Questions and Problems
Chapter Five
1. Dollar Returns. What are the dollar returns on the following investments?
Investment
CD
Stock
Bond
Bike
Original Cost
Selling Price of Distributions
or Invested $
Investment
Received $
Dollar Return
$500.00
$540.00
$0.00
$23.00
$34.00
$2.00
$1,040.00
$980.00
$80.00
$400.00
$220.00
$0.00
ANSWER
CD Dollar Return = $540 + $0 - $500 = $40
Stock Dollar Return = $34 + $2 - $23 = $13
Bond Dollar Return = $980 + $80 - $1,040 = $20
Bike Dollar Return = $220 + $0 - $400 = -$180
Investment
CD
Stock
Bond
Bike
Original Cost
Selling Price of Distributions
or Invested $
Investment
Received $
Dollar Return
$500.00
$540.00
$0.00
$40.00
$23.00
$34.00
$2.00
$13.00
$1,040.00
$980.00
$80.00
$20.00
$400.00
$220.00
$0.00
-$180.00
2. Dollar Returns. What are the dollar returns on the following investments?
Investment
CD
Stock
Bond
Car
ANSWER
Original Cost
Selling Price of Distributions
or Invested $
Investment
Received $
Dollar Return
$500.00
$525.00
$0.00
$34.00
$26.00
$2.00
$955.00
$1000.00
$240.00
$42,000.00
$3,220.00
$0.00
CD Dollar Return = $525 + $0 - $500 = $25
Stock Dollar Return = $26 + $2 - $34 = -$6
Bond Dollar Return = $1,000 + $240 - $955 = $285
Car Dollar Return = $3,220 + $0 - $42,000 = -$38,780
Investment
CD
Stock
Bond
Car
Original Cost
Selling Price of Distributions
or Invested $
Investment
Received $
Dollar Return
$500.00
$525.00
$0.00
$25.00
$34.00
$26.00
$2.00
-$6.00
$955.00
$1000.00
$240.00
$285.00
$42,000.00
$3,220.00
$0.00
-$38,780.00
3. Percentage Returns. What are the percentage returns on the following investments?
Investment
CD
Stock
Bond
Bike
Original Cost
Selling Price of Distributions
or Invested $
Investment
Received $
Percent Return
$500.00
$540.00
$0.00
$23.00
$34.00
$2.00
$1,040.00
$980.00
$80.00
$400.00
$220.00
$0.00
ANSWER
CD Percent Return = ($540 + $0 - $500) / $500 = 0.0800 or 8.00%
Stock Percent Return = ($34 + $2 - $23) / $23= 0.5652 or 56.52%
Bond Percent Return = ($980 + $80 - $1,040) / $1,040 = 0.0192 or 1.92%
Bike Percent Return = ($220 + $0 - $400) / $400 = -0.4500 or -45.00%
Investment
CD
Stock
Bond
Original Cost
Selling Price of Distributions
or Invested $
Investment
Received $
Percent Return
$500.00
$540.00
$0.00
8.00%
$23.00
$34.00
$2.00
56.62%
$1,040.00
$980.00
$80.00
1.92%
Bike
$400.00
$220.00
$0.00
-45.00%
4. Percentage Returns. What are the percentage returns on the following investments?
Investment
CD
Stock
Bond
Car
Original Cost
Selling Price of Distributions
or Invested $
Investment
Received $
Percent Return
$500.00
$525.00
$0.00
$34.00
$2600
$2.00
$955.00
$1000.00
$240.00
$42,000.00
$3,220.00
$0.00
ANSWER
CD Percent Return = ($525 + $0 - $500) / $500 = 0.0500 or 5.00%
Stock Percent Return = ($26 + $2 - $34) / $34 = -0.1765 or -17.65%
Bond Percent Return = ($1,000 + $240 - $955) / $955 = 0.2984 or29.84%
Car Percent Return = ($3,220 + $0 - $42,000) / $42,000 = -0.9233 or -92.33%
Investment
CD
Stock
Bond
Car
Original Cost
Selling Price of Distributions
or Invested $
Investment
Received $
Percent Return
$500.00
$525.00
$0.00
5.00%
$34.00
$2600
$2.00
-17.65%
