Time Value of Money: Perpetuities An annuity that goes on indefinitely is called
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Question
Time Value of Money: Perpetuities An annuity that goes on indefinitely is called a perpetuity. The payments of a perpetuity constitute a/an series. The equation is: stock with no maturity is an example of a perpetuity. You own a security that provides an annual dividend of $155 forever. The security's annual return is 9%. What is the present value of this security? Round your answer to the nearest cent. $ PV of cash flow stream A rookie quarterback is negotiating his first NFL contract. His opportunity cost is 10%. He has been offered three possible 4-year contracts. Payments arc guaranteed, and they would be made at the end of each year. Terms of each contract are listed below: As his adviser, which contract would you recommend that he accept? Contract 3 gives the quarterback the highest present value; therefore, he should accept Contract 3. Contract 1 gives the quarterback the highest present value; therefore, he should accept Contract 1. Contract 1 gives the quarterback the highest future value; therefore, he should accept Contract 1. Contract 2 gives the quarterback the highest present value; therefore, he should accept Contract 2. Contract 3 gives the quarterback the highest future value; therefore, he should accept Contract 3. Future value for v arious compounding periods Find the amount to which $500 will grow under each of these conditions: 7% compounded annually for 5 years. Round your answer to the nearest cent. $?? 7% compounded semiannually for 5 years. Round your answer to the nearest cent. $?? 7% compounded quarterly for 5 years. Round your answer to the nearest cent. $?? 7% compounded monthly for 5 years. Round your answer to the nearest cent. $??Explanation / Answer
8. Never ending series. The Present Value equation is , PV=A/ i , where A=Each instalment of the annuity and i=interest.
A.Preferred Stock with no maturity is an example of Perpetuity [ as one gets dividends every year irrespective of the firm makes a profit or not]
PV=A/i = 155/0.09=1722.22
9. [Problem 5-12]
PV of Contract 1: =3/(1.10^1)+3/(1.10^2)+3/(1.10^3)+3/(1.10^4)=9.50m
PV of Contract 2:=2.5/(1.10^1)+3.5/(1.10^2)+4/(1.10^3)+5.5/(1.10^4)=11.92m
PV of Contract 3:=6.5/(1.10^1)+1/(1.10^2)+1/(1.10^3)+1/(1.10^4)=8.16m
Quaterback should accept Contract-2 as it gives highest PV
10. [Problem 5-23]
a. Future Value=500*(1.07^5)=701.27
b. Future Value=500*(1.035)^(2*5)=705.29 [ Interest Rate per half annual=7/2 , Period=5*2 half annuals ]
c. Future Value=500*(1.0175)^(4*5)=707.38 [ Interest Rate per quater =7/4 , Period=5*4 quaters ]
d.Future Value=500*(1.0058)^(12*5)=707.40 [ Interest Rate per month =7/12 , Period=5*12 months ]
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