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**Unformatted text preview: **Capital Budgeting:
Cash Flow Estimation
Chapters 8 & 9 Main Items of Concern Incremental cash outflows/inflows Tax effects Terminal cash flows Sunk costs
Opportunity costs
Externalities Inflation Opportunities to abandon, expand, delay 2 Initial Cash Outflows Expenditures on fixed assets Change in working capital (= current assets - current
liabilities) 3 Includes shipping, installation, and modification costs Increase in WC is a cash outflow; decrease in WC is an
inflow Incremental Cash Flows Consider only incremental cash flows, i.e., cash flows
resulting from the project Incremental approach is equivalent to comparing two
variations of the firm: (i) with the new project and (ii)
without the project 4 Ignore costs incurred in the past and costs that would have
been incurred regardless of the project acceptance If difference between these variations is positive, then
accept the new project Example: Samurai Tailoring
Samurai Tailoring has $C in cash and expects after-tax cash
flows of $200 in each of the next 2 years. The cost of capital is
5%
Samurai is considering buying a new stitching machine for
$C, which will increase production speed and, therefore,
annual cash flows to $300
The company should buy the machine if the value of the firm
with the machine is greater than the value without the
machine: 300 − 200 300 − 200
+
−C > 0
2
1 + 0.05
(1 + 0.05)
If the NPV of incremental cash flows is positive, undertake
the project 5 Ignore Sunk Costs Costs incurred prior to the project (even if related to
the project) should not be allocated to the project If a future cost will be incurred regardless of the
project acceptance, that cost is irrelevant and should
be ignored 6 Opportunity Costs Opportunity cost of any
chosen act is the value of
the best forsaken
alternative
The use of assets that do not
have a direct price, i.e.,
machines that the firm
already owns, have an
opportunity cost equal to
the profit foregone on the
best alternative production
opportunity Example In year 1, land was purchased for $1M In year 2, the company is considering turning the land into a parking lot $1M paid for land is a sunk cost and is, therefore, irrelevant Suppose, the company has just received an offer of $1.5M for the land $1.5M becomes an opportunity cost. It should enter capital budgeting calculations as a 7 Example: Opportunity Cost Assume that a machine, currently, has an after-tax market value of
$60,000 Using the machine in production, will generate a stream of cash flows
with a present value of $55,000 We should sell the machine. NPV = $60,000 - $55,000 = $5,000. 8 Externalities
Externalities are costs borne
or benefits captured by other
projects of the same firm erosion/cannibalization
synergy Example
An auto firm sells only economy cars. The firm is considering adding midsize cars to its product line. This addition may cause their economy car sales to drop – a negative externality. The possible drop in economy car sales must appear as a negative cash flow in the evaluation of the midsize car project. 9 Treat Inflation Consistently Inflation affects both cash flows and the opportunity cost of capital Nominal cash flows should be discounted at nominal rates. Real
cash flows should be discounted at real rates 1 + nominal interest rate
1 + inflation rate
nominal cash flow
real cash flow =
1 + inflation rate 1 + real interest rate = 10 Example: Inflation Economists at Microsoft predict that the sales of the
Windows operating system will continue in perpetuity They forecast $100M in year-end after-tax cash flows ( in
today’s dollars) each year starting one year from now Inflation is forecasted at 4% The nominal cost of capital, k = 10% What is the PV of the after-tax cash flows? 11 Answer: $1,733.3M Financing Charges Exclude costs of capital (cost of debt, equity, etc.) from cash
flow estimates: they are already included in WACC Example: Project acceptance requires that firm takes out a
loan that will require annual payments of $1M to the bank.
