lecture 15&16

lecture 15&16 - PM 301 AB - Fall 2011 :___ ‘...

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Unformatted text preview: PM 301 AB - Fall 2011 :___ ‘ flte Weighted Average {96; Cost of Capital gflAQQ; Up to this point, we have computed the cost of each type of security, debt and equity, separately- In reality, most firms use a combination of debt and equity (common and preferred) to finance their operations. To compute the cost of capitai for a firm with more than one security, we need to consider the weighted average cost of capital. ) weighted average cost of capital (WAGE); {will as; a in: aw WACC = (debt weight x—"eierzt‘axlcost of debt) + (preferred weight x cost of preferred) + {common 9‘3"”? weight X cost of common equity) 45% “1 W019: +1" 4}“ 4, I. L we: WACC = (EIA) rs + (PIA) rp+ (BIA) rd (1 — T) n. Dl’ WACC : W3 r3 + WP I'p'l' Wu rd (1 — T), ,- .- We have just looked at how weights come from? . i r r. l fink? qpkknfi . A." $2 ‘5 I. . _:- ‘ NW of Debt I Total capital Preferred stock weight = Wp = Common equity weight = wS = Debt weight = Wd'= MV of Preferred stock;r Total capital ~ "9 MV of Common stock 1 Total capital e «mu 1. Bliss. ndTa'ryD NiswLMm 122 I Lecture 15 a 123 ._ fin ‘ . C r J _r,- 7, Example: The market value (MV) debtiequity ratio for HBK Co. is 0.50 (for now, assume there is no preferred stock in the firm's capital structure). What are the appropnate debt and common equity weights, i.e,, Wu and W3 to be used in computing HBK'S WACC‘? i .2 in; L ~' Example: Smashmouth Co. has a debtfequity ratio of 0.15 based on market values. Debtholders require a 7.5% return and equityholders a 14% return. if Smashmouth 5 tax rate is 34%, what is the WACC? 0;": WACC£W§rS+WPrP+Wd Fd(1-T).:. ""33 _ c ,l . :L : "‘ a practice; H_ Blowfish inc. has 10,000 bonds with a market value of $900 “per bond (51 000 face vaiue per bond). 150,000 shares of common stock are outstanding at a pric'e of $55 per Shara Equityholders require a 10% return and debthoiders 5%. If H. Blowfish‘s tax rate is 38%, what is its WACC? «r1. 1.-~t .. iW NIL" '1 rt" " -‘- ' t ' .l 1'1: s‘.‘ 1-." i ‘71.; J ’ I: - - E “L ® — Richard T. Bliss, Babson University a 01:: 7-,! M r: \ antiTeny D. Nixon, Miami University " a m "'7‘" 7 '— "._ f. rein“, T ‘ " 7- “) ' 123 FIN 301 AB - Fall 2011 1 L9, _ _ . . i- Limlts of Debt Financmg M‘- 5% i l l L Question: We don't see finn's using 100% debt in practice. Why? f ‘1 L j; l " gier ,W «a, _ Answer: The use of 100% debt financing is not practical for several reasons: NOTE: rd < eror all firms, i-e., the cost of debt is always less than the cost of equityfor . more debt 3 more risk and higher probabimy of costly bankruptcy any individuaifinn. ‘ . . _ . . l . . _ \ J 0 rd Will not stay constant; as DIA T, each@is In a riskier posrtion and WIN Debi" ‘40,", {23755.3 «We "10.33%" J] 71»; Li: a 4 it" .l want a return t mi. mum" mtg CD. It. bad," - r5 will not stay constant; as DIA T, eac risk increases and they will also want *- '. ’r' "‘ a higher return Cf. L... V.“ 1- I: " flail; ; ‘11; ' ‘ ""'". WNW” h ‘bMPN’F-F wan remainka Given this, we would expect that WACC as ‘ the firm's capital structure to minimize WACC? iii-“hilt ix {WWW _ . d l. What should the debt weightbeli Law Business risk: l1 g-MXtrux, q-‘gv - x ' a 1 ‘ n "Ilm \— -' : ., : «up 11 s‘mtl liq -) WU, LMQ 101?. , L n \J 5 ,. 