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# Time value of money

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Hello,
I need some assistance with the attached questions regarding my financial accounting studies.

For example:

P3-6. PV = FVn x (PVIF i%,n)

a. PV = \$ 20,833.50

b. PV = 21,114.00

c. PV = 19,840.00

Please use the above format and provide your answers to the following questions, found in Chapter 4 (Gitman, 2009) pp. 208 - 211:

1. Single payment loan repayment. A person borrows \$200 to be repaid in 8 years with 14% annually compounded interest. The loan may be repaid at the end of any earlier year with no prepayment penalty.

a. What amount will be due if the loan is repaid at the end of year 1
b. What is the repayment at the end of year 4?
c. What amount is due at the end of the 8th year?

2. Present value concept. Answer each of the following questions

a. What single investment made today, earning 12% annual interest, will be worth \$6000 at the end of 6 years?
b. What is the presnet value of \$6000 to be received at the end of 6 years if the discount rate is 12%?
c. What is the most you would pay today for a promise to repay you \$6000 at the end of 6 years if your opportunity cost is 12%?
d. Compare, contrast, and discuss your findings in parts a through c.

3. Time value and discount rates. You just won a lottery that promises to pay you \$1,000,000 exactly 10years from today. Because the \$1,000,000 payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate single cash payment.

a. What is the least you will sell your claim for if you can earn the following rates of return on similar-risk investments during the 10-year period?
1. 6%
2. 9%
3. 12%

b. Rework part a under the assumption that the \$1,000,000 payment will be received in 15 rather than 10 years
c. On the basis of your findings in parts a and b, discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum.

4. Future value of an annuity. For each case in the accompanying table, anser the questions that follow

Case Ammount of Annuity Interest reate Deposit period (years)
A \$2500 8% 10
B \$500 12% 6
C \$30000 20% 5
D \$11500 9% 8
E \$6000 14% 30

a. Calculate the future value of the annuity assuming that it is
1. an ordinary annuity
2. an annuity due
b. Compare your findings in parts a(1) and a(2). All else being identical, which type of annuity-ordinary or annuity due-is preferable? Explain why

5. Value of a retirement annuity. An insurance agent is trying to sell you an immediate retirement annuity, which for a single amount paid today will provide you with \$12000 at the end of each year for the next 25 years. You currently earn 9% on low risk investments comparable to the retirment annuity. Ignoring taxes, what is the most you would pay for this annunity?

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Henderson Electric Inc., a maker of electronic surveillance equipment, is considering selling to a well-known hardware chain the rights to market its home security system. The proposed deal calls for the hardware chain to pay Henderson \$30,000 and \$25,000 at the end of years 1 and 2 and to make annual year-end payments of \$15,000 in years 3 through 9. A final payment to Henderson of \$10,000 would be due at the end of year 10.

a. Lay out the cash flows involved in the offer on a time line.

b. If Harte applies a required rate of return of 12% to them, what is the present value of this series of payments?

c. A second company has offered Henderson an immediate one-time payment of \$100,000 for the rights to market the home security system. Which offer should Henderson accept and why?

#### Solution Preview

For example:

P3-6. PV = FVn x (PVIF i%,n)

a. PV = \$ 20,833.50

b. PV = 21,114.00

c. PV = 19,840.00

Please use the above format and provide your answers to the following questions, found in Chapter 4 (Gitman, 2009) pp. 208 - 211:

1. Single payment loan repayment. A person borrows \$200 to be repaid in 8 years with 14% annually compounded interest. The loan may be repaid at the end of any earlier year with no prepayment penalty.

a. What amount will be due if the loan is repaid at the end of year 1

PV = FVn x (PVIF i%,n)
200 = FV1 x (PVIF14%,1)
FV1 = 228.00

b. What is the repayment at the end of year 4?

PV = FVn x (PVIF i%,n)
200 = FV4 x (PVIF14%,4)
FV4 = 337.79

c. What amount is due at the end of the 8th year?

PV = FVn x (PVIF i%,n)
200 = FV8 x (PVIF14%,8)
FV8 = 570.52

2. Present value concept. Answer each of the following questions

a. What single investment made today, earning 12% annual interest, will be worth \$6000 at the end of 6 years?

PV = FVn x (PVIF i%,n)
PV = 6,000 x (PVIF12%,6)
PV = 3,039.79

b. What is the present value of \$6000 to be received at the end of 6 years if the discount rate is 12%?

PV = FVn x (PVIF i%,n)
PV = 6,000 x (PVIF12%,6)
PV = 3,039.79

c. What is the most you would pay today for a promise to repay you \$6000 at the end of 6 years if your opportunity cost is 12%?

PV = FVn x (PVIF i%,n)
PV = 6,000 x (PVIF12%,6)
PV = 3,039.79

d. Compare, contrast, and discuss your findings in parts a through c.

The ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer what amount will be due if the loan is repaid at the end of year 1.

\$2.19