The project cash flows will not reflect -$1M 12 Taxation: Capital Cost Allowance (CCA) CCA or depreciation is a deduction from taxable
earnings. In other words, it’s a tax shield The CCA tax shield is [T×CCA], where T is the tax rate CCA itself is not a cash flow. Nevertheless, claiming
CCA creates a cash flow 13 Example: CCA Effect on Cash Flows
Revenues
Less: $100
Expenses $100 $50 $50 CCA
Taxable Income $20
$50 $30 $25 $15 Net Income $25 $15 Add: CCA +$0 +$20 Operating Cash Flows $25 $35 Taxes (at 50%) 14 Tax-deductibility of CCA increases operating cash flows by: T*CCA =
0.5*20 = 10 CCA in Canada Depreciable assets are grouped into ~ 50 asset classes 15 The number of classes, their composition, and respective CCA rates are often
changed by the federal budget 16 CCA Pools Example: All of firm’s vans and trucks are grouped together under that
firm’s Class 10 pool, under CCA rate d = 30% CCAt= CCA claimed at the end of year t UCCt = undepreciated capital cost of a specific asset at the end of year
t, after claiming CCA for year t UCCPt = undepreciated capital cost of a pool of assets at the end of
year t, after claiming CCA for year t Usually, firms have more than one asset in a pool: UCC ≠ UCCP 17 UCCP will be provided for the purposes of our calculations Half-year rule For most CCA classes, only one half of net
additions to a pool of assets may be depreciated in
the first year 18 CCA Example:
Declining balance and the half-year rule
An asset worth $10M is introduced into a CCA pool. The
asset has a depreciation rate d = 5%. Assume that UCC =
UCCP In year 1, the CCA deduction is At the beginning of year 2, the UCC is CCA2 = d × UCC2_beg = 0.05 × 9.75M = $0.4875M At the beginning of year 3, the UCC is 19 UCC2_beg = 10M - 0.25M = $9.75M In year 2, the CCA deduction is CCA1 = d ×10M/2 = 0.05 × 5M = $0.25M UCC3_beg = 9.75 - 0.4875 = $9.2625M CCA Example: CCA calculations Pierre's Boat Co purchases five rowboats for a total of
$2,000. The rowboats fall under Class 7 with a CCA rate of
15%. Fill in the CCA table below. Taxes are 36.5%
Yr. CCA 1 2 3 20 UCCP start UCCP end Tax savings $86.10 CCA Formulas
UCCt _ beg 1 C,
2
=
t −2
C 1 − d 2 (1 − d ) , ( ) for t = 1
for t > 1 and
CCAt = d (UCCt _ beg ), where
UCCt _ beg − UCC in year t before claiming CCA for that year
CCAt − CCA claimed in year t
C − original capital cost of assets
d − CCA rate
21 CCA Example 2: CCA calculations In 2005, Alba Ltd. bought a machine for $100,000. The machine
qualifies for a 25% CCA. Alba spent $15,000 on installation and
modification of the machine. The machine is the only asset in its class.
The tax rate is 36.5%. Calculate the CCA and the tax savings for the
project’s 5th year.
Yr. UCCP start 2005 2006 2007 2008 2009 $3,873.67 22 CCA UCCP end Tax savings Net Acquisition Amount (NAA) rule Applies only in the year of the physical purchase of an asset
Applies if one asset enters the pool in year t, and another asset leaves
the pool in year t
NAA added to a class = capital costs of a new asset minus min {salvage
value, original cost} of the asset sold 23 if NAA is positive, the half-year rule applies
if NAA is negative, the CCA pool is reduced by the NAA. The half-year rule does
not apply CCA Example 3: CCA Calculations In year 1, Pacific Charter purchases a plane for $60,000 In year 2, Pacific purchases another plane for $100,000 At the beginning of year 3, Pacific sells plane 1 for
$40,000 What is the UCCP at the end of year 3 if the CCA rate is
25%? 24 Answer: $65, 156 CCA Example 4: CCA Calculations Same problem statement as that in Example 3, but Pacific
decides to sell the first plane for $50,000 at the beginning of
year 2 What is the CCA for year 3? Answer: $20,781.25 25 CCA Example 5: CCA calculations A firm purchases an asset (d = 25%) for $25,000 and places
it in Class 9 pool. Installation costs are 10% of the purchase
price Additionally, the firm sells an asset from the same pool for
$11,000. Five years ago, the purchase price of this asset was
$36,000 What is the NAA added to the pool? 26 Answer: $8,250 CCA: Capital Gains rule Capital gain is incurred, if a firm sells an asset for a salvage
value, SV, that exceeds the asset’s original cost, C In this case, the firm must pay capital gains tax on one half of
the capital gain i.e., SV>C T× 0.5× (SV-C) In addition, if UCCP > SV > C 27 The firm must reduce the UCCP by C, not by SV CCA Example: Capital Gains Several years ago, the company bought an asset for
$1M. Today, the company is selling the asset for
$1.2M. T = 40%. What happens to UCCP and tax
liabilities? Answer: 28 Tax liability = $0.04M
Reduce UCCP by $1M CCA: Recapture of Depreciation If a company sells an asset for SV, where C > SV >
UCCP, some of depreciation the firm claimed in the
past years is recaptured by the government Tax liability of T×(SV-UCCP) is created
Asset sold may or may not be the last one in the pool Example: A firm with T=40% sells a machine for $1M.