9M": this not {001 delete, w in}. i; :1" '1 it *‘- ii " - ““ “ r'vr: 9: 9i“ 1‘ 1‘ Egg/mph: A firm has a"@ cost of debt of 7% and a cost of common equilyof $2OB(383uT: that no pre ned stock exists for this firm)_ If the firm is financed by Financial risk: I ' 0 Sam and $009.00 Of common equity (assume that these figures are mami . va ues), whats the fiI'IITl s welghted average cost of capita| (WACCP it" A H I r. 11 I a l , l .1212: its 139535314. ' ‘ x 1 i. t: u causes {Roost 0i emit“; {to intimate Example: Use the costs from ' finances its activities with $ the prev'ous example. but now assume that the lm 3 _ . firm's WACC? 00'000 0f debt and $200,000 of common eqwty. Wrlatlsul 541- e,},las ix}; Each firm Wm attempt to find an optimal/capital structure that balances increased financial risk with the use of debt‘fina'ncing. (“if 5-(::: Optimal capital structure: The percentages of debt, preferred stock, and common equity that will maximize shareholder wealth. This is the same as the debtleqmty ratio that minimizes the firm's cost of capital. ) ' . a} i" 7r ‘I v U. in Conclusion' TRUE oriFALs I.” - A I . . ' u E} A i Its capital structure, “aux” H 8'39 equal, a firm should prefer to have 100% deb! i . fl.‘ _\ " «i ""-‘-‘“""~7‘=‘“‘r‘t i“- 1'm-rerls 3:2". pl, n ,. v. i . ‘- ri. i 3" 1"“ (w, {me A I ' "m" ‘ - if ‘, [I ‘ Q-Richm'd Tl Bliss, Babson University yam if 31‘ 5% Cum“ % andTerryD. Nixon, Miami University , -' a in,“ fig lira ill bi 125 Pm 301AB-Fa112011 FIN 3m A,B-Fal12013 ’ U (lithe ' 19‘ _:T— ———~—-——e Lemme 15 M Lecture 15 h I = 127 Lars graphically depict what happens to a finn's rd and rs as its capital structure - '- = ' ' ' ' A ? (measured by Its 923. ratio) changes. Question What are the overall implications of these two graphs for the firm s W CC Answer: Cost Of DBbt _ I tin" . "it-‘2 9 .th . l.) ‘l t % w ill! 3"“ 14‘. iii 1) /" l. Lisa: {)0 w: a "-““ " ‘. WACC ' 1 ,o'r-x‘». l1 ‘Frx -; 1919:: i=9“ % DIA ratio ii (I. 3 DIA ratio (financial leverage) 0/ 1. The WACC declines as small amounts of debt are added to an all equity financed 0 firm. The increase in the cost of equity is not enough to offset the advantages of using debt. 2. A minimum WACC is reached. This identifies the optimal capital structure ' ' shareholder value). It is the best ix of debtande uit because it firm's WACC. minim We“ 6' “WWW” (Llama WAGE 3. WACC rises at DIA ratios beyond the firm's minimum WACC found at (2). Beyond the optimal capital structure. financial risk increases to the pomt that the use increasing levels of debt forces the finn‘s WACC to increase. . ; r . DIA ratio "‘3 it - I e ~ Richard T. Bliss, Baboon University *1 and Terry D. Nixon, Miami University 9 - Richard T. Bliss. BM andTexry D. Nixon. Mimi '1‘:- FIN 30‘! AB ~ Fall 2311 12? FM 301 AB ‘ Fall 2011 Question: How does the cost of preferred stock compare to the cost of debt and ING RELEVANT OPERATIN A F ow of common stock? kCAPITAL BUDGETIN : IDE ls ; a“ P 4 lg Before getting to the cash flows, we will start with a brief refresher on depreciation methods- 1“ Though depreciation is a noncash item, it affects cash flOWS in its role as a tax shield. =13 mini. n ‘ _ 7 Why does this relationship exist? :Elgagfgtii;lti — The penodrc cost assigned for the reduction in usefulness and value of a long-term Yl ail-u. 1‘4 lowest-IV .‘ ._ - - _ _. ale r O {Pi-WT m 5 fish“ gm [Sim Types of Depreciation. l9 ( _ . _ _ an “ a leak. mug {1, mmmfi Lain-I. "I I Stra1ght lme deprecration (SL) _ (b I o Modified accelerated cost recovery system (MACRS) T 31‘ :EBIT \\ in" Terms used in depreciation: .