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Unformatted text preview: Selected Equatim‘is and Tables CHAPTER 3 Stockholders' equity = Paidin capital + Retained earnings Stockholders' equity 2 Total assets — Total liabilities Net working capital = Current assets — (Payables + Accruals) Operating income (or EBIT) 2 Sales revenues — Operating costs FCF = (Elana — T) + Depreciation) — ( Individual Tax Rates in April 2008 Single Individuals If Your Taxable
Income Is
Up to $7,825 9, $7,825—$31,850 l $31,850—$77,100
$77,100—S160,850
$160,850—S349,700
Over $349,700 : If Your Taxable
Income Is Up to $15,650
515,650—563,700
$63,700—S128,500
$128,500—S195,850
$195,850—S349,700
Over $349,700 Corporate Tax Rates as of January 2008 1 l lfaCorporation’s
l Taxable Income ls
1 Up to $50,000 l $50,000—$75,000 ‘1 $75,000—$1oo,ooo l $100,000—5335,ooo $335,000—S10,000,ooo $10,ooo,ooo—$15,ooo,ooo ‘L S15,000,000—$18,333,333
Over $18,333,333 You Pay This
Amount on the
Base of the Bracket $ 0
‘ 782.50
4,386.25
15,698.75
39,148.75
101,469.25 ' Married Couples Filing Joint Returns _ You Pay This
Amount on the
Base of the Bracket S 0
1 ,565.00
8,772.50 24,972.50
43,830.50
94,601 .00 It Pays This
Amount on the
Base of the Bracket S 0 7,500 1 3,750
22,250 1 13,900
3,400,000
5,1 50,000
6,41 6,667 Capital
expenditures + Plus This Percentage
on the Excess over the
Base (Marginal Rate) 10.0% 15.0
25.0
28.0
33.0
35.0 Plus This Percentage
on the Excess over the
Base (Marginal Rate) 10.0% ' 15.0
25.0
28.0
33.0
35.0 Plus This Percentage
on the Excess over the
Base (Marginal Rate) 15% 25
34
39
34
35
38
35 Increase in net
working capital > Average Tax
Rate at
Top of Bracket 10.0%
13.8
20.4
24.3
29.0
35.0 Average Tax
Rate at
Top of Bracket
10.0% 13.8
19.4
22.4
27.0
35.0 Average Tax
Rate at
Top of Bracket
15.0% 18.3
22.3
34.0
34.0
34.3
35.0
35.0 CHAPTER 4 Current assets Current ratio = Current llabllltles Current assets — Inventories
Current liabilities Quick, or acid test, ratio Sales Inventory turnover ratio = ———_
Inventories R ‘ bl
Days, sales, outstanding (050) = ecewa es Sales Fixed assets turnover ratio 2 ~—————
Net ﬁxed assets Sales Total assets turnover ratio = —~——
Total assets Total debt Debt ratio = ——————
Total assets EBIT Timesinterestearned (TIE) ratio = ————
Interest charges D/A
1— D/A D/E
1+ D/E D/E = and D/A = EBITDA + Lease payments Appendix C Selected Equations and Tables Receivables Average sales per day 2 Annual sales/365 EBITDA coverage = operating margin 2 Operating Income (EBIT) Sales
Profit margin 2 W
Sales
Return on total assets (ROA) = w
EBlT Basic earning power (BEP) = m Net income+ Interest Return on investors’ 'capital (ROIC) = Debt +Equity Net income Return on common equity (ROE) = W Price per share Pr‘ Ear ' P E rat' 2 ———————————
lce/ nmgs( / ) '0 Earnings per share Common equity Book value er share 2 ——————
p Shares outstanding Market price per share Market/book ratio (M/B) 2 Book value per Share Interest + Principal payments + Lease payments ROE 2 Proﬁt margin xTotaI assets turnover >< Equity multiplier Sales Total assets Net income X
— ><
Total assets Total common equity _ Sales EVA = EBIT(1 — Corporate tax rate) — (Total i'nvestors' capital) x (Aftertax cost of capital) EVA = Net income — [Equity capital >< Cost of equity capital] 2 (Equity capital)(Net income/Equity capital — Cost of equity capital) = (Equity capita)(ROE — Cost of equity capital) A33 A34 Appendix C Selected Equations and Tables CHAPTER 5 Future value = FVN = PV(1 + l)N Present value 2 PV 2 FVN N
(1 + I) FVAN = PMTU +')N_1 + PMT(1 + I)“—2 + PMT(1 + 0”—3 +. = PMT[————(1 + :)N_1] FVAdue = FVAordinary(1 ‘1") PVAN = PMT/(1+l)1+ PMT/(1+l)2 +~+PMT/(1+)N 1‘ 11I"
=PMT ———(+) PVAdue = PVAordinary(1 + I) p
PV of a perpetuity = E W— CF1 CF2 CFN N CFt
1+ 2+"’ N_Z It
(1+!) (1+0 (1+0 t=1(1+) Stated annual rate _l M
Number of payments per year / Periodic rate (IPER) — Number of periods = (Number of years)(Periods per year) ' ' M
Effective annual rate (EFF%) = (1 +—N%> — 1,0 + PMT(1+I)° =NM CHAPTER 6 Quoted interest rate (r) = r* + IP + DRP + LP + MRP
= I'm: +DRP + LP + MRP rTbill = rRF = r* + W
rTboncl = r: + [Pt + MRPt
robond: r: + lPt + MRPt l DRP: + LPt rRF with crossproduct term 2 r*+ l + (r*>< I) CHAPTER 7
I _ INT lNT L _M_
Bond 5 value (VB) — ——(1 + “)1 + “(1 + rd)2 + + (1+ rd)N + (1+ rd)»: _:”: lNT + M
(=1(1+rd)‘ (1+rd)”
N lNT u. 
