Finance 3001 Midterm 1 guide
Finance 3001 Midterm 1 guide FINA 3001
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This 3 page Study Guide was uploaded by Layan Notetaker on Thursday February 11, 2016. The Study Guide belongs to FINA 3001 at George Washington University taught by Jiyoon Lee in Summer 2015. Since its upload, it has received 94 views. For similar materials see Intermediate Finance in Finance at George Washington University.
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Date Created: 02/11/16
Valuation of a sinTle cash flow FV=C ×(o+r) C PV= T T (1+r) FV=PV (1+r) T [Non annual compounding – [Continuous compounding] [Effective annual rate] [Net present value] m m: # of payments per year] rT r = PV– cost of inv. FV=PV ×e EAR=(1+ m ) −1 mT FV FV=PV 1+ r EAR=e −1t ; PV= T ( ) m (+EAR ) Example: EAR=? If 14.9% compounded continuously 14.9 EAR = e −1 = 0.1607=16.07% $400 monthly car payments with int. rates = 7% on 36month loans I/Y = 7/12 = 0.5883%, N=36 Annuity: stream of const. CF that lasts for a fixed # of periods. (Calculator assumes payment is made 1 year from today) o PV at time 0 Divide PV calculated by (1 + r). || FV6 = FV5 (1+r) Growing annuity: stream of CF that grows at a const. rate for a fixed # of periods (First payment C, is made at time 1) C 1+g T o PV= [1− ( ) ] r−g 1+r (r−g ) o IY= ∗100 (1+g) PMT=C = C o o 1+g Perpetuity: const. stream of CF that lasts forever: o PV= C r Growing perpetuity: stream of CF that grows at a const. rate, forever. o PV= C r−g [Semiannual coupon bonds] N: 2*T I/Y: required return/2 PMT: (rate*FV) / 2 FV: Par value 1 C∗1− T Bond value = PV of coupons + PV of face value = (+r ) F r + T (+r ) If the case is semiannual, to obtain YTM IY must be multiplied by 2 *same in the case of obtaining PMT After calculative PMT, to find the nominal coupon rate divide the PMT / the par value Coupon rate and YTM o If the coupon rate > YTM, the coupon payment is > than investor’s required return investor needs to pay a premium for the bond, i.e. the bond price > par value (premium bond) o If the coupon rate = YTM, bond price = par value o If coupon rate < YTM, bond will be sold at a discount, i.e. bond price < par value (discount bond) Bond value and YTM o When YTM < coupon, bond trades at a premium – decrease to face value o When YTM = coupon, bond trades at par – stays at face value o When YTM > coupon, bond trades at a discount – increase to face value o If market interest rates rises value of outstanding bonds will fall o Factors changing bond prices changes in YTM [r] and passage of time T [time to maturity] YTM and YTC o In calculations: PV (bond price) should be negative, N = years to maturity/call date from NOW o In YTC: FV is the call price o Discount YTM > coupon rate issuer will not call investor gets YTM o Premium YTM < coupon rate issuer will call investor gets YTC If YTM declined by 1%, a longterm, low coupon bond would have the largest % increase in value If market interest rates rise, the value of outstanding bonds will FALL [Determinants ¿f Bond Yield] rt = rf + IP + DRP + LP + MRP ¿ Tbill yield (short term): r t = r f + IP Tbill yield (long term): r = r¿ + IP + MRP t f ¿ Corporate bond (short term): rt = r f + IP + DRP + LP ¿ Corporate bond (long term): rt = rf + IP + DRP + LP + MRP r (Corporate) r (Treasury)= DRP+LP t t r t (Long term) rt (Short term) = MRP IP = sum of inflations / number of years Lower bond rating means higher default risk: (AAA vs. B) Bond rating downgraded from AAA to BBB bond price would fall and DRP would increase [Current yield & Capital gains] Yield to maturity = current yield + capital gains yield o Current yield = coupon payment / current price o Capital gains yield = (Ending price – Beginning price) / Beginning price To calculate coupon payment: % coupon bonds * 10; i.e. 6.2% bonds = $62 Par bond: coupon rate = YTM = current yield capital gains yield = 0 Zerocoupon bond: current yield = 0 YTM = capital gains yield Premium bonds: current yield > YTM Discount bonds: current yield < YTM Inflation & Int. Rates: (1+R)=(1+r)(1+h); R=nominal rate/ r=real rate/ h=expected inflation rate [Pure expectations hypothesis] (1+r )(1+r )T−t= (+r ) o,t t ,T 0,T [Valuation of preferred stock] Price of a preferred stock with fixed dividends and infinite life a perpetuity: P = D / r [Valuation of common stocks] P D1 D 2 ... D 1. Dividend Growth (Gordon) Model Approach 0 (1 s ) (1 s ) (1 s ) MV 0 FCF 1 FCF 2 ... FCF 2. Free Cash Flow Approach (1WACC) 1 (1WACC) 2 (1WACC) [Types of Stocks] ¿ ¿ 1 ¿o(1+g ) Zero growth Po= //// Constant growth Po= = r r−g r−g P =PV D +PV D +…+PV (TV) Nonconstant/ Differential growth o ( )1 ( )2 ( PV of const. growth dividends at the end of nonconstant growth period.) P9=D10/rg P0=P9/(1+r)^9 o Find D1,2,3 & PV1,2,3 [D1=D0(1+g), D2=D1(1+g)|||PV(D1)=D1/(1+rs), PV(D2)=D2/(1+rs)^2 o TV=D4/(rsg)D3(1+g)/(rsg), PV(TV)=TV/(1+rs)^years [rs [Expected return of zero growth stocks] R = D / Po Po = D / R [Expected return of const. growth stock] D P −P = Exp. Div. yield + Expected capital gains yield = 1 + 1 0 (=g=% increase in stock price) P P o o D 1 ¿o 1+g ) D 2 P 0 = ;P 1 rs−g r−g rs−g D 1 D 0(1+g ) rs= +g= +g P 0 P 0 [Free cash flow approach] MV FCF 1 FCF 2 ... FCF 0 (1 WACC ) (1 WACC ) (1 WACC ) FCF 01+g ) FCF 1 MV =0 = WACC−g WACC−g Value of common stocks = MVo – debt – preferred stock Po = Value of common stocks / # of shares outstanding Terminal value: TV2=P2=FCF3/WACCg; value today: PV(FCF1)+PV(FCF2)+PV(TV2) [p/e ratio]: P = p/e ratio * EPS
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