Intro to Corp Finance Cheat Sheet

Given a rate of return r, it takes 72/r years to double value….Given a time Horizon T, a rate of return 72/T will double value (for low r’s slighty overestimates and high r’s slightly underestimates)

PV(constant perpetuity) = CF/r  PV(growing perpetuity) = CF1/(r-g)  PV0 (CF1,CF2,…) = CF1/1+r + CF2/(1+r)2….CFT/(1+r)T + (TVT/(1+r)T)     TVT-1  = CFT/(r-g)    CFT = CFT-1*(1+g) –pay attention to negative g (shrinkage)

PV(constant annuity) = [1-(1/(1+r)T]*CF/r  PV(growing annuity) = [1-((1+g)T/(1+r)T]*CF1/(r-g)      Cash flow in year t: CF1*(1+g)t-1

APR= n*[(1+EAR)1/n – 1]    EAR = (1 + APR/n)n – 1  → if n>1 EAR higher than APR

Rdefl = (1+Rnom)/(1+π) – 1   CFT,nom = CFT,defl *(1+π)T     gnom = (1+gdefl)*(1+π) – 1 ← gdefl = (1+gnom)/(1+π) – 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,↑due to inflation) so debt $ decreases&borrower networth ↑)

Market price: Coupon1/1+YTM + Coupon2/(1+YTM)2 +…..+ CouponT/(1+YTM)T + Principal/(1+YTM)T

Above Par(premium): Price>Principal, YTMAt Par: Price=Principal, YTM=coupon rate Below Par(discount): Pricecoupon rate

When required return increases, YTM increases; PV of future cash flows is reduced so bond is worth less to investors’; When Interest Rates ↑, $ of bond↓, When Interest Rates↓, $ of bond↑

Plan Vanilla Bond: PV(coupon/interest payments/annuity) + PV(principal)      interest = coupon rate*face value (CF1 in annuity formula)      spread: 1bp→.01% (1/100th of %) 100bp→100*(1/100)→ 1% (.001)

-both required returns increased by 100bp→only increase discount rate, do not add to coupon rate –most bonds pay semi-annually (adjust this)

Zero-coupon: x% of Principal = Principal/(1+YTM)T  or YTM = (1/x%)1/T – 1 (ex. 4% of face value=96%of principal)

Perpetual Bond (Perpetuity/Debt): PV = Fixed interest payments/ YTM → YTM = Fixed interest payments/PV

YTM not a good measure of return since it uses promised not expected

Amortizing Loan:

Value of share in one year = PV1 of infinite dividend stream starting with div2 =div2/(1+re) + div3/(1+re)2……PV0 = 1/(1+rE) *[div1+ PV1(div2,div3…)]….. PV0 = 1/(1+rE)* [div1 + (div2/(1+re) + div3/(1+re)2…..] = div1/1+rE + div2/(1+re)2….

PV0 = div1/rE-g assuming dividends form a growing perpetuity  ….price of share is present value of dividends

Stock 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= 4(1+.15)9*(1+.01)1=14.21222….PV10(Div11,12,13...)=14.21222/.16-.01 = 94.748137….PV0=94.748135/(1.1610)=21.477849……..33.175+21.478=54.653

Higher discount rate – future cash flows less valuable – NPV goes down Lower discount rate – future cash flows more valuable – 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  PI<1 reject the project PI=1 may accept the project (Higher PI of project the better)

NPV>0, PI is always greater than 1……NPV<0, PI is always less than 1…….PI can never be 0

IRR>cost of capital (hurdle rate/discount rate)→NPV is always positive—Accept all projects IRR→NPV is always negative— Don’t accept