Reference no: EM132364946
P5-3 Question: Rate of return and investment choice Clare Jaccard has $5,000 to invest. Because she is only 25 years old, she is not concerned about the length of the investment's life. What she is sensitive to is the rate of return she will earn on the investment. With the help of her financial advisor, Clare has isolated four equally risky investments, each providing a single cash flow at the end of its life, as shown in the following table. All the investments require an initial $5,000 payment.
|
Investment Future cash inflow Investment life (years)
A $ 8,400 6
B 15,900 15
C 7,600 4
D 13,000 10
|
a. Calculate, to the nearest 1%, the average annual rate of return on each of the four investments available to Clare.
b. Which investment would you recommend to Clare, given her goal of maximizing the rate of return?
P5-5: Choosing the best annuity Raina Herzig wishes to choose the best of four annuities available to her. In each case, in exchange for paying a lump sum today, she will receive equal, end-of-year cash payments for a specified number of years. She con-siders the annuities equally risky and is not concerned about their differing lives.
Her decision will be based solely on the rate of return she will earn on each annuity. The following table shows the key terms of the four annuities.
|
Annuity
|
Cost of annuity today
|
Annual cash flow
|
Life (years)
|
|
A
|
$30,000
|
$3,100
|
20
|
|
B
|
25,000
|
3,900
|
10
|
|
C
|
40,000
|
4,200
|
15
|
|
D
|
35,000
|
4,000
|
12
|
a. Calculate, to the nearest 1%, the rate of return on each of the four annuities Raina is considering.
b. Given Raina's stated decision criterion, which annuity would you recommend?
P5-12: Present value concept Answer each of the following questions.
a. How much money would you have to invest today to accumulate $6,000 after 6 years if the rate of return on your investment is 12%?
b. What is the present value of $6,000 that you will receive after 6 years if the dis¬count rate is 12%?
c. What is the most you would spend today for an investment that will pay $6,000 in 6 years if your opportunity cost is 12%?
d. Compare, contrast, and discuss your findings in parts a through c.
P5-13: Time value Jim Nance has been offered an investment that will pay him $500 three years from today.
a. If his opportunity cost is 7% compounded annually, what value should he place on this opportunity today?
b. What is the most he should pay to purchase this investment today?
c. If Jim can purchase this investment for less than the amount calculated in part a, what does that imply about the rate of return he will earn on the investment?
P5-20: Present value of an annuity Consider the following cases.
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Case
|
Annuity payment
|
Interest rate
|
Annuity length (years)
|
|
A
|
$ 12,000
|
7%
|
3
|
|
B
|
55,000
|
12
|
15
|
|
C
|
700
|
20
|
9
|
|
D
|
140,000
|
5
|
7
|
|
E
|
22,500
|
10
|
5
|
a. Calculate the present 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.
P5-24 Funding your retirement Emily Jacob is 45 years old and has saved nothing for retire¬ment. Fortunately, she just inherited $75,000. Emily plans to put a large portion of that money into an investment account earning an 11% return. She will let the money accumulate for 20 years, when she will be ready to retire. She would like to deposit enough money today so she could begin making withdrawals of $50,000 per year starting at age 66 (21 years from now) and continuing for 24 additional years, when she will make her last withdrawal at age 90. Whatever remains from her inheritance, Emily will spend on a shopping spree. Emily will continue to earn 11% on money in her investment account during her retirement years, and she wants the balance in her retirement account to be $0 after her withdrawal on her ninetieth birthday.
a. How much money must Emily set aside now to achieve that goal? It may be help¬ful to construct a timeline to visualize the details of this problem.
b. Emily realizes that once she retires she will want to have less risky investments that will earn a slightly lower rate of return, 8% rather than 11%. If Emily can earn 11% on her investments from now until age 65, but she earns just 8% on her investments from age 65 to 90, how much money does she need to set aside today to achieve her goal?
c. Suppose Emily puts all of the $75,000 that she inherited into the account earning 11%. As in part b, she will earn only an 8% return on her investments after age 65. If Emily withdraws $50,000 as planned on each birthday from age 66 to age 90, how much will be left in her account for her heirs after her last withdrawal?
P5-30 Value of a mixed stream For each of the mixed streams of cash flows shown in the following table, determine the future value at the end of the final year if deposits are made into an account paying annual interest of 12%, assuming that no withdrawals are made during the period and that the deposits are made
a. At the end of each year (i.e., the first deposit occurs 1 year from now)
b. At the beginning of each year (i.e., the first deposit occurs immediately)
|
|
|
Cash flow stream
|
|
|
Year
|
A
|
13
|
C
|
|
1
|
$ 900
|
$30,000
|
$1,200
|
|
2
|
1,000
|
25,000
|
1,200
|
|
3
|
1,200
|
20,000
|
1,000
|
|
4
|
|
10,000
|
1,900
|
|
5
|
|
5,000
|
|
P5-36 Relationship between future value and present value: Mixed stream Using the infor-mation in the accompanying table, answer the questions that follow.
|
Year
|
Cash flow
|
|
0
|
$0
|
|
1
|
800
|
|
2
|
900
|
|
3
|
1,000
|
|
4
|
1,500
|
5
|
2,000 |
a. Determine the present value of the mixed stream of cash flows, using a 5% discount rate.
b. Suppose you had a lump sum equal to your answer in part a on hand today. If you invested this sum for 5 years and earned a 5% return each year, how much would you have after 5 years?
c. Determine the future value 5 years from now of the mixed stream, using a 5% interest rate. Compare your answer here to your answers in part b.
d. How much would you be willing to pay for this stream, assuming that you can at best earn 5% on your investments?
P5-43 Deposits to accumulate future sums For each case shown in the following table, determine the amount of the equal, end-of-year deposits necessary to accumulate the given sum at the end of the specified period, assuming the stated annual interest rate.
|
Case
|
Sum to be
accumulated
|
Accumulation
period (years)
|
Interest
rate
|
|
A
|
$5,000
|
3
|
12%
|
|
B
|
100,000
|
20
|
7
|
|
C
|
30,000
|
8
|
10
|
|
D
|
15,000
|
12
|
8
|
P5-48: Loan amortization schedule Joan Messinco borrowed $45,000 at a 4% annual rate of interest that she must repay over 3 years. The loan is amortized into three equal, end-of-year payments.
a. Calculate the end-of-year loan payment.
b. Prepare a loan amortization schedule showing the interest and principal break¬down of each of the three loan payments.
c. Explain why the interest portion of each payment declines with the passage of time.