48 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Solutions to Case Problems
Case 4.1 Coates’s Decision
This case introduces the student to the concepts of opportunity cost and required rate of return. It further
requires students to compute present values and select investments using the “reasonable return” approach
discussed in the chapter.
Year A B
Investment $ (1,050) $ (1,050)
a. Each investment is acceptable because its present value is greater than its initial cost of $1,050. The
b. For projects of unequal risk, we must evaluate each at its required rate of return (adjusted for its level
of risk). Using an 8% discount rate, the net present value of investment B is negative $127.49, so it is
c. Since Investment A was acceptable (had a positive present value) at a discount rate of 4%, its IRR
must be more than 4%. Investment B was acceptable at a discount rate of 4%, so its IRR is also greater
d. Using Excel’s IRR formula, we find that the yield on Investment A is 4.37%, while the IRR on
e. Because Investment A is acceptable at a 4% discount rate while Investment B is unacceptable at an 8%
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49 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
f. His initial investment of $50 would have grown to $67.20 at the end of the 10 years assuming that he
Case 4.2 The Risk-Return Tradeoff: Molly O’Rourke’s Stock Purchase
Decision
The title of this case clearly states its objective. It requires students to review and apply the concept of the
risk-return tradeoff.
a.
+ –
=Current income Ending price Beginning price
HPR Beginning price
HPR for Stock X:
(1) (2) (3) (4)
(2) – (3)
(5)
[(1) (4)]/(3)
Year
Current
Income
Ending
Price
Beginning
Price
Capital
Gain HPR
2007 $1.00 $22.00 $20.00 $2.00 15.00%
2008 1.50 21.00 22.00 –1.00 2.27
HPR for Stock Y:
(1) (2) (3) (4)
(2) – (3)
(5)
[(1) (4)]/(3)
Year
Current
Income
Ending
Price
Beginning
Price
Capital
Gain HPR
2007 $1.50 $20.00 $20.00 $0.00 7.50%
2008 1.60 20.00 20.00 0.00 8.00
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Chapter 4 Return and Risk 50
b.
2
1
( )
1
n
i
i
r r
sN
=
–
=–
å
Investment X:
(1) (2) (3) (4)
Return Average (1) – (2) (3)2
Year riReturn, r ri – r(ri – r)2
2007 15.00% 11.74% 3.26% 10.63%
2008 2.27 11.74 –9.47 89.68
= = =
–
712.97 79.22 8.90%
10 1
X
s
Investment Y:
(1) (2) (3) (4)
Return Average (1) – (2) (3)2
Year riReturn, r ri – r(ri – r)2
2007 7.50% 11.14% –3.64% 13.25%
2008 8.00 11.14 –3.14 9.86
51 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Standard Deviation 8.90% 2.78
Comparing the expected returns calculated in Question 1, Stock X provides a return of 11.74%,
which is only slightly above the expected return of Y (11.14%). Whether the higher return on
Answer to Chapter-Opening Problem
The average annual return (percentage change) in the S&P/Case-Shiller Index is 0.4%. To calculate the
standard deviation, the average return from each year’s actual return, square the difference, and then add
up these values across all 10 years. Finally, divide the sum by 9 (N– 1), and then take the square root. The
standard deviation is 10.3%. Comparing these figures to the similar figures for Target and American Eagle,
we see that residential real estate has a lower average annual return and a lower standard deviation. These
results generally confirm the risk-return relationship developed in Chapter 4.
Year Case/Schiller Index Target American Eagle
2005 15.5% 6.6% –1.4%
2006 0.7% 4.7% 105.8%
Note: Averages and standard deviations were calculated with Excel formulas =average(range of cells
containing returns) and =stdev.s(range of cells containing returns)
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