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15 ?5010.?5 ??PVGrowing Perpetuity A growing stream of cash flows that lasts forever. 0 … 1 C 2 C (1+g) 3 C (1+g)2 The formula for the present value of a growing perpetuity is: ???????????? 322 )1()1()1()1()1( rgCrgCrCPVgrCPV??Growing Perpetuity: Example The expected dividend next year is $ and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream? 0 … 1 $ 2 $ () 3 $ ()2 $.$ ???PVAnnuity A constant stream of cash flows with a fixed maturity. 0 1 C 2 C 3 C The formula for the present value of an annuity is: TrCrCrCrCPV)1()1()1()1( 32 ???????? ?????????? TrrCPV)1(11T C ?Annuity: Example If you can afford a $400 monthly car payment, how much car can you afford if interest rates are 7% on 36month loans? 0 1 $400 2 $400 3 $400 ,12$)(1112/07.400$36 ??????????PV36 $400 ?Growing Annuity A growing stream of cash flows with a fixed maturity. 0 1 C The formula for the present value of a growing annuity: TTrgCrgCrCPV)1()1()1()1()1(12 ??????????????????????????????????TrggrCPV)1(11?2 C (1+g) 3 C (1+g)2 T C (1+g)T1 Growing Annuity A definedbenefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by 3percent each year. What is the present value at retirement if the discount rate is 10percent? 0 1 $20,000 ,265$1.000,20$40??????????????????PV?2 $20,000 () 40 $20,000 ()39 What Is a Firm Worth? ? Conceptual