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# Applications of basic TVM concepts

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1. Jean Splicing will receive \$50,000 in 50 years or \$2,000 today. If long-term rates are 7 percent, what choice would you recommend?
a. What is the current value of the future payments
b. What is the current value, if they are received at the beginning of each year?

2. "Red" Herring will receive \$11,000 a year for the next 18 years as a result of his patent. At present 9 percent is an appropriate discount rate.
a. Should he be willing to sell out his future rights now for \$100,000 ?
b. Would he be willing to sell his future rights now for \$100,000, if the payments will be made at the beginning of each year?

3. Larry Doby invests \$50,000 in a mint condition "1952 "Rocket" Richard Topps hockey card. He expects the car to increase in value 8 percent per year for the next five years. How much will his card be worth after five years?

4. You need 28,974 at the end of 10 years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year.
a. What single payment could be made at the beginning of the first year to achieve this objective?
b. What amount could you pay at the end of each year annually for 10 years to achieve this same objective?

5. If you can invest money elsewhere at 8% compounded semi-annually, what should be the market value (present value) for a 20-year \$1,000 bond that pays 7% annual interest (with payments received every six months), as well as returning your \$1,000 at the end of 20 years? (Note: Due to rounding in tables, answers using tables may differ by a few hundred dollars from those found using a business calculator.)

6. March Hair Ltd. just paid a dividend of \$1.80, which it expects to be \$2.90 next year and \$4 the next year. After that time, the dividend will likely decline 5 percent per year forever. With required rates of return at 14 percent, what should investors pay for March Hair?

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#### Solution Preview

1. Jean Splicing will receive \$50,000 in 50 years or \$2,000 today. If long-term rates are 7 percent, what choice would you recommend?

Option A : Receive \$50000 in 50 years
Future Value=FV=\$50,000
Discount rate=i=7%
Number of periods=n=50 years
Present Value =PV=?

PV=FV/(1+i)^n=50000/(1+7%)^50=\$1697.39

Current value of the future payment =\$1697.39

Option B: Receive \$2000 today
PV of option B=\$2000
PV of option B is higher. So, he should accept \$2000 today.

a. What is the current value of the future payments
Option A : Receive \$50000 in 50 years
Future Value=FV=\$50,000
Discount rate=i=7%
Number of periods=n=50 years
Present Value =PV=?
PV=FV/(1+i)^n=50000/(1+7%)^50=\$1697.39
Current value of the future payment =\$1697.39

b. What is the current value, if they are received at the beginning of each year?
Discount rate=i=7%
Number of periods=n=50 years
Present Value =PV=?
We know that PV of a future cash flow if it is made at the beginning of period
PV=FV/(1+i)^n*(1+i)=50000/(1+7%)^50*(1+7%)=\$1816.21
Current value of the future payment =\$1816.21

2. ...

#### Solution Summary

There are 6 problems. Solutions to these problems depict the steps to estimate present value and future values. Calculations are carried out by using appropriate TVM formulas.

\$2.19