Intro to Corp Finance Cheat Sheet
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Given a rate of return r, it takes 72/r years to double valueā¦.Given a time Horizon T, a rate of return 72/T will double value (for low rās slighty overestimates and high rās slightly underestimates)PV(constant perpetuity) = CF/r Ā PV(growing perpetuity) = CF1/(r-g) Ā PV0Ā (CF1,CF2,ā¦) = CF1/1+r + CF2/(1+r)2ā¦.CFT/(1+r)T + (TVT/(1+r)T) Ā Ā TVT-1 Ā = CFT/(r-g) Ā Ā CFTĀ = CFT-1*(1+g) āpay attention to negative g (shrinkage)PV(constant annuity) = [1-(1/(1+r)T]*CF/r Ā PV(growing annuity) = [1-((1+g)T/(1+r)T]*CF1/(r-g) Ā Ā Ā Cash flow in year t: CF1*(1+g)t-1APR= n*[(1+EAR)1/nĀ ā 1] Ā Ā EAR = (1 + APR/n)nĀ ā 1 Ā āĀ if n>1 EAR higher than APRRdeflĀ = (1+Rnom)/(1+Ļ) ā 1 Ā CFT,nomĀ = CFT,deflĀ *(1+Ļ)TĀ Ā Ā gnomĀ = (1+gdefl)*(1+Ļ) ā 1 āĀ gdeflĀ = (1+gnom)/(1+Ļ) ā 1 (real interest rates can be negative if inflation>nominal interest rates but nominal cant be negative)-Unexpected inflation reduces PV of future payments (ex. Homeowners with fixed-rate mortgages benefit; their lenders suffer:nominal fixed(but,ādue to inflation) so debt $ decreases&borrower networth ā)Market price: Coupon1/1+YTM + Coupon2/(1+YTM)2Ā +ā¦..+ CouponT/(1+YTM)TĀ + Principal/(1+YTM)TAbove Par(premium): Price>Principal, YTMAt Par: Price=Principal, YTM=coupon rate Below Par(discount):Ā Pricecoupon rateWhen required return increases, YTM increases; PV of future cash flows is reduced so bond is worth less to investorsā; When Interest Rates ā, $ of bondā, When Interest Ratesā, $ of bondāPlan Vanilla Bond: PV(coupon/interest payments/annuity) + PV(principal) Ā Ā Ā interest = coupon rate*face value (CF1 in annuity formula) Ā Ā Ā spread: 1bpā.01% (1/100thĀ of %) 100bpā100*(1/100)āĀ 1% (.001)
-both required returns increased by 100bpāonly increase discount rate, do not add to coupon rate āmost bonds pay semi-annually (adjust this)Zero-coupon: x% of Principal = Principal/(1+YTM)TĀ or YTM = (1/x%)1/TĀ ā 1 (ex. 4% of face value=96%of principal)Perpetual Bond (Perpetuity/Debt): PV = Fixed interest payments/ YTM āĀ YTM = Fixed interest payments/PVYTM not a good measure of return since it uses promised not expectedAmortizing Loan: Value of share in one year = PV1Ā of infinite dividend stream starting with div2 =div2/(1+re) + div3/(1+re)2ā¦ā¦PV0Ā = 1/(1+rE) *[div1+ PV1(div2,div3ā¦)]ā¦.. PV0Ā = 1/(1+rE)* [div1Ā + (div2/(1+re) + div3/(1+re)2ā¦..] = div1/1+rEĀ + div2/(1+re)2ā¦.PV0Ā = div1/rE-g assuming dividends form a growing perpetuity Ā ā¦.price of share is present value of dividendsStock example: PV(growing/constant annuity) + TV(growing/constant perpetuity)—-$4 dividend/share, growth rate 15% until year 10, then 1% indefinitely: PV(growing annuity)=(1-(1.15/1.16)10) * 4/(.16-.15) CF11=Ā 4(1+.15)9*(1+.01)1=14.21222ā¦.PV10(Div11,12,13)=14.21222/.16-.01 = 94.748137ā¦.PV0=94.748135/(1.1610)=21.477849ā¦ā¦..33.175+21.478=54.653Higher discount rate ā future cash flows less valuable ā NPV goes down Lower discount rate ā future cash flows more valuable ā NPV goes up Profitability Index = NPV/Startup cost (higher index, more valuable project, cut-off is 0-when NPV is 0)PI=(PV of future cash flows)/Startup cost(cut off is 1-NPV is 0) PI>1 accept the project Ā PI<1 reject the project PI=1 may accept the project (Higher PI of project the better)NPV>0, PI is always greater than 1ā¦ā¦NPV<0, PI is always less than 1ā¦ā¦.PI can never be 0IRR>cost of capital (hurdle rate/discount rate)āNPV is always positiveāAccept all projects IRRāNPV is always negativeā Donāt accept