CHAPTER 13
CASHFLOWS IN CAPITAL BUDGETING
CASH FLOW ESTIMATION
IN VALUING A CAPITAL PROJECT WE NEED TO KNOW THE AFTER-TAX
CASH FLOWS ASSOCIATED WITH THE PROJECT.
THESE ARE USUALLY
FORECASTS BASED ON REVENUE AND COST PROJECTIONS.
TO BE MEANINGFUL, CASH FLOWS
1. MUST BE AFTER TAX
2. MUST BE INCREMENTAL
3. MUST NOT INCLUDE SUNK COSTS
4. MUST INCLUDE OPPORTUNITY COSTS
THAT IS, THEY MUST BE RELEVANT, INCREMENTAL AFTER-TAX CASH
FLOWS.
IT IS EASY TO CLASSIFY CASH FLOWS AS:
1. INITIAL INVESTMENT
2. NET OPERATING CASH FLOWS
3. TERMINATION OR END-OF-PROJECT CASH FLOWS
INITIAL INVESTMENT (I0 0R CF0)
ALL NORMAL PROJECTS REQUIRE INITIAL INVESTMENT IN FIXED
ASSETS AND WORKING CAPITAL.
IT IS COMPUTED AS FOLLOWS:
INITIAL INVESTMENT I0 =
PRICE OF ASSET
+ MODIFICATION COSTS
+ SHIPPING & INSTALLATION COSTS
+ LEGAL COSTS ETC.
+ INCREASE IN NET WORKING CAPITAL
OF THESE COST, INCREASE IN NET WORKING CAPITAL IS NOT
DEPRECIABLE.
IT IS ASSUMED TO BE RECOVERED, FULLY OR
PARTIALLY, DEPENDING ON THE NATURE OF WORKING CAPITAL, AT
THE END OF THE PROJECT.
NET OPERATING CASH FLOWS (NOCF)
ONCE A PROJECT IS IMPLEMENTED, IT IS EXPECTED TO BRING IN
CASH FLOWS AFTER TAX.
FLOWS.
THESE ARE THE NET OPERATING CASH
THEY WILL OCCUR IN EACH OF THE PRODUCTIVE YEARS OF
THE PROJECT.
∆NOCFt = [∆Rt - ∆Ct)*(1-T) + (∆DEPRECIATION
WHICH IS THE SAME AS
∆NET OPERATING INCOMEt + ∆DEPRECIATIONt
t
* T)
TERMINATION CASH FLOWS
(TCF)
THESE CASH FLOWS OCCUR IN THE LAST YEAR (PERIOD) OF A
PROJECT WHEN IT IS TERMINATED OR ENDED.
THESE CASH FLOWS
WOULD ARISE FROM THE AFTER-TAX SALVAGE VALUE OF THE
PROJECT’S ASSETS, OTHER AFTER-TAX CASH FLOWS ASSOCIATED
WITH A PROJECT’S TERMINATION (E.G. CLEAN UP COSTS) AND ANY
RECOVERY OF INVESTMENT IN NET WORKING CAPITAL MADE AT TIME
0.
THESE CASH FLOWS CAN BE REPRESENTED ON A TIME LINE AS
FOLLOWS:
TCFn
NOCF1
NOCF2
NOCF3…..........NOCFt...........NOCFn
__________________________________________________________
0
1
2
3 ........... t ............ n
-CF0
ONCE THE CASH FLOWS HAVE BEEN ESTIMATED, THE PROJECT CAN BE
EVALUATED USING ANY OF THE TECHNIQUES STUDIED EARLIER.
INDEPENDENT PROJECT (PROBLEM 13-5)
a. The net cost is $89,000:
Price
Modification
Change in NWC
($70,000)
(15,000)
(4,000)
($89,000)
b. The operating cash flows follow:
After-tax savings
Depreciation shield
Net cash flow
Year 1
Year 2
Year 3
$15,000
11,220
$26,220
$15,000
15,300
$30,300
$15,000
5,100
$20,100
Notes:
1. The after-tax cost savings is $25,000(1 – T) =
$25,000(0.6)= $15,000.
2. The depreciation expense in each year is the
depreciable basis, $85,000, times the MACRS
allowance percentage of 0.33, 0.45, and 0.15 for
Years 1, 2 and 3, respectively.
Depreciation
expense in Years 1, 2, and 3 is $28,050, $38,250,
and
$12,750.
