Questions and Problems

Questions and Problems

Chapter Five

1. Dollar Returns. What are the dollar returns on the following investments?

Investment / Original Cost or Invested $ / Selling Price of Investment / Distributions Received $ / Dollar Return
CD / $500.00 / $540.00 / $0.00
Stock / $23.00 / $34.00 / $2.00
Bond / $1,040.00 / $980.00 / $80.00
Bike / $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 / Original Cost or Invested $ / Selling Price of Investment / Distributions Received $ / Dollar Return
CD / $500.00 / $540.00 / $0.00 / $40.00
Stock / $23.00 / $34.00 / $2.00 / $13.00
Bond / $1,040.00 / $980.00 / $80.00 / $20.00
Bike / $400.00 / $220.00 / $0.00 / -$180.00

1. Dollar Returns. What are the dollar returns on the following investments?

Investment / Original Cost or Invested $ / Selling Price of Investment / Distributions Received $ / Dollar Return
CD / $500.00 / $525.00 / $0.00
Stock / $34.00 / $26.00 / $2.00
Bond / $955.00 / $1000.00 / $240.00
Car / $42,000.00 / $3,220.00 / $0.00

ANSWER

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 / Original Cost or Invested $ / Selling Price of Investment / Distributions Received $ / Dollar Return
CD / $500.00 / $525.00 / $0.00 / $25.00
Stock / $34.00 / $26.00 / $2.00 / -$6.00
Bond / $955.00 / $1000.00 / $240.00 / $285.00
Car / $42,000.00 / $3,220.00 / $0.00 / -$38,780.00

1. Percentage Returns.What are the percentage returns on the following investments?

Investment / Original Cost or Invested $ / Selling Price of Investment / Distributions Received $ / Percent Return
CD / $500.00 / $540.00 / $0.00
Stock / $23.00 / $34.00 / $2.00
Bond / $1,040.00 / $980.00 / $80.00
Bike / $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 / Original Cost or Invested $ / Selling Price of Investment / Distributions Received $ / Percent Return
CD / $500.00 / $540.00 / $0.00 / 8.00%
Stock / $23.00 / $34.00 / $2.00 / 56.62%
Bond / $1,040.00 / $980.00 / $80.00 / 1.92%
Bike / $400.00 / $220.00 / $0.00 / -45.00%

1. Percentage Returns. What are the percentage returns on the following investments?

Investment / Original Cost or Invested $ / Selling Price of Investment / Distributions Received $ / Percent Return
CD / $500.00 / $525.00 / $0.00
Stock / $34.00 / $2600 / $2.00
Bond / $955.00 / $1000.00 / $240.00
Car / $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 / Original Cost or Invested $ / Selling Price of Investment / Distributions Received $ / Percent Return
CD / $500.00 / $525.00 / $0.00 / 5.00%
Stock / $34.00 / $2600 / $2.00 / -17.65%
Bond / $955.00 / $1000.00 / $240.00 / 29.84%
Car / $42,000.00 / $3,220.00 / $0.00 / -92.33%

1. Holding Period and Annual (Investment) Returns. GaryBaker 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 = 4.1429or 414.29%

Annual Return = (1 + 4.1429)1/5 – 1 = 1.3875 – 1 = 0.3875 or 38.75%

1. Holding Period and Annual (Investment) Returns. Bohenick Classic Automobilesrestores 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%

1. 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.

1. 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.

1. 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

1. 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 / Forecasted Returns for Each Economy
Boom / Stable Growth / Stagnant / Recession
Stock / 25% / 12% / 4% / -12%
Corporate Bond / 9% / 7% / 5% / 3%
Government Bond / 8% / 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%

1. 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.