44

Capital Rationing


5%

10%

15%

20%

25%

$

11 22 33 44 55

Capital Rationing


5%

10%

15%

20%

25%

$

11 22 33 44 55

$X

Our budget is limitedso we accept only projects 1, 2, and 3.

Capital Rationing


5%

10%

15%

20%

25%

$

11 22 33

$X

Our budget is limitedso we accept only projects 1, 2, and 3.

Capital Rationing

• Ranking projects by IRR is not always the best way to deal with a limited capital budget.

• It’s better to pick the largest NPVs.

• Let’s try ranking projects by NPV.

Problems with Project Ranking

1) Mutually exclusive projects of unequal size (the size disparity problem)

• The NPV decision may not agree with IRR or PI.

• Solution: select the project with the largest NPV.

Size Disparity example

Project A

year cash flow

0 (135,000)

1 60,000

2 60,000

3 60,000

required return = 12%

IRR = 15.89%

NPV = $9,110

PI = 1.07


Project B

year cash flow

0 (30,000)

1 15,000

2 15,000

3 15,000


IRR = 23.38%

NPV = $6,027

PI = 1.20

Project A

year cash flow

0 (135,000)

1 60,000

2 60,000

3 60,000


IRR = 15.89%

NPV = $9,110

PI = 1.07


Project B

year cash flow

0 (30,000)

1 15,000

2 15,000

3 15,000


IRR = 23.38%

NPV = $6,027

PI = 1.20

Project A

year cash flow

0 (135,000)

1 60,000

2 60,000

3 60,000


IRR = 15.89%

NPV = $9,110

PI = 1.07

Problems with Project Ranking

2) The time disparity problem with mutually exclusive projects.

• NPV and PI assume cash flows are reinvested at the required rate of return for the project.

• IRR assumes cash flows are reinvested at the IRR.

• The NPV or PI decision may not agree with the IRR.

• Solution: select the largest NPV.

Time Disparity example

Project A year cash flow

0 (48,000)

1 1,200

2 2,400

3 39,000

4 42,000


IRR = 18.10%

NPV = $9,436

PI = 1.20


Project B year cash flow

0 (46,500)

1 36,500

2 24,000

3 2,400

4 2,400


IRR = 25.51%

NPV = $8,455

PI = 1.18


0 (48,000)

1 1,200

2 2,400

3 39,000

4 42,000


IRR = 18.10%

NPV = $9,436

PI = 1.20


Project B year cash flow

0 (46,500)

1 36,500

2 24,000

3 2,400

4 2,400


IRR = 25.51%

NPV = $8,455

PI = 1.18


0 (48,000)

1 1,200

2 2,400

3 39,000

4 42,000


IRR = 18.10%

NPV = $9,436

PI = 1.20

Mutually Exclusive Investments with Unequal Lives

• Suppose our firm is planning to expand and we have to select 1 of 2 machines. • They differ in terms of economic life and

capacity. • How do we decide which machine to

select?

• The after-tax cash flows are:

Year Machine 1 Machine 2

0 (45,000) (45,000)

1 20,000 12,000

2 20,000 12,000

3 20,000 12,000

4 12,000

5 12,000

6 12,000

• Assume a required return of 14%.

Step 1: Calculate NPV

• NPV1 = $1,433

• NPV2 = $1,664

• So, does this mean #2 is better?

• No! The two NPVs can’t be compared!

Step 2: Equivalent Annual Annuity (EAA) method

• If we assume that each project will be replaced an infinite number of times in the future, we can convert each NPV to an annuity.

• The projects’ EAAs can be compared to determine which is the best project!

• EAA: Simply annuitize the NPV over the project’s life.

EAA with your calculator:

• Simply “spread the NPV over the life of the project”

• Machine 1: PV = 1433, N = 3, I = 14,

solve: PMT = -617.24.

• Machine 2: PV = 1664, N = 6, I = 14,

solve: PMT = -427.91.

• EAA1 = $617

• EAA2 = $428

• This tells us that:

• NPV1 = annuity of $617 per year.

• NPV2 = annuity of $428 per year.

• So, we’ve reduced a problem with different time horizons to a couple of annuities.

• Decision Rule: Select the highest EAA. We would choose machine #1.

Step 3: Convert back to NPV


• Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return.



• NPV 1 = 617/.14 = $4,407



• NPV 1 = 617/.14 = $4,407

• NPV 2 = 428/.14 = $3,057



• NPV 1 = 617/.14 = $4,407

• NPV 2 = 428/.14 = $3,057

• This doesn’t change the answer, of course; it just converts EAA to a NPV that can be compared.