$955.00
$1000.00
$240.00
29.84%
$42,000.00
$3,220.00
$0.00
-92.33%
5. Holding Period and Annual (Investment) Returns. Gary Baker Trading Cards
Incorporated originally purchased the rookie card of Hammerin’ Hank Aaron for
$35.00. After holding the card for five years, Baker Trading Cards auctioned off the
card for $180.00. What are the holding period return and the annual return on this
investment?
ANSWER
Holding Period Return = ($180 - $35) / $35 = 4.1429 or 414.29%
Annual Return = (1 + 4.1429)1/5 – 1 = 1.3875 – 1 = 0.3875 or 38.75%
6. Holding Period and Annual (Investment) Returns. Bohenick Classic Automobiles
restores and rebuilds old classic cars. Bohenick purchased a classic 1957 T-Bird
convertible and restored the car six years ago for $8,500. Today at auction the car
sold for$50,000. What are the holding period return and the annual return on this
investment?
ANSWER
Holding Period Return = ($50,000 - $8,500) / $8,500 = 5.8824 or 588.24%
Annual Return = (1 + 5.8824)1/6 – 1 = 1.3792 – 1 = 0.3792 or 37.92%
7. Comparison of Returns. Looking back at problems five and six, which investment
had the higher holding period return? Which the higher annual return?
ANSWER
Holding Period Return for Trading Card = ($180 - $35) / $35 = 4.1429 or 414.29%
Holding Period Return for Classic Car = ($50,000 - $8,500) / $8,500 = 5.8824 or
588.24%
Trading Card HPR < Classic Car HPR
Trading Car Annual Return = (1 + 4.1429)1/5 – 1 = 1.3875 – 1 = 0.3875 or 38.75%
Classic Car Annual Return = (1 + 5.8824)1/6 – 1 = 1.3792 – 1 = 0.3792 or 37.92%
Trading Card Annual Return > Classic Car Annual Return.
8. Comparison of Returns. Wei Guan Investors are looking at three different investment
opportunities. Investment One is a five year investment with a cost of $125 and a
promised payout of $250 at maturity. Investment Two is a seven year investment with
a cost of $125 and a promised payout of $350. Investment Three is a ten year
investment with a cost of $125 and a promised payout of $550. Wei Guan Investors
can only take one of the three investments. Calculate the annual return for each
investment and select the best investment choice if all three investment opportunities
have the same level of risk.
ANSWER
Holding Period Return for Investment One = ($250 - $125) / $125 = 1.00 or 100.00%
Annual Return Investment One = (1 + 1.00)1/5 – 1 = 1.1487 – 1 = 0.1487 or 14.87%
Holding Period Return for Investment Two = ($350 - $125) / $125 = 1.80 or 180.00%
Annual Return Investment Two = (1 + 1.80)1/7 – 1 = 1.1585 – 1 = 0.1585 or 15.85%
Holding Period Return for Investment Three = ($550 - $125) / $125 = 3.40 or
340.00%
Annual Return Investment Three = (1 + 3.40)1/10 – 1 = 1.1596 – 1 = 0.1596 or 15.96%
Investment Three has the highest annual return rate of the three choices. If all choices
have the same level of risk, choose Investment Three.
11. Standard Deviation. Calculate the standard deviation of the U.S. Treasury Bills,
Long-Term Government Bonds, and Large Company Stocks for the 90s from
Table 5.1. Which had the highest and which had the lowest variance?
