FE 323 Review Session Jessica Crusco and Jay Chen Topics EAR vs APR Bonds Stocks Dividend growth rate dividend yield stock price in future year Supernormal dividends NPV IRR Mutually exclusive projects Operating Cash Flow Using EAR and APR EAR annualized rate adjusted for compounding APR compounded reinvested each period EAR APR compounded annually EAR APR compounded semiannually quarterly etc Use EAR to convert APR Need to convert when payments per year are different than APR compounded times Ex Annual payments need EAR or APR annually Ex Semi annual payments need APR semi annually Example EAR and APR 1 You want to buy a new sports coupe for 68 500 and the finance office at the dealership has quoted you a 6 9 APR loan for 6 years to buy the car Assume monthly compounding a What is your monthly payment P YR 12 N 72 6 x P YR PV 68 500 I YR 6 9 PMT 1 164 57 P YR 1 N 72 6 x 12 PV 68 500 I YR 0 575 6 9 12 PMT 1 164 57 Example EAR and APR 1 You want to buy a new sports coupe for 68 500 and the finance office at the dealership has quoted you a 6 9 APR loan for 6 years to buy the car Assume monthly compounding b What is your effective annual rate Continuing from previous slide touch EFF Or repeat steps in previous slide P YR 12 NOM 6 9 EFF 7 1224 Example EAR and APR c Suppose they were semi annual payments What is the semi annual payment What is the effective annual rate Need APR with semi annual compounding but given monthly compounding so need to convert P YR 12 NOM 6 9 EFF EFF 7 1224 P YR 2 NOM 7 1224 Used later for other question 7 If you now RCL I YR you ll see 7 is already there so no need to insert it into I YR to finish the problem Example EAR and APR With APR of 7 compounded semi annually we have the right APR and can continue P YR 2 N 12 6 x 2 I YR 7 PV 68 500 PMT P YR 1 N 12 6 x 2 I YR 3 5 7 2 PV 68 500 PMT 7 088 64 7 088 64 What is your effective annual rate In case you forgot RCL EFF 7 1224 Bonds FV Face Value always 1 000 Watch out for Coupon Rate vs Yield to Maturity Coupon rate of 1000 total coupon for the year If semi annual payments and coupon 10 each payment is 50 If annual payments and coupon 10 each payment is 100 PV always negative outflow you pay today FV and PMT always positive inflow in future Holding period yield vs Yield to Maturity YTM rate of return on a bond held to maturity assumes reinvestment at same rate Holding period yield HPY is what you actually earn on a bond HPY PV price purchased FV price sold for current price N years held PMT coupon payment Solve for I YR Rate of return or HPY Bonds YTM and HPY 2 Suppose that today you buy a 12 percent annual coupon bond for 995 The bond has 13 years to maturity a What is the yield to maturity on this bond P YR 1 PV 995 FV 1 000 PMT 120 12 x 1 000 N 13 I YR 12 08 Bonds YTM and HPY b Two years from now the yield to maturity has declined by 1 percent and you decide to sell What is your holding period yield I YR 11 08 12 08 1 Rcl I YR 1 I YR N 11 PV 1 057 02 Value of bond in 2 years PV now becomes FV make it positive FV 1 057 02 PV 995 PMT 120 12 x 1 000 N 2 I YR 14 96 Stocks Constant growth is treated like a perpetuity Pt Dt 1 r g Recall that you are treating the dividends as cash payments that you will receive in the future Remember to use timelines to visualize Don t forget that in constant growth using above equation like a perpetuity you capture the PV of all future cash flows which falls in the period prior to the first cash flow i e Pt is one period before Dt 1 Pt can be considered a cash flow because it represents all those dividend payments in constant growth and the stock could be sold for that value we call this terminal value in valuing cash flows in finance You can now discount Pt and all dividends up to and including Pt at the appropriate discount rate r Finding Dividend Growth Rate 3 Home Canning Products common stock sells for 44 96 a share and has a market rate of return of 12 8 percent The company just paid an annual dividend of 1 04 per share What is the dividend growth rate Pt Dt 1 r g 44 96 1 04 x 1 g 12 8 g g 10 25 Finding Dividend Yield 4 Great Lakes Health Care common stock offers an expected total return of 9 2 percent The last annual dividend was 2 10 a share Dividends increase at a constant 2 6 percent per year What is the dividend yield Pt Dt 1 r g r g Dt 1 Pt What is r g Dividend yield So dividend yield 9 2 2 6 6 6 Finding Stock Value in Future Year 5 Winter Time Adventures is going to pay an annual dividend of 2 86 a share on its common stock next year This year the company paid a dividend of 2 75 a share The company adheres to a constant rate of growth dividend policy What will one share of this common stock be worth five years from now if the applicable discount rate is 11 7 percent What is the growth rate g D1 D0 D0 g 2 86 2 75 2 75 g 04 Pt Dt 1 r g P5 D6 r g P5 3 4796 117 04 P5 45 19 Dt D0 1 g t D6 D0 1 g 6 D6 2 75 1 04 6 D6 3 4796 Supernormal Dividends 6 Rizzi Co is growing quickly Dividends are expected to grow at a 30 percent rate for the next three years with the growth rate falling off to a constant 6 percent thereafter If the required return is 13 percent and the company just paid a 1 80 dividend what is the current share price Step 1 find the price of stock when the dividend levels off Pt Dt 1 r g P3 D4 r g P3 4 1919 13 06 P3 59 8839 STO 3 D4 D0 1 g1 3 1 g2 1 D4 1 8 1 3 3 1 06 1 D4 4 1919 P3 is known as a terminal value in finance it captures all the value of the future cash flows and the stock could be sold for this at t 3 P0 captures the value of P3 …