Cashflows in Capital Budgeting

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. THESE ARE THE NET OPERATING CASH FLOWS. THEY WILL OCCUR IN EACH OF THE PRODUCTIVE YEARS OF THE PROJECT.

∆NOCFt = [∆Rt - ∆Ct)*(1-T) + (∆DEPRECIATION t * T)

WHICH IS THE SAME AS

∆NET OPERATING INCOMEt + ∆DEPRECIATIONt

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 ($70,000)

Modification (15,000)

Change in NWC (4,000)

($89,000)

b.The operating cash flows follow:

Year 1 Year 2 Year 3

After-tax savings $15,000 $15,000 $15,000

Depreciation shield 11,220 15,300 5,100

Net cash flow $26,220 $30,300 $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 $30,000

Tax on SV* (9,620)

Return of NWC 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.

1. The project has an NPV of -$6,705. Thus, it should

not be accepted.

Year Net Cash Flow PV @ 10%

0 ($89,000) ($89,000)

1 26,220 23,836

2 30,300 25,041

3 44,480 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. SALES ARE NOT EXPECTED TO CHANGE. 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. THE FIRM’S TAX RATE IS 34 PERCENT. THE APPROPRIATE DISCOUNT RATE IS 15 PERCENT.

1. IF THE NEW MACHINE IS PURCHASED, WHAT IS THE AMOUNT OF THE INITIAL CASH FLOW AT YEAR 0?
2. WHAT INCREMENTAL OPERATION CASH FLOWS WILL OCCUR AT THE END OF YEARS 1 THOUGH 5 AS A RESULT OF REPLACING THE OLD MACHINE?
3. WHAT INCREMENTAL NONOPERATING CASH FLOW WILL OCCUR AT THE END OF YEAR 5 IF THE NEW MACHINE IS PURCHASED?
4. 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 = ($150,000)

SALE OF OLD MACHINE (BEFORE-TAX) = $ 65,000

TAX ON SALE OF OLD MACHINE = ($3,400)

INCREMENTAL AFTER-TAX CASH FLOW

AT TIME 0 = ($ 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

5 9,000 (9,000)

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 50,000 * .66 = 33,000 + 40,500*.34 = 13,770 = 46,770

2 50,000 * .66 = 33,000 + 58,500*.34 = 19,890 = 52,890

3 50,000 * .66 = 33,000 + 13,500 * .34 = 4,590 = 37,590

4 50,000 * .66 = 33,000 + 1,500 *.34 = 510 = 33,510

5 50,000 * .66 = 33,000 + (9,000) * .34 = (3,060) = 29,940

INCREMENTAL AFTER-TAX TERMINATIONCASH FLOWS

SALVAGE VALUE ON NEW MACHINE NET OF TAX = 0

SALVAGE VALUE ON OLD MACHINE NET OF TAX

(OPPORTUNITY COST) = (10,000)

INCREMENTAL AFTER-TAX TERMINATION CASH FLOW = (10,000)

SUMMARY OF INCREMENTAL AFTER-TAX CASH FLOWS

YEAR AFTER-TAX CASH FLOW

0 (88,400)

1 46,770

2 52,890

3 37,590

4 33,510

5 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 RISKTHIS 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.

1. ESTIMATE THE MARGINAL TAX RATE AND CAPITAL STRUCTURE OF THE FIRM EVALUATING THE PROJECT.
2. 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.

1. 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.

1. ESTIMATE THE BEFORE-TAX COST OF DEBT Kd FOR THE PROJECT.
2. 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)

1. 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. All three firms have a marginal tax rate of 34 percent. Williams’s before-tax cost of debt is 14 percent.

1. What is the project’s unlevered beta, bu?
2. What is the beta of the project if undertaken by Williams?
3. Should the firm accept the project?

PURE PLAY METHOD PROBLEM SOLUTION

a. ΒU = βL/[1+{(1-T)* D/S}]

= 1.2/ [1+ {(1-.34)* (.5/.5)}]

= 1.2/[1+ {(.66*1)}]

= 1.2/1.66

= 0.72

b. 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

c. kSL = kRF + βL * [kM - kRF]

= 10 + (1.04 * 5)

= 15.2%

1. 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!