\ fl. #1,", {5: Y X P ‘ 0 Class life — The number of years over which a specific asseic agification may be :4, ti, 1 in r r ‘ depreciated. W“;— t' r 1 I Actual life — The actual number of years an asset is used ***Note: Class life may differ from actual life. Class life is used for tax reasons; therefore we use it to evaluate capital budgeting. Depreciable basis iadjusted for salvage value when used in tax reporting. Straight Line Depreciation A method of recording depreciation such that the historical cost of an asset is written off in equal amounts during each mgod of me asset’s life. A firm will then arrive at a ratio. Egg—capital Structure or gigs-'93 in which to keep thei'm maximized when a fi (i.e., their minimum goat _ ‘ ' ©-RichardT.Btiss,BahsmUnrvmity _- and Terry t1 Nixon, Miami University 9 ~ meme 1 Bass. ma Terry D. Nam. M3" ‘ " FIN 301 A,B~ Fall 2011 Lecture 16 129 FIN 301 A.B-Fall 2011 _ 7, ————_: Egeml Imm— ~ 21V Historical Cost — The Sum Of 311 00515 W get the CQUiPmem fimmonal- . Straight Line Depreciation 20 £100 ‘ ' 6959} 9W1 1310'] Der. Ex nse Euni- lbl’fli- ‘ >1 Purchase pnce . ‘ $4,002; 10 '00 0 j m 99mg if i ‘4) 000 i > Sales tax , 1 $1,000 1 _ 4,000 > Dehvery charges :4 000 3,3: g - -fl 201660 ' ' ‘P Installation charges w {QMqA S 0 (mm n c M “i chi “$505 How do we get the rate of depreciation for SL? This rate is equal to (llclass life). Example: A $20,000 truck has a class life of 5 years. I The annual depreciation expense will be: Historical cost * annual dept. rate =_._2_9_ * $20,000 = $4 000 t ‘ . - . - mill Accelerated Depreciation (MACRS) compmes take one half-year S depremanon m the fim year " Modified Accelerated _C_ost Recovery §ystem - ' ' (13 up depreciation. ery ' - - h ethod of deprecrauon that spec penod out one more year, so 3-year class life property is depreciated MACRS IS anot er or over 4 years. Similarly, 5-year class life assets are deprec' MACRS Characteristics Straight Line Depreciation Example: a Produces larger depreciation expenses that straight line for the beginning years. ' ti f r the remaining years. ASSCI: $20’000 truck With a class life of 5 years a. MACRS has smaller deprecm on o As we calculated before I i 9 . iatlon for MACRS ' - rate of depreciation = .20 How do yo“1:311:11::aE-‘iiieiiifezedepreciation schedule depending on the Class Of mvesment (see I annual depreciation expense = $4 000 MAC p Table 12A-2 on page 435 of your text). Some MACRS tables round decimals, others do not. On a test, use whatever table I provide you. a - Ridu'd ‘1’. Hits, Babson University and Terry D‘ Nixon, Miami Univelsity D- Richatd'l‘. 31mm . and Terry 0.14am. M” - ' 131 FIN 301 no - Fall 2011 RN 301 as — Fall 2011 Example: Asset: $100,000 equipment with a 3—year class life. MACRS Schedule PM 1 = 1101355 lifelx l: 1/3 » __._.___.—-—-'—" S-L rate of depreciation S-L annual depreciation expense = (1/3) * $100,000 = $33,333.33 MACRS vs. S-L (with 1f2 year convention) Important Points V’ Most firms use S -L de ' ' . shareholders. Premium to mp0“ perfomance m their m reWrt to RN 301 A,B—Falt 2011 Depreciation as a Tax Shelter Cash flows increase because less moneyr goes to the IRS. Tax savings (shield) = Marginal tax rate * Depreciation expense __,_____ Example: Asset: $100,000 of equipment with 3—year class life Tax rate: 34% Discount rate:@ ;{ Straight Line Depreciation (with le year) :10} Year I Q, =.3.4* Der. Ex t . PV Tax Savins .- $16,666.667 $5,666.6667 $5,151.5152 $33,333,333 $11,333.3333 $9,366.4912 $33,333,333 3113333333 $3,514.9011 , . new. 0710.0' JH 333_=,3/U_D"" '3 55% Islmfi 507nm {(4.1}? $16,666.66? $5,666.6667 $3 870 4096 $100,000 ~ $34,000 $26,903 2170 MACRS Depreciation Tax Savings aid,“ Der. Ex. Tax savings for both methods are the same. Should we be indifferent between S-L and MACRS? No. Using Time Value of Money, we see that MAC RS gives a higher present value for the tax shield. a - Richmi T. Bliss, Baboon University and Terry D. Nixon, Miami University 133 FEN 301 AB — F81! 