The
depreciation
shield
is
calculated as the tax rate (40%) times the
depreciation expense in each year.
c. The additional end-of-project cash flow is $24,380:
Salvage value
Tax on SV*
Return of NWC
$30,000
(9,620)
4,000
$24,380
*Tax on SV = ($30,000 - $5,950)(0.4) = $9,620.
Note that the remaining BV in Year 4 = $85,000(0.07)
= $5,950.
d. The project has an NPV of -$6,705.
not be accepted.
Year
0
1
2
3
Net Cash Flow
($89,000)
26,220
30,300
44,480
Thus, it should
PV @ 10%
($89,000)
23,836
25,041
33,418
NPV = ($ 6,705)
Alternatively, with a financial calculator, input
the following:
CF0 = -89000, CF1 = 26220, CF2 =
30300, CF3 = 44480, and I = 10 to solve for NPV = $6,703.83.
REPLACEMENT ANALYSIS
THE DURST EQUIPMENT COMPANY PURCHASED A MACHINE 5 YEARS AGO
AT A COST OF $100,000.
IT HAD AN EXPECTED LIFE OF 10 YEARS
AT THE TIME OF PURCHASE AND AN EXPECTED SALVAGE VALUE OF
$10,000 AT THE END OF THE 10 YEARS.
IT IS BEING
DEPRECIATED BY THE STRAIGHT LINE METHOD TOWARD A SALVAGE
VALUE OF $10,000, OR BY $9,000 PER YEAR.
A NEW MACHINE CAN BE PURCHASED FOR $150,000, INCLUDING
INSTALLATION COSTS.
OVER ITS 5-YEAR LIFE, IT WILL REDUCE
CASH OPERATING EXPENSES BY $50,000 PER YEAR.
EXPECTED TO CHANGE.
SALES ARE NOT
AT THE END OF ITS USEFUL LIFE, THE
MACHINE IS ESTIMATED TO BE WORTHLESS.
MACRS DEPRECIATION
WILL BE USED, AND IT WILL BE DEPRECIATED OVER A 3-YEAR
RECOVERY PERIOD RATHER THAN ITS 5-YEAR ECONOMIC LIFE.
THE OLD MACHINE CAN BE SOLD TODAY FOR $65,000.
FIRM’S TAX RATE IS 34 PERCENT.
THE
THE APPROPRIATE DISCOUNT
RATE IS 15 PERCENT.
a. IF THE NEW MACHINE IS PURCHASED, WHAT IS THE AMOUNT OF
THE INITIAL CASH FLOW AT YEAR 0?
b. WHAT INCREMENTAL OPERATION CASH FLOWS WILL OCCUR AT
THE END OF YEARS 1 THOUGH 5 AS A RESULT OF REPLACING
THE OLD MACHINE?
c. WHAT INCREMENTAL NONOPERATING CASH FLOW WILL OCCUR AT
THE END OF YEAR 5 IF THE NEW MACHINE IS PURCHASED?
d. WHAT IS THE NPV OF THIS PROJECT? SHOULD THE FIRM
REPLACE THE OLD MACHINE?
SOLUTION TO REPLACEMENT ANALYSIS PROBLEM DISCUSSED IN
CLASS
THE OLD MACHINE WAS ACQUIRED 5 YEARS AGO FOR $100,000, HAD AN
ESTIMATED SALVAGE VALUE OF $10,000 AND AN ESTIMATED USEFUL
LIFE OF 10 YEARS. IT IS DEPRECIATED ON A STRAIGHT LINE BASIS TO
EXPECTED SALVAGE VALUE of $10,000
OLD DEPRECIATION = (100000-10000)/10 = $9000/YEAR
BOOK VALUE NOW = 100000-(5*9000) = $ 55000
OLD MACHINE CAN BE CURRENTLY SOLD FOR $65000
GAIN = $65000 – 55000 = $10000
TAX ON GAIN = 10000* .34 = $3400
INCREMENTAL AFTER-TAX INITIAL INVESTMENT, I.E.,
(INCREMENTAL AFTER-TAX CASH FLOW AT TIME 0) :
PRICE NEW MACHINE
SALE OF OLD MACHINE (BEFORE-TAX)
TAX ON SALE OF OLD MACHINE
INCREMENTAL AFTER-TAX CASH FLOW
AT TIME 0
= ($150,000)
= $ 65,000
= ($3,400)
= ($ 88,400)
TO DETERMINE THE INCREMENTAL AFTER-TAX NET OPERATING CASH
FLOWS DUE TO REPLACEMENT, WE NEED TO DETERMINE THE
INCREMENTAL DEPRECIATION AND TAX SHELTER.