Prior to the sale, the UCCP of the pool is $0.7M. What
is the firm’s tax liability due to recapture? 29 Answer: $0.12M CCA: Terminating a Pool If a pool is terminated, and salvage value of the last
asset is less than UCCP Terminal loss = UCCP-SV
Claim a tax deduction T×(UCCP-SV) Example: A firm with T=40% sells a machine for
$40K. UCCP prior to sale is $50K. Machine is the last
asset in the pool What is the amount of tax deduction a firm may claim What if the machine is not the last asset in the pool? 30 Answer: $4,000 Answer: No terminal loss and no tax shield. UCCP is reduced
by $40K Combined Capital Gains and Depreciation
Recapture Occurs if SV > C > UCCP Capital gain tax = T×0.5×(SV-C)
Tax liability due to recapture = T×(C-UCCP) Example: Some time ago, a firm purchased an asset for
$50,000. At the beginning of the current year, UCCP =
$40,000. The firm sells the asset for $55,000. T = 0.3.
What is the total tax liability that results from the sale? 31 Answer: $3,750 PV of CCA Tax Shields (PVCCATS)
Assumption: the pool is not terminated at the end of the
project PVCCATS = PV of tax shields forever minus PV of tax
shields lost after an asset leaves the pool C × d × T 1 + 0.5k 1 min{SVn , C} × d × T PVCCATS = 1 + k − (1 + k ) n k+d k + d where,
T − tax rate
d − CCA rate
C − asset capital cost
k − cost of capital
SV − asset salvage value
n − life of the project
32 Terminal Year Cash Flows Salvage value, SV Recovery of working capital Tax effects 33 General Rule: The only effect of selling an asset is a reduction of
UCCP by SV. This reduces ability to claim CCA in future years
Exceptions: capital gains, depreciation recapture, terminal loss Tax loss carrybacks and carryforwards Companies can “carry back” losses for 3 years
Companies can “carry forward” losses for 20 years
Example: Fixar Corp. has outstanding tax loss
carryforwards worth $10M. If Fixar earns $6M per
year in EBT during the next 5 years, when will it first
pay taxes? What will be Fixar’s tax bill in that year?
T=40%. 34 Answer: in year 2, Fixar will pay $0.8M to CRA Summary: Cash Flow Estimation Conventional structure of project cash flows: Net cost of the assets purchased Annual after-tax net benefits or costs Tax shields generated by depreciable assets Tax shields lost due to the salvage of assets Salvage value of the assets Changes in NWC Compute the present values of all cash flows accruing to the
project at discount rate k (WACC) Two methods Spreadsheet method for PB, DPB, IIRR, and IPI Formula method for NPV, IRR, and PI
35 Spreadsheet Method Example: Project XY Project XY requires an investment of $1,000 and
generates annual revenues of $600 and annual
expenses of $300. The CCA rate is 0.25. All cash flows
occur at year end. The project will last for 5 years, at
which time the machine will be useless. The firm’s tax
rate is 36%. What is the project’s payback period? If
the firm’s cost of capital is 10%, what is the project’s
discounted payback period? Answer: 36 PB = 5 years
DPB: does not pay back when k is accounted for Example: Project XY (contd.)
Year
Capital Investment 0
1000 Project Cash Flow
P V Cash Flows
NPV 37 -$1,000.00
-$26.71 4 5 600
300
300
108 600
300
300
108 600
300
300
108 600
300
300
108 192 192 192 192 500
125
45
-1000 3 192 UCC
Depreciation
Tax Shield 2 600
300
300
108 Cash flows:
Revenues
Expenses
Cash flows from operations
Taxes
AT Cash flows from
operations 1 875.00
218.75
78.75 656.25
164.06
59.06 492.19
123.05
44.30 369.14
92.29
33.22 237.00 270.75 251.06 236.30 225.22 $215.45 $223.76 $188.63 $161.39 $139.85 Formula Method
5 steps: 1.
