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1. Holding-Period Returns
a. Last year Marla purchased 100 shares of stock for $ 8 per share. She paid a flat $ 75 to purchase the
shares. Since making her purchase, she has received $ 200 in dividends. Marla is concerned that the
stock price will fall below its current FMV of $ 7. Calculate her holding-period return if she sells today
and pays a $ 75 commission.
b. Swarn bought 200 shares of a stock for $ 36 per share. He paid $ 245 in trading commissions. He has
received dividends in the amounts of $ 98, $ 156, and $ 300 over the last three years, respectively.
Assuming that Swarn is in the 15% marginal tax bracket for capital gains and dividends, what is his
holding-period return if he sells all of the shares at $ 40 each with a $ 245 trading commission? What is
Swarn?s tax-adjusted holding period rate of return?
2. Dollar-Weighted Returns
a. Brad purchased 10 shares of stock for $ 10 per share. He paid a $ 5 commission. One year later, he
purchased another 10 shares at $ 9 per share. Again, he paid a $ 5 commission. In the second year, his
disappoint got the best of him and he sold 10 shares at $ 7 per share, paying another $ 5 commission. At
the end of third year, Brad liquidated his holdings, paying $ 5 in commissions at $ 8 per share. What was
his dollar-weighted rate of return?
b. Buckley purchased a collectible stamp for $ 600. He was thrilled to learn that the stamp price had
moved up, so one year later he purchased another stamp for $ 700. At the end of the second year, he
sold one of the stamps for $ 800. He held his original stamp for the third year. Buckley then sold his
stamp at the end of the fourth year for $ 1,000. What was Buckley?s dollar-weighted rate of return?
3. Time-weighted Returns
a. Camerin purchased one ounce of gold for $ 1,400. The following year, the price of gold shot up to $
1,800, but in the third year prices fell back to $ 1,500. What was Camerin?s time-weighted return?
b. Marybeth purchased one share of stock for $ 92. At the end of year 1, the stock was worth $ 95. At the
end of year 2, the stock was worth $ 100; and at the end of year 3, the stock was worth $ 92. What was
Marybeth?s time-weighted return? How does this compare to her holding period rate of return?
4. Mean Returns
a. Maurice purchased a coin collection several years ago. Each year he has had the collection appraised
by a reputable coin dealer. Maurice has calculated the yearly percentage gain or loss based on the
appraisal, as shown below:
What is the average (mean) return of the coin collection over the seven-year period?
Use the rate of return data provided by Maurice to calculate the geometric mean return. How does this
compare to the mean return?
5. Weighted Average Returns
a. Sherman is a novice investor. The following table shows his portfolio holdings and market values for
each holding. Please calculate Sherman?s weighted average return for his portfolio.
b. Sonya and Josh own several pieces of expensive jewelry. The following table summarizes their most
important gem assets: Use this information to calculate the holding-period return.
6. Real and Nominal Rates
a. Consumer prices have been averaging 3.50% in South Korea. If So-Hyun can earn a nominal rate of
return on her investment portfolio of 10.25%, what is her real rate of return, assuming continuous
b. Farrell wants to retire in six years. To have sufficient assets to fund retirement, Farrell needs to
accumulate an additional $ 400,000 between today and retirement. As his advisor, you assume that
inflation will average 5%. You are also confident that you can build a portfolio that will generate an 8%
compounded annual after-tax return. What serial payment should Farrell invest at the end of the first
year to fund this goal?
7. Tax-exempt and Taxable Rates
a. Thomas Jones is in the 25% marginal federal tax bracket, the 4% marginal state tax bracket, and the 2%
marginal city tax bracket. If he earns 9.25% on his portfolio, what is his after-tax rate of return?
b. Stephanie is considering purchasing a fixed-income investment. She has narrowed her list of bond
choice to two AAA-rated investments. The first is a corporate bond that matures in seven years. The
bond yields 6.35%. The second bond also matures in seven years; however, this bond is a municipal bond
issued by the state in which Stephanie resides. The bond has a current coupon rate at 4.79%. Stephanie
is in the 25% marginal federal tax bracket and the 3.50% marginal state tax bracket. Which bond should
she invest in to maximize her after-tax rate of return?
