FNCE AID2

# FNCE AID2 - Perpetuity: P=C/r Growing Perpetuity: P = C /...

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Perpetuity: P = C / r Growing Perpetuity: P = C / r-g Annuity: C ( 1/r ) ( 1 – 1/(1+r) T ) Growing Annuity : C / r-g (1- (1-g)/(1+r) T ) (1+r) (1+inf) = (1+n) n = nominal r = real inf = inflation EAY v. APR EAY = Effective Annual Yield APR = Annual % Rate EAY = APR (annual Compounding) EAY > APR (More Freq. Compounding) Conversion FV = (1+ APR/n) nT = (1 + EAY) T Continuous Compounding FV = e APR(T) Mortgage Payments (Monthly) Term = 20 yrs * 12 = 240 Pds APR = 12% / 12 = 1% r = 1% Each Payment: Balance x r = Interest Payment Monthly Payment – Interest Payment = Principle Reduction Balance A - Principle Reduction=Balance B Comparing Assets w/ Unequal Lives 1. Find NPV for 1 life cycle 2. Find Cost / yr PV = x * A 3. Compare Ax and Bx Determining Cash Flow Cash = (Revenue – Cash Costs)(1 - .34) + . 34(Depreciation) What happens to Cash Flow… 1. Sales rise by \$1? Down .34 tax Up .66 2. Materials costs rise by \$1? Pay \$1 Retain .40 Down .60 Depreciation expense rises by \$1? Income Down \$1 Tax down .34 Cash up .34 Calculate: NPV of Project: -30 + 21/1.12 + 21/1.12^2 IRR : -30 + 21 / (1+r) + 21 / (1+r) ^2 = 0 Cash Effects of Purchase and Sale of Assets 1. Initial cash outlay: -1000 @ C 0 (Cannot be expensed) 2. Depreciation Expense = 1000 Depreciation expense each Year: D1 = .200 (1000) = 200 C1 = 68 D2 = .320 (1000) = 320 C2 = 108.8 D3 = .192 (1000) = 192 C3 = 65.28 D4 = .115 (1000) = 115 C4 = 39.10 D5 = .115 (1000) = 115 C5 = 39.10 D6 = .058 (1000) = 58 C6 = 19.72 A. D * T (.34) = C B. Discount All Cash Flows C. Sum to Get NPV of Depreciation Tax Shield * For ever 1\$ Depreciation… Pre Tax Income Down 1\$ 3. Resale of Used Asset Resale Price 500K Book Value - 0 ------------------------- Taxable gain 500K C5 = 500 ( 1 - .34) = 330 Stock Valuation: Constant Dividends: Div1 / r Constant Growth: Div1 / r-g To determine g: A. Next years earnings will be the same unless a NET INVESTMENT is made A. Earnings Next Yr. = R.E. This yr +R.E. This yr x ROE B. Divide all by earnings this year So… g = Retention Ratio x ROE Earnings = 2M Retention Ratio = 1 – Payout ratio = .4 Historical ROE = .16 1. Will Retain: Retention Ratio x Earnings .4 x 2M 2. This yrs Earnings = Earnings x ROE 2M x .16 = 128k 3. g = Change in Earnings = 128k = .064 Total Earnings 2M 4. This Implies Earnings in 1 yr will be: Total earnings x (1 + g) = 2M x 1.064 = 1,128,000 Stock: 1M Outstanding (P = 10) Payout Ratio = .6 Earnings = 1,128,000 Solve For Div: Payout = Div / Earnings Div = \$1.28 P (growth)= Div / r-g Now… Solve for r Finally, r =.192 or 19.2% NVPGO EXAMPLE 1. Earnings constant 2. EPS = Div (Cash Cow Value of a share = EPS / r = Div / r Now Firm retains entire dividend @ Date 1 to invest in a single project Date 0: NPV of Project = NPVGO # of Shares Thus, Value of a Share after commit to Project: EPS / r + NPVGO Earnings / yr = 1M Stock: 100k outstanding EPS = 10 A. @ Date 1 Firm can spend 1M on a Mktg Campaign which will increase subsequent earnings by 210, 000 or increase EPS by 21%

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## FNCE AID2 - Perpetuity: P=C/r Growing Perpetuity: P = C /...

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