2.
3.
4.
5. 38 I
PVATOCF
PVCCATS
PVSV
PVNWC 1. I I – initial (time 0) investment Cost of equipment, facilities, and land*
All other costs related to the investment (e.g.,
equipment shipping, installation, and modification cost) *Land does not depreciate
39 2. PVATOCF OCF1, OCF2, ..., OCFn – before-tax year-end cash flows
n Variable CFs : PVATOCF = ∑
t =1 OCFt (1 − T )
(1 + k ) t ( ) OCF (1 − T ) 1 − (1 + k )
Annuity : PVATOCF =
k
n
1
1 1+ g Growing annuity : PVATOCF = OCF (1 − T ) − , k − g k − g 1+ k where g - growth rate 40 −n 3. PVCCATS Assumption: the pool is not terminated upon project
termination C × d × T 1 + 0.5k 1 min{SVn , C} × d × T PVCCATS = 1 + k − (1 + k ) n k+d k + d 41 4. PVSV No capital gains
SVn
PVSV =
n
(1 + k ) Capital gains
SVn − 0.5T ( SVn − C )
PVSV =
(1 + k ) n 42 5. PVNWC NWC = CA – CL Increase in NWC is a cash outflow. ΔNWCn
PVNWC = ΔNWC0 +
n
(1 + k ) Example: Inventories increase by $1M at t0 and
decrease by $0.3M at tn 43 CF0 = -1M; CFn= 0.3M NPV of an Expansion Project Assume that expansion entails a purchase of new equipment
and an increase in NWC. Also, assume no capital gain on SV. NPV = − I + PVATOCF + PVCCATS + PVSV + PVNWC
n = −I + ∑
t =1 + 44 OCFt (1 − T ) C × d × T 1 + 0.5k min{SVn , C} × d × T 1 + − t (1 + k ) n (1 + k )
k +d k + d 1 + k SVn
∆NWCn
− ∆NWC0 +
(1 + k ) n
(1 + k ) n Project XY: NPV, PI, and IRR (also see spreadsheet) NPV = -I + PVATOCF + PVCCATS 45 I = 1000
PVATOCF = 727.83
PVCCATS = 245.45
NPV = -$26.72
IRR = 9% using Excel
PI = 0.973 Example: Oddflew Co. Expansion Oddflew Co. is considering a $10M investment. Its tax rate is 40%,
and k = 12.33%. Eighty percent of the $10 million investment will be
used to purchase equipment with d = 30%. The remainder of the
initial investment represents the required increase in inventories and
accounts receivable. Inventories and accounts receivable will not be
liquidated upon project termination. The machinery is expected to
have SV of $2.5M at the end of 6 years. The project is expected to
produce pre-tax operating income of $1.5M at the end of the first year,
and this amount is projected to increase by 10% a year over the
remaining 5 years of the project. Should Oddflew undertake this
project? 46 Example Solution: Oddflew (also see spreadsheet) I = 8M
PVATOCF = 4.56477M
PVCCATS = 1.7906M
PVSV = 1.244416M
PVNWC= -2M
NPV = -$2.4M
PI = (-2.4/10) + 1 = 0.76
IRR = 4.14% 47 Example: Smith Industries Expansion Smith Industries is purchasing a fleet of trucks for
$105,000 and will pay $5,000 to ship the trucks to its main
location. The trucks will have d = 30%, a useful life of 3
years, and a SV of $10,000 at the time of sale. Incremental
cash inflows and outflows will be $80,000 and $20,000 per
year, respectively. T = 40% and k = 14%. Should the fleet
be purchased? 48 Example Solution: Smith (also see spreadsheet) I = 110K
PVATOCF= 83.5788K
PVCCATS = 26.31706K
PVSV = 6.749715K
NPV = 6.6455K
IRR = 17%
PI = 1.06 49 NPV of a Replacement Project
NPV = ΔI + ΔPVATOCF + ΔPVCCATS + ΔPVSV + ΔPVNWC
n = ΔI + ∑
t =1 + ΔOCFt (1 − T ) ΔC × d × T 1 + 0.5k ΔSVn × d × T 1 + − (1 + k ) n (1 + k ) t
k + d 1 + k k +d ΔSVn
∆NWCn
− ∆NWC0 +
, where
n
n
(1 + k )
(1 + k ) ΔI 0 = − I new0 + SVold 0
ΔSVn = SVnew n − SVold n 50 Example: Jones Industries Replacement Jones Industries owns a machine that was purchased 3 years
ago for $250,000. The machine belongs to the CCA class 8,
with a CCA rate of 20%. The machine will be operational
for 5 more years, at which time its resale value will be $7,500,
but it could be sold now for $20,000. If Jones buys a new
machine now, it will reduce annual expenses from $255,000
to $100,000. The new machine would require a $10,000
increase in inventory. This increase in inventory will be
liquidated at the end of 5 years. The new machine costs
$500,000 and belongs to CCA class 8. It has a life of 5 years,
and its net resale value then will be $25,000. T = 40% and k
