Chapter V
Risk and Return
P5-1: Rate of return, kt=(Pt-Pt-1+Ct)/Pt-1
• Douglas Keel, a financial analyst for Orange Industries,
wishes to estimate the rate of return for two similar-risk
investments, X and Y. Keel’s research indicates that the
immediate past returns will serve as reasonable estimates of
future returns. A year earlier, investment X had a market
value of $20,000, investment Y of $55,000. During the year,
investment X generated cash flow of $1,500 and investment
Y generated cash flow of $6,800. The current market values
of investments X and Y are $21,000 and $55,000,
a. Calculate the expected rate of return on investments X and
Y using the most recent year’s data.
b. Assuming that the two investments are equally risky, which
one should Keel recommend? Why?
Solution P5-1
P5-1: Rate of return, kt=(Pt-Pt-1+Ct)/Pt-1
X: Pt-1=20000, Ct=1500, Pt=21000
Y: Pt-1=55000, Ct=6800, Pt=55000
a) X: kt = (21000-20000+1500)/20000= 12,5%
Y: kt= (55000-55000+6800)/55000= 12,36%
b) Investment X should be selected because it has a higher
rate of return for the same level of risk.
Problem 5-2
P5-2: Return calculations, kt=(Pt-Pt-1+Ct)/Pt-1
For each of the investments shown in the following table,
calculate the rate of return earned over the unspecified time
Solution P5-2
P5-2: Rate of return, kt=(Pt-Pt-1+Ct)/Pt-1
A: kt=(1100-800-100)/800= 25%
B: kt=(118000-120000+15000)/120000= 10,83%
C: kt=(48000-45000+7000)/45000= 22,22%
D: kt=(500-600+80)/600= -3,33%
E: kt=(12400-12500+1500)/12500= 11,2
Problem 5-5
P5-5: Risk and Profitability
Micro-Pub, Inc., is considering the purchase of one of two microfilm
cameras, R and S. Both should provide benefits over a 10-year period,
and each requires an initial investment of $4,000. Management has
constructed the following table of estimates of rates of return and
probabilities for pessimistic, most likely, and optimistic results:
a. Determine the range for the rate of return for each of the two cameras.
b. Determine the expected value of return for each camera.
c. Purchase of which camera is riskier? Why?
Solution P5-5
P5-5: Risk and Profitability
a) Range:
Camera R
30-20= 10%
Camera S
35-15= 20%
b) Expected Return
Most likely
Most likely
Probability, Expected Weighted value Expected
return, ki of return, ki*Pri Return
c) Camera S is considered more risky than camera R because
it has a much broader range of outcomes.
Problem 5-7
P5-7: Coefficient of Variation, CV = σk/k
Coefficient of variation Metal Manufacturing has isolated four
alternatives for meeting its need for increased production
capacity. The data gathered relative to each of these
alternatives is summarized in the following table.
a. Calculate the coefficient of variation for each alternative.
b. If the firm wishes to minimize risk, which alternative do you
recommend? Why?
Solution P5-7
P5-7: Coefficient of Variation, CV = σk/k
a) A: CV= 7/20= 0,35
B: CV= 9,5/22= 0,4318
C: CV= 6/19= 0,3158
D: CV= 5,5/16= 0,3438
b) Asset C has the lowest CV and is the least risky relative to
other choices
Problem 5-8
P5-8: Standard Deviation vs Coefficient of Variation
Greengage,Inc., a successful nursery, is considering several expansion
projects. All of the alternatives promise to produce an acceptable return.
The owners are extremely risk-averse; therefore, they will choose the
least risky of the alternatives. Data on four possible projects follow.
a. Which project is least risky, judging on the basis of range?
b. Which project has the lowest standard deviation? Explain why standard
deviation is not an appropriate measure of risk for purposes of this
c. Calculate the coefficient of variation for each project. Which project will
Greengage’s owners choose? Explain why this may be the best measure
of risk for comparing this set of opportunities.
Solution P5-8
P5-8: Standard Deviation vs Coefficient of Variation
a) Project A is least risky based on range with a value of 0,04.
b) Project A is least risky based on standard dev. with a value
of 0,029. But standard dev. is not the appropriate measure
of risk since the projects have different returns.
c) A: CV=0,029/0,12=0,2417
B: CV=0,032/0,125=0,256
C: CV=0,035/0,13=0,2692
D: CV=0,03/0,128=0,2344
In this case D is the best alternative since it provides the least amount
of risk for each percent of return earned. CV is probably the best
measure in this instance since it provides a standardized method of
measuring the risk/return trade-off for investments with differing returns.
Problem 5-18
P5-18: Interpreting Beta
A firm wishes to assess the impact of changes in the market
return on an asset that has a beta of 1.20.
a. If the market return increased by 15%, what impact would
this change be expected to have on the asset’s return?
b. If the market return decreased by 8%, what impact would
this change be expected to have on the asset’s return?
c. If the market return did not change, what impact, if any,
would be expected on the asset’s return?
d. Would this asset be considered more or less risky than the
market? Explain.
Solution P5-18
P5-18: Interpreting Beta
Beta = 1,2
a) 1,2*15%= 18% increase
b) 1,2*(-8%)= -9,6% decrease
c) 1,2*0= 0 no change
d) The asset is more risky than the market portfolio, which has
a beta of 1. The higher beta makes the return move more
than the market.
Problem 5-22
P5-22: Capital Asset Pricing Model, kj=RF+[bj*(km-RF)]
For each of the cases shown in the following table, use the
capital asset pricing model to find the required return.
Solution P5-22
P5-22: Capital Asset Pricing Model, kj=RF+[bj*(km-RF)]
A: kj = 5+[1,3*(8-5)] = 8,9%
B: kj = 8+[0,9*(13-8)] = 12,5%
C: kj = 9+[-0,2*(12-9)] = 8,4%
D: kj = 10+[1*(15-10)] = 15%
E: kj = 6+[0,6*(10-6)] = 8,4%
Problems 5-10, 5-12, 5-16, 5-27
are included in excel spreadsheet
Reminder – MidTerm!
On the 12th of November
Chapters – 1, 2, 3, 4, 5
Thank You for Your attention