YEAR MACRS
DEPRECIABLE DEPRECIATION DEPRECIATION
CHANGE
RECOVERY BASIS ON NEW ON NEW
ON OLD
%
MACHINE
MACHINE
MACHINE
1
33
$150,000
$49,500
$9,000
$40,500
2
45
150,000
67,500
9,000
58,500
3
15
150,000
22,500
9,000
13,500
4
7
150,000
10,500
9,000
1,500
9,000
(9,000)
5
INCREMENTAL AFTER-TAX NET OPERATING CASH FLOWS
Δ NOCFt = (Δ Rt – Δ Ct ) * (1-TAX RATE) + Δ DEPRECIATIONt * TAX RATE
REPLACEMENT WILL HAVE NO IMPACT ON SALES & REVENUE
OPERATING COSTS WILL BE REDUCED BY $50,000 BEFORE TAX EACH
YEAR
YEAR (Δ Rt – Δ Ct )*( 1-TAX RATE) +(Δ DEPRECIATION *TAX RATE) = Δ
NOCFt
1
2
3
4
5
50,000 * .66 = 33,000
50,000 * .66 = 33,000
50,000 * .66 = 33,000
50,000 * .66 = 33,000
50,000 * .66 = 33,000
+
+
+
+
+
40,500*.34 = 13,770
58,500*.34 = 19,890
13,500 * .34 = 4,590
1,500 *.34 = 510
(9,000) * .34 = (3,060)
= 46,770
= 52,890
= 37,590
= 33,510
= 29,940
INCREMENTAL AFTER-TAX TERMINATIONCASH FLOWS
SALVAGE VALUE ON NEW MACHINE NET OF TAX
SALVAGE VALUE ON OLD MACHINE NET OF TAX
(OPPORTUNITY COST)
INCREMENTAL AFTER-TAX TERMINATION CASH FLOW
=0
= (10,000)
= (10,000)
SUMMARY OF INCREMENTAL AFTER-TAX CASH FLOWS
YEAR
AFTER-TAX CASH FLOW
0
1
2
3
4
5
(88,400)
46,770
52,890
37,590
33,510
29,940 + (10,000) = 19,940
NPV @ 15% = $46,051
SINCE INCREMENTAL NPV > 0, THE FIRM SHOULD REPLACE THE OLD
MACHINE
RISK IN CAPITAL BUDGETING
THE CONCEPTS OF RISK AND RETURN DEVELOPED IN CHAPTERS 2 & 3
CAN BE APPLIED IN THE CONTEXT OF CAPITAL BUDGETING.
THE
DIFFERENT TYPES OF RISK IN CAPITAL BUDGETING CAN BE
DESCRIBED AS FOLLOWS:
STAND ALONE RISK
THIS IS THE RISK OF A PROJECT IF HELD
ISOLATION.
THIS IS SIMILAR TO TOTAL
RISK AND, THEREFORE, INCLUDES A
PROJECT’S SYSTEMATIC AND UNSYSTEMATIC
RISK.
CORPORATE RISK
THIS IS THE RISK A PROJECT CONTRIBUTES
TO THE FIRM AND WOULD DEPEND VERY MUCH
ON THE CORRELATION BETWEEN THE PROJECT
AND THE FIRM’S PORTFOLIO OF OTHER
PROJECTS.
OBVIOUSLY, IT WILL INCLUDE
THE PROJECT’S SYSTEMATIC RISK AND SOME
UNSYSTEMATIC RISK DEPENDING ON
PROJECT’S CORRELATION WITH THE FIRM.
MARKET RISK
THIS IS THE RISK OF A PROJECT IN THE
CONTEXT OF A LARGE, WELL-DIVERSIFIED
PORTFOLIO (MARKET PORTFOLIO).
THIS IS
THE SYSTEMATIC RISK OF THE PROJECT AND
CAN BE MEASURED BY THE PROJECT’S BETA.
PURE PLAY METHOD
PURE PLAY METHOD IS USED TO ESTIMATE A PROJECT’S BETA.
THE
FOLLOWING MAJOR STEPS ARE INVOLVED:
1. IDENTIFY ONE OR MORE PURE PLAYS (COMPANY OR DIVISION)
IN A LINE OF BUSINESS SAME AS THE PROPOSED PROJECT.
2. ESTIMATE THE BETA, MOST LIKELY, THE LEVERAGED BETA,
CAPITAL STRUCTURE AND MARGINAL TAX RATE OF THE PURE
PLAY (AVERAGE BETA, CAPITAL STRUCTURE AND MARGINAL TAX
RATE, IF MORE THAN ONE PURE PLAY).