= 15%. Should Jones Industries replace their old machine? 51 Example Solution: Jones (also see spreadsheet) ∆I = -480K
∆PVATOCF = 311.7504K
∆PVCCATS = 100.5703K
∆PVNWC = -5.02833K
∆PVSV = 8.700593
NPV = -64.0069K
IRR = 10%
PI = 0.869 52 Example: POS Bid A large retailer has asked you to submit a bid to supply POS
credit checking systems. Twenty systems are required per year
for 3 years. To manufacture the POS systems, you will need to
invest in new equipment that costs $1M, on which you will claim
CCA at a rate of 25%. No salvage value and changes in NWC
are expected. Assume that there are other assets in the pool to
which new equipment will be allocated. Labour and material
cost per one POS system equals $0.1M. The tax rate is 44%.
What selling price should you bid per a POS system, if you
require a 16% return on you investment? 53 Answer: at least $129,825 per system Example: Shmapple Industries Shmapple Industries owns Machine A that was purchased 3 years ago for $550,000. At the same time,
Shmapple spent $30,000 to purchase a piece of land Z for purposes unrelated to usage of Machine A
Machine A belongs to the CCA Class 8, with a CCA rate of 20%
Machine A may stay operational for 12 more years, at which time its resale value will be $75,000, but
it could be sold now for $130,000
If Shmapple buys a new machine now (Machine B), its annual before-tax revenues will decrease by
$20,000, and annual before-tax expenses will decline by $80,000
Machine B would trigger a $10,000 decrease in inventories and a $4,000 decrease in accounts
receivable. Seventy percent (70%) of the decrease in accounts receivable will be reversed at the end of
12 years. The change in inventories will be fully reversed at the end of 12 years. The sale of Machine
A will result in a $12,000 increase in accounts payable, whether sold today or 12 years from now
Machine B costs $400,000 and belongs to the CCA Class 8. Shipping and installation expenses will
amount to 15% of the cost of Machine B
The Piece of Land Z where Machine B will be housed may be alternatively sold, today, to Rogers
Tavern for a pre-tax amount of $40,000
Machine B has projected life of 12 years, and its net resale value at the end of 12 years will be $0. Pool
8 will not be closed at the end of the 12th year
T = 30% and k = 10%
Shmapple Industries will not pay taxes in years 3, 4, and 5 due to a special agreement with the CRA.
The CCA tax shields unrealized during these three years will be lost
Should Smith Industries replace Machine A with Machine B? 54 Example Solution: Shmapple ∆I = -368,500
∆PVATOCF = 323,170
∆PVCCATS = 43,613
∆PVNWC = 18,098
∆PVSV = -23,897
NPV = -7,516
No, do not replace 55 Valuing Projects with Unequal Lives Suppose a firm is deciding between 2 mutually exclusive projects
with different projected lives E.g., choose 1 out of 2 machines to upgrade production: Machine L
has a useful life of 5 years, and Machine S has a useful life of 3 years 56 If comparison is between one Machine L versus one
Machine S, calculate NPV as before
But if comparison is between two policies: always use
Machine L vs. always use Machine S, one must use either
Replacement Chain or Equivalent Annual NPV methods Replacement Chain: replicate projects over common time
horizon, then calculate the NPV of the chain
EANPV: convert NPV to an annuity Unequal Lives: EANPV Replace the uneven stream of cash flows over a project’s lifetime
with a simple annuity as follows:
EANPV = NPV 1 − (1 + k ) −t k When comparing two projects, the project with a higher EANPV will
correspond to the better policy 57 Example: Unequal lives A firm needs to decide between 2 mutually exclusive policies:
always use L vs. always use S. The after-tax CFs are:
Year 0 1 2 3 4 5 Policy L 52,000 15,000 15,000 15,000 15,000 15,000 Policy S $40,000 18,000 18,000 18,000 Which policy should the firm adopt if cost of capital is 9%? Answer: EANPVL= 1.631K; EANPVS= 2.198K. Choose Policy
S.
