Capital Budgeting

1
Capital Budgeting

• General criteria for investment analysis
• It should focus on cash flows rather than
  accounting earnings
• It should place higher weight on earlier cash
  flows
• It should penalize the expected cash flows from
  riskier projects more heavily

2
Capital budgeting. Certainty case

• Discounted cash flow techniques
• Net Present Value (NPV) criterion
• Internal Rate of Return (IRR) criterion
• Nondiscounted cash flow techniques
• Payback Period (can be discounted)
• Accounting Rate of Return
• How to deal with
• Mutually exclusive projects
• Capital rationing
• Projects with unequal lives
• Note. Definition Projects A and B are
  independent if they dont affect each others
  cash flows

3
NPV criterion

• Under no resource constraints, no mutual
  exclusive projects accept the project if NPV gt 0
  and reject if NPV lt 0.
• When two projects are mutually exclusive and both
  have NPV gt 0, accept the project with the higher
  NPV.
• Under resource constraints choose the combination
  of projects such that NPV is max, s.t. to the
  constraints.
• R is the opportunity cost of funds or required
  return
• Value Additivity If C is independent of A and B,
  thenA gt B ? A C gt B C
• If X and Y are independent NPV(XY)
  NPV(X)NPV(Y) satisfies value additivity

4
Calculating A Projects NPV- An Example

• Quickie Enterprises Microprocessor Plant
• Cash Flows in million
• Year Cash Flow PVIF_at_12 Present Value
• 0 -400 1.0000 -400.00
• 1 100 0.8929 89.29
• 2 110 0.7972 87.69
• 3 120 0.7118 85.41
• 4 130 0.6355 82.62
• 5 140 0.5674 79.44
• NPV 24.45

5
Internal Rate of Return (IRR) Criterion
IRR solves

• Accept the project if IRR gt R, otherwise reject
  it
• Among two mutually exclusive project choose the
  one with the higher IRR
• Isnt it equivalent to the NPV criterion? For a
  decision whether to accept or not a classical
  single project yes. But in general NO.

6

• Problems with IRR
• Problems with ranking mutually exclusive projects
• scale effect
• timing effect
• Does not satisfy value additivity principle
• Multiple IRR when some CF are negative
• Sometimes no IRR exists

7
Example of IRR problems

• NPV(1) gt NPV(3), but IRR(1) lt IRR(3)
• IRR(1) gt IRR(2), but IRR(13) lt IRR(23)

8
Is IRR ever helpful?

• Can be as a relative measure of efficiency
• But if NPV is properly used then NPV is the
  besti.e. max NPV (m), s.t. I ? I, m?M,where M
  is the set of all possible projects

9
Payback period

• How long does it take for a project to recover or
  pay back its initial investment?
• If recovery time lt threshold accept, otherwise
  reject.
• Discounted Payback Period

10

• Disadvantages of DPP
• Ignores the cash flows after the payback period
  (what if they are negative?)
• Arbitrary standard for setting the period
• Advantages of DPP
• Simple
• Measure of project liquidity
• Measure (rough) of project risk

11
Other criteria

• Accounting (average) Rate of Return
• ARR Average Net Income / Average Investment
  (book value)
• Simple BUT ignores time value of money and is
  based on accounting income rather than cash flow.
• Moreover, what is the target rate?
• Profitability IndexPI PV of cash flows
  subsequent to initial investment / I0
• For independent projects compare PI with 1
  equivalent to NPV
• Dont use for mutually excusive projects (scale
  effect)

12
Some guidelines for estimating project cash flows

• Use only incremental cash flows (i.e. the changes
  in the firms cash flows that occur as a
  consequence of the project)
• Note pay attention to side effects
• Ignore sunk costs
• Dont ignore opportunity costs
• Dont forget working capital requirements
• Dont forget abandonment costs or terminal values
• Be careful with inflation

13
The Baldwin Company An Example

• Costs of test marketing (already spent)
  250,000.
• Current market value of proposed factory site
  (which we own) 150,000.
• Cost of bowling ball machine 100,000
  (depreciated according to ACRS 5-year life).
• Production (in units) by year during 5-year life
  of the machine 5,000, 8,000, 12,000, 10,000,
  6,000.
• Price during first year is 20 price increases
  2 per year thereafter.
• Production costs during first year are 10 per
  unit and increase 10 per year thereafter.
• Working Capital initially 10,000, changes with
  sales, falls to 0 at the end of year 5.

14
The Worksheet for Cash Flows of the Baldwin
Company
( thousands) (All cash flows occur at the end
of the year.)

• Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
• Investments
• (1) Bowling ball machine 100.00 21.76
• (2) Accumulated 20.00 52.00 71.20 82.72 94.24
  depreciation
• (3)Adjusted basis of 80.00 48.00 28.80 17.28
  5.76 machine after
  depreciation (end of year)
• (4) Opportunity cost 150.00 150.00(warehouse
  )
• (5) Net working capital 10.00
  10.00 16.32 24.97 21.22 0 (end of year)
• (6) Change in net 10.00 6.32 8.65 3.75
  21.22 working capital
• (7) Total cash flow of 260.00 6.32
  8.65 3.75 192.98 investment(1) (4)
  (6)

The ending market value of the capital investment
is 30,000. The capital gain is 24,240 (
30,000 5,760). The capital gains tax due is
0.34 ? (30,000 5,760). The after-tax salvage
value is 30,000 0.34 ? (30,000 5,760)
21,760
15
Investments

• Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
• (1) Bowling ball machine 100.00 21.76
• (2) Accumulated 20.00 52.00 71.20 82.72 94.24
  depreciation
• (3)Adjusted basis of 80.00 48.00 28.80 17.28
  5.76machine after depreciation (end of
  year)
• (4) Opportunity cost 150.00 150.00(warehouse
  )
• (5) Net working capital 10.00
  10.00 16.32 24.97 21.22 0 (end of year)
• (6) Change in net 10.00 6.32 8.65 3.75
  21.22 working capital
• (7) Total cash flow of 260.00 6.32
  8.65 3.75 192.98 investment(1) (4)
  (6)

At the end of the project we can sell the
warehouse.
16
Income

• Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
• Income
• (8) Sales Revenues 100.00 163.00 249.72 212.20
  129.90

Recall that production (in units) by year during
5-year life of the machine is given by (5,000,
8,000, 12,000, 10,000, 6,000). Price during first
year is 20 and increases 2 per year
thereafter. Sales revenue in year 3
12,00020(1.02)2 249,720.
17
Income

• Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
• Income
• (8) Sales Revenues 100.00 163.00 249.72 212.20
  129.90
• (9) Operating costs 50.00 88.00 145.20
  133.10 87.84
• (10) Depreciation 20.00 32.00 19.20
  11.52 11.52

Depreciation is calculated using the Accelerated
Cost Recovery System (shown at right) Our cost
basis is 100,000 Depreciation charge in year 4
100,000(.1152) 11,520.
Year ACRS 1 20.00 2 32.00 3 19.20
4 11.52 5 11.52 6 5.76 Total 100.00
18
Income and taxes

• Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
• Income
• (8) Sales Revenues 100.00 163.00 249.72 212.20
  129.90
• (9) Operating costs 50.00 88.00 145.20
  133.10 87.84
• (10) Depreciation 20.00 32.00 19.20 11.52
  11.52
• (11) Income before taxes 30.00 43.20 85.32
  67.58 30.54 (8) (9) - (10)
• (12) Tax at 34 percent 10.20 14.69 29.01
  22.98 10.38
• (13) Net Income 19.80 28.51 56.31 44.60
  20.16

19
Incremental After Tax Cash Flows
20
Accounting for inflation

• Simply discount cash flows correctly
• If real values are used, use real R.
• If nominal values use nominal R.
• 1 Rn (1 Rr)(1 i)
• Rr ? Rn I
• CFrt CFnt/(1 i)t

21
Investments with unequal lives

• There are times when application of the NPV rule
  can lead to the wrong decision. Consider a
  factory which must have an air cleaner.
• There are two choices
• The Cadillac cleaner costs 4,000 today, has
  annual operating costs of 100 and lasts for 10
  years.
• The cheaper cleaner costs 1,000 today, has
  annual operating costs of 500 and lasts for 5
  years.
• Which one should we choose?

22

• At first glance, the cheap cleaner has the lower
  NPV (r 10)

This overlooks the fact that the Cadillac
cleaner lasts twice as long. When we incorporate
that, the Cadillac cleaner is actually cheaper.
23

• The Cadillac cleaner time line of cash flows

The cheaper cleaner time line of cash flows
over ten years
24

• How to take into account the difference in lives?
• Matching cycles
• Lives x and y years
• Find the least common multiple of x and y LCM
  z. Compare the sequences of each project over z
  years (NPV)
• Replacement chain repeat the projects forever,
  find the PV of that perpetuity.
• Equivalent annual value (equivalent annual cost)

25
Equivalent annual value (equivalent annual cost)
method

• NPV ANPV ART , where ART is the annuity of
  1 for T years discounted at R
• Choose the one with the highest ANPV
• If the machines (projects) differ only by costs
  its called EAC methodNPV of Cost EAC ART
  
• Choose the one with the lowest EAC
• Matching cycles, replacement chain and EAV give
  the same answer

26
Example Replacement Problem.

• Consider a dentists office he needs an
  autoclave to sterilize his instruments. He has an
  old one that is in use, but the maintenance costs
  are rising and so is considering replacing this
  indispensable piece of equipment.
• New Autoclave
• Cost 3,000 today,
• Maintenance cost 20 per year
• Resale value after 6 years 1,200
• NPV of new autoclave (at r 10)

EAC of new autoclave -553.29
27

• Existing Autoclave
• Year 0 1 2 3 4 5
• Maintenance 0 200 275 325 450 500
• Resale 900 850 775 700 600 500
• Total Annual Cost

435
478
340
620
660
Total Cost for year 1 (900 1.10 850) 200
340
Total Cost for year 2 (850 1.10 775) 275
435
Total Cost for year 3 (775 1.10 700) 325
478
Total Cost for year 4 (700 1.10 600) 450
620
Total Cost for year 5 (600 1.10 500) 500
660
Note that the total cost of keeping an autoclave
for the first year includes the 200 maintenance
cost as well as the opportunity cost of the
foregone future value of the 900 we didnt get
from selling it in year 0 less the 850 we have
if we still own it at year 1.
28

• New Autoclave
• EAC of new autoclave -553.29
• Existing Autoclave
• Year 0 1 2 3 4 5
• Maintenance 0 200 275 325 450 500
• Resale 900 850 775 700 600 500
• Total Annual Cost

435
478
620
660
340

• We should keep the old autoclave until its
  cheaper to buy a new one.
• Replace the autoclave after year 3 at that point
  the new one will cost 553.29 for the next years
  autoclaving and the old one will cost 620 for
  one more year.