8. Effective Rate Conversion Problems
a. A client was earning an EAR of 7%. The client was contributing to the account on a monthly basis.
What would be the appropriate EPR?
b. A client wants to compute the estimated future value of a bank account. The account pays a
semiannual rate of 4% (EPR). The client is investing in the account on a biweekly basis. What is the
appropriate EPR to be able to solve for an estimated future value for the client?
9. Future Value Problems
a. Ted has $ 1,000. He can earn an annual effective rate of 5%. How much will he have in 10 years?
b. Lanisha currently earns $ 45,000 per year. She expects her salary to increase by 3.5% per year. She
plans to work for another 20 years. How much will she earn in her final year of work?
10. Present Value Problems
a. Tammy has determined that she will need $ 3 million when she retires in 45 years. The current
interest rate is 7% (EAR). How much does she need today to fully fund this goal at that rate?
b. David and Iantha expect their 10-year-old daughter to get married someday. They estimate that her
wedding would cost $ 30,000 today. Wedding costs will increase by 3% per year, and she will marry in 15
years. David and Iantha earn a pre-tax annual rate of 5%. They are in the 20% marginal tax bracket. What
amount do they need to set aside today for their daughter?s wedding?
11. Future Value of Annuity Problems
a. Sue wants to save $ 1,000,000 in 20 years. She estimates she can earn 8.5% on savings. She intends to
make deposits at the beginning of every year in a series of equal payments starting today. How much
does she need to save each year to reach her goal?
b. Merita has been offered a choice of either receiving $ 100,000 in 10 years or receiving $ 7,000 per
year (at the end of each year) for the next 10 years. Which is the better option if her required annual rate
of return is 7%?
12. Present Value of Annuity Problems
a. Mike needs to receive $ 40,000 per year (at the beginning of each year) from his investments for the
next 30 years. His opportunity cost of money is 5%. How much does he need in an account
b. Roshanna has just won the lottery. Her required rate of return is 6%. Should she take the annual
annuity payment of $ 125,000 for the next 20 years or an immediate lump-sum payout of $ 1.5 million?
13. Future Value of Growing Annuity Problems
a. Martha wants to start saving for college. She estimates that she will need $ 50,000 when she starts
college four years from now. She plans to save $ 9,500 this year and increase deposits by 5% annually
(payments at the end of each year). She can earn 7% on her savings. Will she meet her savings goal of $
50,000 for college four years from now?
b. Todd is saving $ 3,000 annually into an account (payments at the end of each year). He plans to
increase the annual level of savings by 5% each year. He can earn 9% annually. How much will he have in
the account at the end of 20 years?
14. Present Value of Growing Annuity Problems
a. Mike wants to receive $ 40,000 per year pretax from his investments for the next 30 years. He is
concerned about inflation, which he expects to average 3%. He can earn a pretax rate of 6% on his
money. How much does he need in an account to generate $ 40,000 in annual inflation-adjusted income
(payments at the end of each year)?
b. A client is doing some investment/ retirement planning. She is attempting to determine how much of
her estate she needs to set aside today to fully fund her retirement. She desires annual beginning-ofperiod withdrawals for the next 25 years. She would like inflation-adjusted withdrawals that start at $
50,000 per year. Assume an annual post-tax rate of return of 7.5% and that inflation will increase at an
annual effective rate of 3.5%. What amount does she need to dedicate to this goal?
15. Present Value of Delayed Annuity Problems
a. Jonas desires fixed annual income of $ 85,000 beginning 20 years from now and lasting for 20 years.
He plans to deplete the account. His annual required return is 9.5%. How much does he need to invest
today to achieve his goal?
b. An investor has two options: (1) $ 50,000 received at the end of this year, or (2) $ 10,000 received
each year for 10 years but beginning 10 years from now. Assume the rate of return is 7%. Which option
has the higher present value?
16. Present Value of Perpetuity Problems
a. An investment would provide end-of-year annual income of $ 2,000. The client?s required rate of
return is 12.5%. What price should the client be willing to pay for the investment?
b. Jose Marie and his wife, Ayna, want to ensure that they do not outlive their money. They want to
make end-of-year withdrawals that start at $ 80,000 after tax and increase by 4% per year. They can earn
an annual effective rate of 7.2% after tax. How much do they need to have invested to make withdrawals
that last forever?