58 EANPV vs. Replacement Chain Method EANPV does not allow for the impact of inflation or changes
in technology If there are changes in project cash flows in the future
(first machine L differs from the second machine L), one
must use Replacement Chain method instead of EANPV For the Replacement Chain method, repeat one or both
projects until both policy chains run for the same length of
time, and then compare the NPV of the two chains. Common time horizon is the lowest common multiple 59 Example: Replacement chain We, actually, do not need Replacement Chain method
here, since cash flows do not change in this example.
We will use Replacement Chain for purely illustrative
purposes Compare chain of 3 L’s with chain of 5 S’s NPV of chain of 3 L’s = $13.148K
NPV of chain of 5 S’s = $17.713K 60 Hence, Policy S is better Example: Replacement Chain Method A firm, with k = 10%, is submitting a bid to produce widgets for 4
years. Two production options are available Machine A has an after-tax installation cost of $50,000 and is expected to
generate after-tax returns of $20,000 per year for 4 years. After 4 years,
the machine has no salvage value
Machine B only has a 2-year lifetime and an after-tax installation cost of
$30,000. For the first 2 years, it is expected to produce after-tax returns
of $20,000 a year. When it is replaced after the first 2 years, the machine
should generate after-tax returns of $22,000 a year for 2 years because of
expertise gained in the first 2 years Should the firm submit a bid for the contract? If so, should it plan to
use machine A or machine B? Answers: Yes, should bid. NPVA= $13,397; NPV2Bs= 4,710.7+6,761.8 =
$11,473. Thus, A is a better option 61 Real options Expansion Option: If after a trial period, the project turns out to
be very profitable, the firm may choose to expand the project Abandonment Option: If after a trial period, the project turns
out to be unattractive, the firm may choose to end the project
prematurely Option to Delay: Investment now may be profitable, but
investment next year may be even more profitable 62 Example: Option to abandon You are studying the feasibility of launching a new video game The project is expected to generate annual after-tax cash flows of
$0.75M for the next 10 years The discount rate is 12% The initial investment is $6M If the project is abandoned at the end of year 1, you will recoup
$5M of the initial investment What is the NPV ignoring the option to abandon? Answer: -$1.76M 63 Example: Option to abandon (contd.) Assume that, at the end of year 1, you will be able to determine if the
project is a success or a failure and then exercise the abandonment
option If successful, the project will generate annual after-tax cash flows
of $1.5M for the remaining 9 years If failed, annual after-tax cash flow will be $0 Success and failure are equally probable What is the NPV taking account of the option to abandon? Answer: $0.47M Thus, the option to abandon turns a Reject decision into an Accept
decision
64 Example: Abandoning a mine You own a copper mine. The price of copper is currently $1.5 per
pound. The mine produces 1 million pounds of copper per year and
costs $2 million per year to operate. It contains enough copper to
operate for 100 years
Shutting the mine down is expected to cost $5 million in any year.
Shutdown option is available only once a year, at the end of the year.
Let’s ignore inflation
Reopening the mine once it has been shut down is not an option
The price of copper is equally likely to go up or down by 25% each year
for the next two years and then will stay at that level forever. You sell
copper at the end of the year at end-of-year prices
Your cost of capital is 15%
Should you abandon the mine or should you keep operating? 65 Answer: The mine will lose money on average, with E(PVCF) ≈ -$2.82M.
Nevertheless, shutting the mine down would cost even more, i.e., $5M. Thus,
you should keep operating ...

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