chapter 10 cash flows and other issues in capital budgeting

Chapter 10

Cash Flows and Other Issues in Capital Budgeting

Overview Capital Rationing Cash Flow Estimation Comparing Projects with Unequal

Lives

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 22 33 44 55

Capital Rationing


IRR

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


IRR

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 B year cash flow 0 (30,000) 1 15,000 2 15,000 3 15,000required return = 12%IRR = 23.38%NPV = $6,027PI = 1.20

Project A year cash flow 0 (135,000) 1 60,000 2 60,000 3 60,000required return = 12%IRR = 15.89%NPV = $9,110PI = 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 B year cash flow 0 (46,500) 1 36,500 2 24,000 3 2,400 4 2,400required return = 12%

IRR = 25.51%NPV = $8,455PI = 1.18

Project A year cash flow 0 (48,000) 1 1,200 2 2,400 3 39,000 4 42,000required return = 12%

IRR = 18.10%NPV = $9,436PI = 1.20

Capital Budgeting Steps

1) Evaluate Cash FlowsLook 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


1) Evaluate 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

Cash Flow Estimation Need to estimate incremental after incremental after

taxtax cash flowscash flows that the project is expected to generate.

General form: Cash Flow = Incremental Net Income + Depreciation

Other “special” cash flows Initial costs Extra ending or terminal cash flows at the

end of the project’s expected useful life.

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.

Calculate Project’s NPV and IRR to make this decision.


Imperial Defense Co. Death Star Replacement Project

Six years ago in a galaxy far, far away, the Imperial Defense Co. (IDC) built the original Death Star at a cost of $100 billion. This original project is being depreciated on a simplified straight-line basis over a 10-year period to zero.

IDC is considering building a new and improved Death Star at a cost of $160 billion and would require an initial increase in net working capital of $15 billion over the old Death Star. The old death star can be sold for scrap today for $20 billion.

IDC Death Star Replacement Project Info(cont.) The new Death Star is estimated to have a 4-

year class and expected useful life and will be depreciated using the simplified straight-line method. The new Death Star is expected to increase “protection” revenues by $50 billion in year 1 and $90 billion in years 2 through 4 Rebel defense expenses are expected to increase by $10 billion in year 1, $20 billion in year 2, $30 billion in year 3 and $40 billion in year 4.

The new Death Star has an estimated salvage value of $30 billion at the end of its 4-yr useful life and the original Death Star has a $5 billion salvage value at the end of its useful life.

Death Star Replacement Project Tasks Estimate the cash flows of the

replacement project assuming a marginal tax rate of 40%.

Should the old Death Star be replaced if Imperial Defense Co.’s cost of capital is 10%.

Replacement Project CF Analysis Assume old project is sold today and

replaced be the new one. Receive inflow from the sale of old

project today, but give up any future expected inflows (opportunity costs).

General form: Increase in Net Income + (Depreciation on New - Depreciation on Old) – Increase in Net Working Capital

Step 1: Evaluate Cash Flowsa) Initial Outlay: What is the cash flow at

“time 0?”General Steps (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

After-tax Proceeds from sale of Old Death Star($billion). Tax Rate = 40%

Salvage value = $20 Original Cost and Depreciable asset = $100 Annual Old Depreciation = $100/10 = $10 Book value = depreciable asset - total

amount depreciated. Book value = $100 – 6($10) = $40. Capital gain = SV - BV = $20 - $40 = ($20) Tax refund = $20 x .4 = $8 Total After Tax Proceeds = Salvage Value +

Tax Refund = $20 + $8 = $28

Initial Outlay of Death Star Replacement ($billion)

($160) Cost of New Depreciable Asset

($15) Increase in Net Working Capital After-tax Proceeds from sale of

+ $28replaced asset ($147) Initial Outlay

Step 1: Evaluate Cash Flows b) Annual Cash Flows: What

incremental cash flows occur over the life of the project?

For Each Year, Calculate: Incremental revenue

- Incremental costs- Depreciation increase on project Incremental earnings before taxes- Tax on incremental EBT Incremental earnings after taxes+ Depreciation increase reversal- annual increase in net working capital(none here)

Annual Cash Flow

Death Star Replacement Project Depreciation($billion) Annual Depreciation on Old = $100/10

= $10 Annual Depreciation on New = $160/4

= $40 Annual Increase in Depreciation due

to Replacement = $40 - $10 = $30 for years 1 through 4.