17. Internal Rate of Return
a. Ruth invested $ 16,000 in an exchange-traded fund six years ago. Dividends and earnings were
automatically reinvested in new shares. Although Ruth considers herself to be a buy-and-hold investor,
she nonetheless made a few trades during the time period, as follows: $ 3,025 redemption at the end of
the second year $ 1,825 redemption at the end of the third year $ 4,200 additional investment into the
fund at the end of the fifth year $ 19,885 received at the end of the sixth year, when Ruth redeemed the
shares. What was Ruth?s internal rate of return on the investment?
b. Lawrence Block is considering investing in a gold coin. The coin costs $ 47,500. He anticipates
spending $ 1,000 to have the coin?s value reevaluated by experts at the end of the first year. Lawrence
believes that he can receive $ 3,500 in exhibitor fees by allowing a major museum to showcase his coin
during the second year of ownership. He would like to sell the coin, but he will need to market and
promote it first. He anticipates spending $ 2,000 by the end of the third year on the process. If he can
receive $ 50,000 at the end of the fourth year, should Lawrence make this investment if he needs to earn
4.50% on it?
18. Net Present Value
a. Derek invested $ 12,000 in a mutual fund five years ago. He received a dividend check for $ 1,000
after the first year. He received $ 750 after the second year. At the end of the third year, he received a
check for $ 1,500. After the fourth year, he collected $ 750. His final dividend check of $ 1,000 was
received at the end of the fifth year. Assume that Derek sold the mutual fund at the end of the fifth year
for $ 18,000. What was Derek?s internal rate of return on this investment?
b. Kristy purchased shares of a mutual fund five years ago. She has since made the following additional
transactions: End of year 2, invested additional $ 2,500 in the fund End of year 3, invested additional $
9,000 in the fund End of year 5, redeemed all of her shares in the fund, receiving $ 16,000 Kristy just told
you she achieved an annual return of 9% in this investment. If Kristy is correct, what was her initial
investment in the fund?
19. Loan Amortization Problems
a. Willy and Ursha have just purchased a new car for $ 38,000. They financed $ 35,000 for five years at
6.75% (APR). What is the monthly payment and total interest expense?
b. Assume an initial loan amount of $ 150,000, an APR of 6.5%, fixed monthly payments, and an
amortization period of 20 years. What is the outstanding balance on the loan after 60 payments have
20. Kristin and Dan Peterson wonder how much they will need to save to fully fund four years of college
for their daughter, Samantha, who is 12 years old today. She plans to attend college at age 18. They know
that their first choice of college currently costs $ 13,000 per year. College costs are increasing 5%
annually. They feel that it is possible to earn an effective annual rate of 8.3% (8% compounded monthly),
both before and during college.
a. How much will Samantha?s first year of college cost?
b. How much do the Peterson?s need to fully fund college costs when Samantha begins college?
c. How much do Kristin and Dan need to deposit in an account today to fully fund four years of
d. How much will they need to save on a monthly basis starting at the end of this month to fully fund
four years of expenses?
21. Tony has been eyeing a new car. Last weekend, he went to the dealership and noted that his dream
car would cost $ 23,000 if purchased today. Tony currently has $ 9,000 saved. He does not want to go
into debt to buy the car, so he has decided to save toward the purchase for three years. Tony estimates
that inflation will average 4.5% per year. He earns 7% (EAR) on his savings.
a. How much will the car cost in exactly three years?
b. How much must he save per year (at end of each year) to purchase the car in three years?
22. John is an avid stamp collector. He has been noting the rapid rise in prices for stamps printed in the
19th century. Some of the best stamps from that time period have been increasing in value by 12% per
year. John has the rare opportunity to purchase several impressive stamps from a reputable dealer. The
dealer has offered to sell the stamps to John for $ 65,000 today. As an alternative, John can put down $
10,000 toward the purchase today and buy the stamps outright for an additional $ 89,500 in four years.
Assume an annual discount rate of 12%. Assuming John has the cash for either deal, which should he
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