2011 In" EA...” . , ______'__“ I Lecture 16 m. Qash Flow Estimation Relevant Cash Flows - Irrelevant Cash Flows — When _we analyze capital budgeting decisions, we must focus on operating cash flows. lncmmenta firm's future operating cash flows with or without a project. the incremental Sunk Costs Opportunity Costs Externalities Financing Costs Pk Taxes FIN 301 AB - Fali 201‘! (operating cash flows are the difference between a ease 135.] inflation Shipping and Installation Costs Change in Net Working Capital (NW6) Macks ———._——_. Flotation Expenses Calculating 02erating gash Flows Aste -b -ste a roach to ca ital bud etin is the onl wa to solve these roblerns! The ob'ective is to create a timeline containin all of the ro'ect's relevant cash flows. For most capital budgeting decisions, we can consider three discrete categories of cash flows: - initial, or time 0, cash flows I annual operating cash flows 0 terminal, or end-of-project, cash flows Timeline: 9 - Richard T. Bliss, Bat-non University and Terry D. Nixon, Miami University 135 FIN 301 A,B - Fall 2011 7- r—m Once we have this, it is easy to apply the information from previous lectures. Incremental after—tax cash expenses: INITIAL INVESTMENT OUTLAYS Afterntax cash flow (ATCF) from old asset: (-) Installed cost of the asset (i) Net working capital change i - Incremental after-tax cash ex enses 5 I43) After—tax cash flow from old agset After~tax CF from Asset Sale = Market Value — [Market Value — Book Value] I! T (‘) expenses 2 _ x T INITIAL CASH OUTLAY where: T = corporate marginal tax rate Installed cost of the asset: nlatlsetxalue: ! W: Net working capital change: Example 1: EV = $1 000 NW = $1,700 T = 40% What is the after tax CF? ATCF from Asset Sale = MV {MV - 3V] " T = Examflle 2. EV ._. $5 000 MV : $3.200 T = 40% What is the after tax CF? I .7 cwnem Mae-IS F” {Mutt Iiei‘w‘i‘fi ATCF from Asset Sate = MV *[MV - BV] X T = e - Ricimd T. Bliss. Bahson Universin . . and Terry D. Nixon, Miami Universn‘y‘ e - Richard T. Bliss. WW“ and T D. Nixon. W" - 1, FIN 301 AB — Fall 2011 - "‘3 13? FiN 301 AB - Fall 2011 skeet shun—L: 138 _ e—w Leann-16 139 '1 How can the after-tax cash flow be greater than the price we sell the maChine for? Examgle {continued}: Now assume that Cena is no longer 100% equity financed. Cena's optimal capital structure is 65% common equi and 35% debt. The facility stiil costs $8 million (excluding flotation expense). Cena's f5 is 10% and it®debt flotation i cost) is 7%. Calculate the flotation expense in dollars. 0 l Flotation Expenses: . I l Flotation costs can be stated on a dollar ($) or percentage (%) basis. Let's examine-W calculation through an example. Examgle: The Cena Chain Mfg. Co. has decided to build a new manufacturing facflfll- 3‘ the Company is 100% financed by equity Let is . . ' ‘ ' ' ount for the molusron of preferred stock? Ck) flotation cost (do not confuse this with the Gustaf Question. How would we acc faCi'itY Wilt Cost $8 million (excluding the flotation expense In dollars. We know, ‘ initially, we wili initially assume th ' ' ' ' rt of the initial cash F0? u oses of this class. we wrtl include the flotation expense as pa I outtapy rEFhere are other methods for handling the flotation expense, but this seems to be - the most popular at this time. e - Richard T. Bliss, Babson University lid Terry D. Nixon, Miami University 139 FIN 301 AB - Fall 2011 FIN 301 AB — Fall 2011 __ Egge 141 ) OPERATING CASHFLOWS OVER THE PROJECTS LIFE Example 3: United Manufacturing is evaluating the purchase of a new machine to replace the one