Practice Problems:Cash Flows & Other Topics

in Capital Budgeting

Project Information:• Cost of equipment = $400,000

• Shipping & installation will be $20,000

• $25,000 in net working capital required at setup

• 3-year project life, 5-year class life

• Simplified straight line depreciation

• Revenues will increase by $220,000 per year

• Defects costs will fall by $10,000 per year

• Operating costs will rise by $30,000 per year

• Salvage value after year 3 is $200,000

• Cost of capital = 12%, marginal tax rate = 34%

Problem 1a

Problem 1a• Initial Outlay:

(400,000)Cost of asset

+ ( 20,000)Shipping & installation

(420,000)Depreciable asset

+ ( 25,000)Investment in NWC

($445,000) Net Initial Outlay

220,000 Increased revenue

10,000 Decreased defects

(30,000) Increased operating costs

(84,000) Increased depreciation

116,000 EBT

(39,440) Taxes (34%)

76,560 EAT



For Years 1 - 3: Problem 1aProblem 1a

• Terminal Cash Flow:

Salvage value



Terminal Cash Flow

Problem 1aProblem 1a




• Book value = $168,000.

• Capital gain = SV - BV = $32,000

• Tax payment = 32,000 x .34 = ($10,880)








Problem 1a Solution:

• NPV and IRR:

• CF(0) = -445,000

• CF(1 ), (2), = 160,560

• CF(3 ) = 160,560 + 214,120 = 374,680


• IRR = 22.1%

• NPV = $93,044. Accept the project!

Project Information:

• For the same project, suppose we can only get $100,000 for the old equipment after year 3, due to rapidly changing technology.

• Calculate the IRR and NPV for the project.

• Is it still acceptable?

Problem 1b


Salvage value



Terminal Cash Flow

Problem 1bProblem 1b




• Book value = $168,000.

• Capital loss = SV - BV = ($68,000)

• Tax refund = 68,000 x .34 = $23,120




23,120 Tax on capital gain




Problem 1b Solution

• NPV and IRR:

• CF(0) = -445,000

• CF(1 ), (2), = 160,560

• CF(3 ) = 160,560 + 148,120 = 308,680


• IRR = 17.3%

• NPV = $46,067. Accept the project!

Automation Project:

• Cost of equipment = $550,000

• Shipping & installation will be $25,000

• $15,000 in net working capital required at setup



• Current operating expenses are $640,000 per yr.

• New operating expenses will be $400,000 per yr.

• Already paid consultant $25,000 for analysis.

• Salvage value after year 8 is $40,000


Problem 2

Problem 2 • Initial Outlay:

(550,000) Cost of new machine

+ (25,000) Shipping & installation

(575,000) Depreciable asset

+ ( 15,000) NWC investment

(590,000) Net Initial Outlay

240,000 Cost decrease

(115,000) Depreciation increase

125,000 EBIT

(42,500) Taxes (34%)

82,500 EAT



For Years 1 - 5: Problem 2

240,000 Cost decrease

( 0) Depreciation increase

240,000 EBIT

(81,600) Taxes (34%)

158,400 EAT

0 Depreciation reversal


For Years 6 - 8:Problem 2






Problem 2

Problem 2 Solution:

• NPV and IRR:

• CF(0) = -590,000

• CF(1 - 5) = 197,500

• CF(6 - 7) = 158,400

• CF(10) = 158,400 + 41,400 = 199,800


• IRR = 28.13% NPV = $293,543

• We would accept the project!

Replacement Project:

Old Asset (5 years old):

• Cost of equipment = $1,125,000



• Current salvage value is $400,000


Problem 3

Replacement Project:• New Asset:• Cost of equipment = $1,750,000• Shipping & installation will be $56,000• $68,000 investment in net working capital.• 5-year project life, 5-year class life• Simplified straight line depreciation• Will increase sales by $285,000 per year • Operating expenses will fall by $100,000 per year• Already paid $15,000 for training program• Salvage value after year 5 is $500,000• Cost of capital = 14%, marginal tax rate = 34%

Problem 3

Problem 3: Sell the Old Asset:



• Book value = $1,125,000 - $562,500

= $562,500.

• Capital gain = SV - BV

= 400,000 - 562,500 = ($162,500)

• Tax refund = 162,500 x .35 = $56,875

Problem 3• Initial Outlay:

(1,750,000) Cost of new machine

+ ( 56,000) Shipping & installation

(1,806,000) Depreciable asset

+ ( 68,000) NWC investment

+ 456,875 After-tax proceeds (sold old machine)

(1,417,125) Net Initial Outlay

385,000 Increased sales & cost savings

(248,700) Extra depreciation

136,300 EBT

(47,705) Taxes (35%)

88,595 EAT


337,295 = Differential Cash Flow

For Years 1 - 5:Problem 3






Problem 3

Problem 3 Solution:

• NPV and IRR: • CF(0) = -1,417,125• CF(1 - 4) = 337,295• CF(5) = 337,295 + 393,000 = 730,295• Discount rate = 14%• NPV = (55,052.07)• IRR = 12.55%• We would not accept the project!

Documents

Chapter 10: Cash Flows and Other Topics in Capital Budgeting