3. APPLY HAMADA MODEL TO BETA TO ESTIMATE THE UNLEVERED
(BUSINESS RISK) BETA:
ΒU = βL/[1+{(1-T)* D/S}]
WHERE ΒU, βL, D/S, AND T ARE, RESPECTIVELY, THE
UNLEVERED BETA, LEVERED BETA, CAPITAL STRUCTURE, AND
MARGINAL TAX RATE OF THE PURE PLAY ESTIMATED IN STEP 2.
4. ESTIMATE THE MARGINAL TAX RATE AND CAPITAL STRUCTURE
OF THE FIRM EVALUATING THE PROJECT.
5. FIND THE PROJECT’S LEVERED BETA FOR THIS FIRM BY
APPLYING HAMADA MODEL:
βL = βU
*
[1+{(1-T)* D/S}]
WHERE βU , D/S, AND T ARE, RESPECTIVELY, THE
UNLEVERED BETA IN STEP 3, AND CAPITAL STRUCTURE AND
MARGINAL TAX RATE IN STEP 4.
6. APPLY CAPM TO FIND THE
COST OF EQUITY FINANCING, KS,
FOR THE PROJECT:
KS = KRF + βL * [KM – KRF]
WHERE KRF AND KS ARE, RESPECTIVELY, THE RISK-FREE AND
MARKET PORTFOLIO RETURNS AND βL IS FROM STEP 5.
7. ESTIMATE THE BEFORE-TAX COST OF DEBT Kd FOR THE
PROJECT.
8. ESTIMATE THE PROJECT’S WEIGHTED AVERAGE COST OF
CAPITAL (WACC)
WACC = wd * Kd * (1-T) + ws * KS
WHERE wd AND ws ARE THE PROPORTIONS OF DEBT AND EQUITY
IN THE PROJECT’S MARGINAL CAPITAL STRUCTURE, T, THE
PROJECT’S MARGINAL TAX RATE (FROM STEP 4)
9. USE WACC IN STEP 8 TO EVALUATE THE PROJECT USING NPV
OR IRR.
PURE PLAY APPROACH
Williams Company has a target capital structure of 40
percent debt and 60 percent equity, and it will apply
this structure to the project under consideration.
The
firm’s beta, which is an average of five estimates by
financial service firms, is 1.5.
Williams is evaluating
a new project which is totally unrelated to its existing
line of business.
However, it has identified two proxy
firms exclusively engaged in this business line.
They,
on average have a beta of 1.2 and a debt ratio of 50
percent.
Williams’s new project has an estimated IRR of
13.5 percent.
The risk-free rate is 10 percent, and the
market risk premium is 5 percent.
marginal tax rate of 34 percent.
All three firms have a
Williams’s before-tax
cost of debt is 14 percent.
a. What is the project’s unlevered beta, bu?
b. What is the beta of the project if undertaken by
Williams?
c. Should the firm accept the project?
PURE PLAY METHOD PROBLEM SOLUTION
a.
ΒU = βL/[1+{(1-T)* D/S}]
=
=
=
=
b.
c.
d.
1.2/ [1+ {(1-.34)* (.5/.5)}]
1.2/[1+ {(.66*1)}]
1.2/1.66
0.72
βL = βU * [1+{(1-T)* D/S}]
= 0.72* [1+{(1-.34)*(.4/.6)}]
= 0.72* [1+ (.66*.67)]
= 0.72 * 1.44
= 1.04
kSL = kRF + βL * [kM - kRF]
= 10 + (1.04 * 5)
= 15.2%
WACC = [wd * kd * (1-T)] + [ws * kSL]
= [0.4*14*.66]+ [0.6*15.2]
= 12.81%
SINCE IRR=13.5% > WACC=12.81%, ACCEPT THE
PROJECT
WHAT CAN GO WRONG? WILLIAMS COMPANY’S BETA=1.5 IF
THIS BETA WERE TO BE USED (ERRONEOUSLY) AS THE
PROJECT’S BETA, kSL = kRF + βL * [kM - kRF]
= 10 + (1.54 * 5)
= 17.5%
WACC = [wd * kd * (1-T)] + [ws * kSL]
= [0.4*14*.66]+ [0.6*17.5]
= 14.2%
SINCE IRR=13.5% < WACC=14.2%,THE PROJECT WILL BE
REJECTED!