that is presently in use. You are given the following information about the proposal: What are com onents of Annual 0 ratin Cash Flows? . . «a. ,P. pa 9 1. The original cost of the old machine three years ago was $6,000,000. It had a class Incremental Sales x (1 - life of 10 years and was being straight-line depreciated (no half-year convention) to - Incremental Operating osts x (1 — T) zero. + Depreciation for new asset x T 2 _ _ . You can sell the old machine today for $2,500,000. [T he cost to remove the old - Deprecratlon for old assetx T if , machine is $220.0003iemom at aid asset.) = Annuat Operating Cash Flow 3. The new machine costs $300,900 and has a ctass life of 7 years with straight-line depreciatio . Installation costs on the new machine are $350390, It is estimated that the new machine can be sold for $150,000 at the end of its useful life. 4. Additional working capital of $500,000 is required if the new machine is purchased. 5. United’s sates will increase by $4,250,000 each year. Variable costs are 56% of sales and incremental fixed costs will be $150,000 annually. 6. United’s optimal capital structure is 80% equity and 20% debt. Flotation costs are 8% for equity and 4% for debt. 7. The finn's tax rate is 34%. Incrementai Sales: Incremental Operating Costs: What are the NPV, [RR and Payback Period for this investment? Dapremafion for new asset :3.- Can‘t answer this now. This will be an extension of our cash flow analysis studied in an upcoming lecture. Better question (for now), what are the net operating cash flows from this project? Depreciation for old asset; Let's work it in parts: raise £37 2:000 3- (—) Installed cost of the asset 9109:3000) } b. (i) Net working capital change Lynne) ‘6: (-) Incremental after-tax cash expe es @ d. (+) After—tax cash flow from old asset $078100: J e. H Flotation expenses L502 is .53 mm INITIAL CA3“ OUTLAY “’3 7"" '37?” i 1* «97.7. + ' :— : :wa invested at start of project gs‘DOJOOU t 350,000 1,190,030 :00 50300 (WW ,i27.q3 a ’ismm a tam-30%?) W ‘W Wig-bazaar) 0 — TERMINAL CASH FLOW - x 5: 3oz 437.43 ~ i Mimi: MV-tMV—-E\JJT azsmae-va‘th-m W 6 -Richani T. Bliss, Babson University W -_ 3’ 07%! 0d) MTmD.Nixm,MimiUnivmity 0{. mi 301 A,B - Far 2011 F” E; : ,%L_o<a)+.7,(et) : .072. 141 FIN 301 N3 -Fati 2011 0C}: a. Incremental Sales x i1 - T) 33053090 , Example 4: Your floral delivery service is considering a new vehicle purchase. The old to, - Incremental Operating Costs Alli» U 3 W800) truck is halfway through its 10~year class life, but just can't cut it anymore. It is on the c_ + Depreciation for new asset x® 431?, :7 I It} books for $10,000, but the local dealer will only give you $7,500 for it. It is being d_ , Depreciation for old asset £2 Mow) deprecrated at $2,000 per year. The new truck costs $25,000 and has a 5 year class life, with an estimated value of $5,000 after five years. It will be straight—line depreciated (no half—year convention) to zero. Fewer breakdowns will increase your sates by $8.000 per ) _ year; costs average 73% of sales. lnyentory will increase by $1,500 due. to the increased 3' *FEO i000 (but) :2 505.000 531135. Your firm’s marginal tax rate is 35%. b)[_t§kxlr.190.000)T 'C°'°°°.QJDU"W) : "3"“ q 3°“ = Annual Operating Cash Flow g 1,2,79,77I-‘l; What are net operating cash flows from this project? 