Cheat Sheet - APR = Annual Percentage Rate stated annual interest rate 1 nominal interest rate 1 real interest rate = 1 inflation rate EAY =(1 r 2

# Cheat Sheet - APR = Annual Percentage Rate stated annual...

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- APR= Annual Percentage Rate, stated annual interest rate- 1+nominal interest ratereal interest rate = 11inflation rate-+-(1)1mrEAYm=+-effective annual yield or interest rate; is the annual value gained with or without compoundingEAY = APR (annual Compounding)EAY > APR (More Freq. Compounding)- Continuous Compounding= 0rTCe-PV of Perpetuity= Cr-PV of Growing Perpetuity= Crg-R must be greater than g for formula to work- PV0of an Annuity= 1(1)(1)TCrr-+-PV0of a Growing Annuity11()1TgCrgr+--+Mortgage Payments (Monthly)Term = 20 yrs * 12 = 240 PdsAPR = 12% / 12 = 1%r = 1%Each Payment:Balance x r = Interest PaymentMonthly Payment – Interest Payment = Principle ReductionBalance A - Principle Reduction=Balance BComparing Assets w/ Unequal Lives1. Find NPV for 1 life cycle2. Find Cost / yrPV = x * A3. Compare Ax and BxDetermining Cash FlowCash = (Revenue – Cash Costs)(1 - .34) + .34(Depreciation)What happens to Cash Flow…1. Sales rise by \$1? Down .34 tax Up .662. Materials costs rise by \$1? Pay \$1Retain .40Down .60Depreciation expense rises by \$1?Income Down \$1Tax down .34Cash up .34Calculate:NPV of Project: -30 + 21/1.12 + 21/1.12^2IRR : -30 + 21 / (1+r) + 21 / (1+r) ^2 = 0Cash Effects of Purchase and Sale of Assets1. Initial cash outlay: -1000 @ C 0(Cannot be expensed)2. Depreciation Expense = 1000Depreciation expense each Year:D1 = .200 (1000) = 200 C1 = 68D2 = .320 (1000) = 320 C2 = 108.8D3 = .192 (1000) = 192 C3 = 65.28D4 = .115 (1000) = 115 C4 = 39.10D5 = .115 (1000) = 115 C5 = 39.10D6 = .058 (1000) = 58 C6 = 19.72A. D * T (.34) = CB. Discount All Cash FlowsC. Sum to Get NPV of Depreciation Tax Shield* For ever 1\$ Depreciation…Pre Tax Income Down 1\$3. Resale of Used AssetResale Price 500KBook Value - 0-------------------------Taxable gain 500K11011111()DivEPSPNPVGOrgrEPSREDivEPSPORDiv==+-=+=NVPGO EXAMPLE1.Earnings constant2.EPS = Div (Cash CowValue of a share = EPS / r = Div / rNow Firm retains entire dividend @ Date 1 to invest in a single projectDate 0: NPV of Project = NPVGO# of SharesThus, Value of a Share after commit to Project:EPS / r + NPVGOEarnings / yr = 1MStock: 100k outstandingEPS = 10A. @ Date 1 Firm can spend 1M on a Mktg Campaign which will increase subsequent earnings by 210, 000 or increase EPS by 21%1. Cash Cow (Pays out all Earnings)P = EPS / r = 10 / .10 = \$100Value of MKTG campaign @ Date 1:-1M + 210,000 / .10 = 1.1M@ Date 1 @ Date 2Value of MKT campaign @ Date 0: = Discount 1 Period: 1.1M / 1.1 = 1MThus NVPGO = 1M / 100k = \$10Now EPS = EPS / r + NPVGO\$100 + \$10 = \$110OR METHOD 2Value created b/c: Rate of Return (21%) > Discount Rate (10%)Else Earnings would be increasing because of a postitive Rate of Return but they would be
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