Answer from data is:
Standard Deviation for U.S. Treasury Bill for 90s: 1.37%
Standard Deviation for U.S. Long-Term Government Bonds for 90s: 12.38%
Standard Deviation for U.S. Large Company Stocks for 90s: 14.21%
Standard Deviation for U.S. Small Company Stocks for 90s: 21.78%
Highest was Small Company Stocks, Lowest was 3 Month T-Bills
13. Expected Return. Rob Hull Consultants, a famous think tank in the Midwest, has
provided probability estimates for the four potential economic states for the
coming year. The probability of a boom economy is 10%, the probability of a
stable growth economy is 15%, the probability of a stagnant economy is 50%, and
the probability of a recession is 25%. Estimate the expected return on the
following individual investments for the coming year.
INVESTMENT
Stock
Corporate Bond
Government Bond
Boom
25%
9%
8%
Forecasted Returns for Each Economy
Stable Growth
Stagnant
Recession
12%
4%
-12%
7%
5%
3%
6%
4%
2%
ANSWER
Expected Return Stock = 0.10 x 0.25 + 0.15 x 0.12 + 0.50 x 0.04 + 0.25 x (-0.12)
= 0.0250 + 0.0180 + 0.0200 - 0.0300 = 0.0330 or 3.3%
Expected Return Corp. Bond = 0.10 x 0.09 + 0.15 x 0.07 + 0.50 x 0.05 + 0.25 x 0.03
= 0.0090 + 0.0105 + 0.0250 + 0.0075 = 0.0520 or 5.2%
Expected Return Gov. Bond = 0.10 x 0.08 + 0.15 x 0.06 + 0.50 x 0.04 + 0.25 x 0.02
= 0.0080 + 0.0090 + 0.0200 + 0.0050 = 0.0420 or 4.2%
14. Variance and Standard Deviation (expected). Using the data from problem 13,
calculate the variance and standard deviation of the three investments, stock,
corporate bond, and government bond. If the estimates for both the probabilities
of the economy and the returns in each state of the economy are correct, which
investment would you choose considering both risk and return? Why?
ANSWER
Variance of Stock = 0.10 x (0.25 – 0.033)2 + 0.15 x (0.12 – 0.033)2
+ 0.50 x (0.04 – 0.033)2 + 0.25 x (-0.12 – 0.033)2
= 0.10 x 0.0471 + 0.15 x 0.0076 + 0.50 x 0.0000 + 0.25 x 0.0234
= 0.0047 + 0.0011 + 0.0000 + 0.0059 = 0.0117 or 1.17%
Standard Deviation of Stock = (0.0117)1/2 = 0.1083 or 10.83%
Variance of Corp. Bond = 0.10 x (0.09 – 0.052)2 + 0.15 x (0.07 – 0.052)2
+ 0.50 x (0.05 – 0.052)2 + 0.25 x (0.03 – 0.052)2
= 0.10 x 0.0014 + 0.15 x 0.0003 + 0.50 x 0.0000 + 0.25 x 0.0005
= 0.0001 + 0.0000 + 0.0000 + 0.0001 = 0.000316 or 0.0316%
Standard Deviation of Corp. Bond = (0.0004)1/2 = 0.01776 or 1.78%
Variance of Gov. Bond = 0.10 x (0.08 – 0.042)2 + 0.15 x (0.06 – 0.042)2
+ 0.50 x (0.04 – 0.042)2 + 0.25 x (0.02 – 0.042)2
= 0.10 x 0.0014 + 0.15 x 0.0003 + 0.50 x 0.0000 + 0.25 x 0.0005
= 0.0001 + 0.0000 + 0.0000 + 0.0001 = 0.000316 or 0.0316%
Standard Deviation of Gov. Bond = (0.000316)1/2 = 0.01776 or 1.78%
The best choice is the corporate bond. First comparing the corporate bond and the stock,
the corporate bond has a higher expected return and a lower variance (standard
deviation). Second comparing the corporate bond and the government bond the corporate
bond has a higher return and the same variance (standard deviation). This result is due to
the low probabilities of “good” economic states where the stock performs best.