001 Macao/1 )L-Vrllwzflsillz (he no - '. _ a. H Installed cost of the asset KLEOWJ New I 0) by” ' l 00" n00 b. (i) Net working capital change (_ 1500) ' ‘15» H Incremental after—tax cash expenses d. (+) After—tax cash flow from old asset 8 379 e. (—) Flotation expenses —- INITIAL CASH OUTLAY 1 g—lw 0‘) 251000 la) NM: CA‘ CL: 600- 021900 mum-Jew- O : true 1% d) 7300 qusm,io,ooo)L-ss‘)=8375’ e : NWC invested at start r - - ) 0L "'7 " - I ‘ - 5 2‘50 0 mole“ 5% m0 8. Incremital Sales x (1 — T) m t 37%) + After-tax cash flow from asset sale qq m b. — Incremental Operating Costs x (1 - T) l 7 so = TERMINAL CASH FLOW ““lu‘ °' + DepreCiafim for new asset x T L m Sqqrom d. — Depreciation for old asset x T . ) P‘T 1 m a Um. B“ = Annual Operating Cash FIOW EELS U” fix 1. - ' 1' ‘- . LISD’DOU) wjkgtl): ‘illsoo _ 00 W C l- 3215): 9:1‘00 0 1:01:13 [3000)] U _ 33) : 3—7qu TIMELINE: L) 0500013) L39 21750 N (L)L1000)L.3§'):700 Wile-n at) “Flog-{LB _ _ _ .— ~. - 1,3705”! o-Richa'dT.Bliss.BabsonUnivcrsity + gqsm .‘ MTmD.Nixm,MiuniUnivexsity 143 FIN 301 AB - Fall 2011 FIN 301 AB - Fall 201-1 {range '1"_‘—“— fw—fih—‘a _' *— 77__7 limes—~Tga'frria 1' fiww “ __ 7A _ In LH§,_:Emm " fifiwg‘m El Practice: You own a mail—Order book company. You are muttering a new computerized voice—mail system that will handle all incoming calls to vow sales I ch mvested a. stem of project [5007 department. Because it is never on coffee break or tied up With a personal call. your . Afler‘ta ~ annual sales should Increase by 10,000 books. Average selling pnoe is $13 95 and _.qm_.l7,._._%§~cww 3150 average variable cost is $9.30. The system costs 580.000. Will be straight-line = TERMINAL CASH FLOW “so depreciated (no half year convention) to zero over 10 years. and carries fixed annual fl T a; r m _ LN 4, V )T costs of $5,000. It will be sold for $2,500 at the end of its useful We The increased sales mean average inventory will increase by approximater 1.000 books (based on the books cost not selling price). Your firm's tax rate is 37% What are net operating cash flows from this project? it“, _ r "' a. H installed cost of the asset : b. (t) Net working capital change ' c. H Incremental after-tax cash expenses d. (+) After-tax cash flow from old asset e Flotation expenses T|MEUNE 0 l ‘ H ‘ wm_‘______..r__,.____ l N lNthAL CASH OUTLAY rm ‘ . "" ' x ‘ 1‘61" {+13% - . r 3- Incremental Sales x (1 - T) b- — Incremental Operating Costs x (1 - T)‘ ‘ C- + Depreciation for new asset x T ‘ » d- - Depreciation for old asset x l; __ #_‘____W____hw__‘ __ _I p = Annual Operating Cash Flow ,_ ' r 0 ~1MY MAM Museum . .n a mu rem G‘RWTfifismflabemmW __ my m mm, Fm 30': A‘B~Falt 2011 demyD_Nixon,Mim1iUM _ mmfifia‘fifl 29” a r 1‘4 145 . .:l m ‘W W‘1*___.__;;:tff,;_j ;_;,_:'_' ___'fl.iy_.i THE TERMINAL CASH FLows a Incremental Sales x (1 —T) t _ b. - Incremental Operating Costs )1 (1 - T) __ . -_ c + Depreciation for new asset x T 163 r ‘ d - Depreciation for old asset x T %%m__.._._,...._... ,. i . , . = Annual Operating Cash Flow stir? _ NWC invested at start of project 3130 C + After-tax cash flow from asset safe :5 1*: WM = TERMINAL CASH FLOW ' Mei-5 TIMELINE: THE TERMINAL CASH FLows D D C: 'U (D -| "< m . m "1 O we. 0 1+ p t' t Th - m NWC invested at start of project - era "‘9 cos 3. e urpme j v r I . year me With Straight ""8 depreciation :zero. A! + After-tax cash flow from asset sale i A w i = TERMINAL CASH FLOW : (-) Installed cost of the asset ES *1 r CC C E . - n a a er_tax ex ‘1 V_ i | d 1, Mt _ penses . - g ( ) er tax cash fl0W from old asset fl ‘ ‘NITIAL ‘3 lg. ‘.---.r x: '7: :- ,. I 7/ H" 2?: a 9 -WT amen-m Lem“, “Tm I). Mime. Miami Univka 6 - Richard T. Bliss. 13m {Jr-Emit! 55 FIN 301 A3 - Fall 2011 and my D” mm“ Mi WW ' 147 Fm 3’01 A’a ' Fa" 2m 1 146 51: I ...
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lecture 15&amp;16 - PM 301 AB - Fall 2011 :___ ‘...

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