Death Star Replacement Project Annual Free Cash Flows($billion)

Year 1 2 3 4Inc in Rev 50 90 90 90-Inc in Exp 10 20 30 40-Inc in Dep 30 30 30 30EBT 10 40 30 20-Tax(40%) 4 16 12 8EAT 6 24 18 12+Inc in Dep 30 30 30 30Cash Flow 36 54 48 42

Step 1: Evaluate Cash Flows

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

New Salvage value

-/+ Tax effects of new capital gain/loss- Old Salvage value- (-/+) Tax effects of old capital gain/loss+ Recapture of all increase in net working

capital Terminal Cash Flow

Tax Effects of Sale of Asset ($billion) New Salvage value = $30 Book value = depreciable asset - total amount

depreciated. Book value = $160 - $160 = $0. Capital gain = SV - BV = $30 - 0 = $30 New Tax payment = $30 x .4 = $12 Old Salvage Value = Opportunity Cost = $5 Old Book Value = $0 Old Capital Gain = $5. Old Tax Payment = $5 x .4 = $2 Net Old Salvage Value = $5 – $2 = $3

Death Star Replacement Terminal Cash Flows ($billion)

at t=4New Salvage Value $30-Taxes on New SV = .4(30-0) $12-Old Net Salvage Value $3+Recovery of Net Working Capital $15Total Terminal CF (t = 4) $30

Death Star Replacement Project Decision Time ($billion)

Year Cash Flow0 (147) CF01 36 C012 54 C023 48 C034 42 + 30 = 72 C04 NPV at 10% = $15.59 Billion, PI = 1.11 IRR = 14.3%, MIRR = 12.8%

Other Incremental Cash Flow Issues

Sunk costs = exclude. Ask yourself if rejecting the project affects this cost.

Financing costs = EXCLUDE. Already included in WACC.

Opportunity Costs = INCLUDE. Generally revenues forgone from using land or building for another purpose other than the project.

Other Incremental Cash Flow Issues (continued) Externalities = effects of a project on

cash flows in other part of the firm. Can be positive or negative and should be INCLUDED as part of the project’s incremental cash flows.

Cannibalization = INCLUDE. A negative externality, occurs when the introduction of a new product diminishes the sales of existing products.

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 12,000Assume 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, CPT: PMT = -617.24. Machine 2: PV = 1664, N = 6, I = 14, CPT: PMT = -427.91.

Decision Time 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 2 = 428/.14 = $3,057

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

Alternative Decision Technique: Replacement Chain Approach Find the shortest common life between the two

mutually exclusive projects with unequal lives. In our case, 6 years.

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 12,000Assume a required return of 14%.

Replacement Chain Step 2 Repeat each project as often as necessary over

the shortest common life. In our case, we would buy Machine 1 again at end of year 3.

Year Machine 1 Machine 2 0 (45,000) (45,000) 1 20,000 12,000 2 20,000 12,000 3 20,000 – 45,000 = (25,000) 12,000 4 20,000 12,000 5 20,000 12,000 6 20,000 12,000Assume a required return of 14%.

Replacement Chain Step 3 Find the (extended) NPV of each project’s cash

flows over the shortest common life. For Machine 2, we already know its NPV over 6

years is $1664. For Machine 1: ext NPV = -45,000 + 20,000/(1.14)

+ 20,000/(1.14)2 – 25,000/(1.14)3 + 20,000/(1.14)4 + 20,000/(1.14)5 + 20,000/(1.14)6 = $2340

Machine 1 shortcut: one-time NPV = 1443, receive this NPV each time we purchase Machine 1. Ext NPV = 1443 + 1443/(1.14)3 = $2340

Choose Machine 1 like we did with EAA: higher NPV over 6 years.

One replacement chain advantage: can assume project CFs will change when re-purchasing the project in the future.

Karsten Ping Golf: New Project CF Analysis As an analyst at MAD Inc. you have been asked

to work with a client seeking capital budgeting advice, Ping Golf. Ping is considering making a new line of over-sized irons aimed at mid to high handicap golfers (known as mere mortal golfers or most of the people who play golf). These new irons would be called the Ping Kings, and would have a 3-year product life. Ping has already researched and designed these new golf clubs. Ping has given MAD Inc. the following information in order for you to estimate the project’s cash flows.