Price of callable band 2 E __t + Ca PrlC:
t=1 (1+ rd) (1+ rd) 2N
INT/2 M
VB " E t l 2N
t=1 (1+ rd/Z) (1+ rd/z) CHAPTER 8 Expected rate of return (f) = P1 n + le’z + ' ‘ ' + PNrN N
: Z Piri
i=1 CHAPTER 9 Value of stock (Ea) = PV of expected future dividends — ———D' + D2 + + ————D°°
(1+ rs)1 (1+ r5)2 (1 + rs)°°
w .
= Z L
t=1 (1 'l' rs)‘ .
A D 1 ‘ D 1 2 D 1 °°
Constant growth stock: P0 = M + °( +9) + + jig.)— (1 +r5)l (1 + r92 (1 + rs)°°
: D00 +9) : D1
rs — 9 rs — 9 Expected rate _ Expected Expected growth rate, or
of return _ dividend yield capital gains yield
r D' +
s — Po 9 Growth rate = (1 — Payout ratio)ROE ~ D
Zero growth stock: P0 = —r
5 A D
Horizon value = PM = “+1
rs ” g
A D1 D2 DN DN+1 Doc
NonconstantzPo=————+——++ + +~l
(1+ rs)‘ (1 + rs)2 : (1+ rs)“ (1 + rs)“+‘ (1+ rs)”
D1 Dz DN [SN — + . + +
(1+ r5)1 (1 + r5)2 (1+ rs)" (1+ r5)”
= PV of nonconstant dividends+PV of horizon value, ISM Market value V 2
of company ( Company) PV of expected future free cash flows _ mm + FCF2 + + FCFOO
(1+WAcc)‘ (1+WACC)2 (1+WAcc)°° Horizon value (VCompany at t=N) = FCFN+l/(WACC_ gFCF) Market value of equity = Book value + PV of all future EVAs D
VD:—p rp
FF22 VP CHAPTERIO _
% Aftertax % of Cost of % of Cost of WACC = of cost of + preferred preferred + common common
debt _ debt stock stock equity equity
2 wdrd(1 — T) + WPrP + . wcrs Aftertax cost of debt : Interest rate on new debt — Tax savings = rd — rdT = rd(1 — T)
DP
Component cost of preferred stock 2 rp = P—
p Required rate of return 2 Expected rate of return
rs :rRF+RP=D1/Po+g=Fs
r5 = rRF —— (RPM)bi
= I'm:  (I'M  rRF)bi A D1 D2 Doc P =—————+ ++————
° 0+m‘ U+nf u+om
i 0‘
1:=1(1+r5)t
A D1
p = .
o rs‘g
. D
rs=rs=—1+Expectedg
Po
Cost ofe uit from new stock—r — D1 +
q Y —e—Po(1_F) 9 Addition to retained earnings for the year
Equity fraction Retained earnings breakpoint = CHAPTERII
CF CF
NPV=CFo+ ‘1+CF22++ “N
(1+r) (1+r) (1+r)
t=o(1+")t
CFo+—C—F—1—,+———Cﬂ—2+...+——EFN—N=0
. (1+IRR) (1+IRR) (1+lRR)
i CFt _
t=0(1+IRR)‘
N t=0
TV
PV costs = (1 + MIRR)N
Unrecovered cost
Number of at start of year
Cash ﬂow during full recovery year Payback 2 years prior to +
full recovery ...
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 Fall '09
 FIN221

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