Ping cash flow information Ping has already spent $500,000 to

research and design the Ping Kings. Ping will need to buy $4,000,000 in new

manufacturing equipment plus $500,000 in shipping and installation costs, which would be depreciated over 5 years using the simplified straight-line depreciation.

At the end of the project’s 3-year life, Ping estimates they can sell this equipment for $800,000.

Ping cash flow information (cont) Ping will also need $700,000 in additional

working capital at the beginning of the project.

Ping estimates they can sell 10,000 sets of Ping Kings in year 1, 15,000 sets in year 2, and 9,000 in year 3. They also estimate they can sell the Ping Kings for $640 a set in years 1 & 2, but they will only be able to sell them for $540 a set in year 3. Variable costs will be $350 a set for all three years and Ping also expects to have $300,000 in fixed manufacturing costs annually for this project.

Ping cash flow information (cont) Ping’s marginal tax rate is 40%. Ping’s required rate of return is

18%. What are the free cash flows for

this Ping King project? Should Ping go ahead with the Ping

Kings?


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

General Steps (Purchase price of the asset)+ (shipping and installation costs) (Depreciable asset)+ (Investment in working capital) Net Initial Outlay

Initial Outlay for Ping Kings Cost of Equipment

$4,000,000 Shipping&Installation 500,000 Depreciable Asset

$4,500,000 Increase in WC 700,000 Initial Outlay $5,200,000

Step 1: Evaluate Cash Flows b) Annual Cash Flows: What

incremental cash flows occur over the life of the project?

For Each Year, Calculate: Incremental revenue

- Incremental costs- Depreciation increase on project Incremental earnings before taxes- Tax on incremental EBT Incremental earnings after taxes+ Depreciation increase reversal- annual increase in net working capital(none here)

Annual Cash Flow

Ping King Annual Depreciation Depreciable Asset = $4,500,000 5-year simplified straight-line

depreciation. Annual Depreciation = $4,500,000/5

= $900,000 Book Value at the end of year 3:$4,500,000 – 3($900,000) =

$1,800,000

Annual CFs for Ping KingsYear 1 2 3Unit Sales 10,000 15,000 9,000$/Unit $640 $640 $540VC/Unit $350 $350 $350Revenue($000) 6,4009,600 4,860-Variable Costs 3,5005,250 3,150-Fixed Costs 300 300 300-Depreciation 900 900 900EBIT 1,700 3,150 510Tax(40%) 680 1,260 204Earnings After Tax 1,0201,890 306+Depreciation 900 900 900Cash Flow 1,920 2,790 1,206


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

New Salvage value

-/+ Tax effects of new capital gain/loss+ Recapture of all increase in net working

capital Terminal Cash Flow

Ping King Termination CF Salvage Value(SV)

$800,000 Taxes on Salvage Value

-T(SV-BV) = -.4(800k-1800k) 400,000 Recovery of Working Capital

700,000 Termination CF at end of 3$1,900,000

Coronate Ping Kings?

Year Cash Flow0 ($5,200,000)1 $1,740,0002 $2,610,0003 1,206k+1,900k =$3,106,000

NPV at 18% = $321,261 IRR = 21.5%

What about this? Ping’s current line of irons is the Ping

i3, which have an estimated product life of 1 year remaining. Should Ping go ahead with the Ping Kings project if they thought next year’s Ping i3 sales and variable costs would decrease by $1,000,000 and $500,000 respectively on a BEFORE-TAX basis.

This would affect the year 1 CF: cannibalization!

Year Orig 1 ChangeNew 1

Revenue($000) 6,400 (1,000) 5,400-Variable Costs 3,500 (500) 3,000-Fixed Costs 300 300-Depreciation 900 900EBIT 1,700 (500) 1,200Tax(40%) 680 (200) 480Earnings After Tax 1,020 (300) 720+Depreciation 900 900Cash Flow 1,920 (300) 1,620

New CFs with cannibalization

Year Cash Flow0 ($5,200,000)1 $1,620,0002 $2,790,0003 1,206k+1,900k =$3,106,000

NPV at 18% = $67,023 IRR = 18.7%

chapter 10 cash flows and other issues in capital budgeting

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