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Chapter 2 Securities Markets and Transactions 15
Suggested Answers to Discussion Questions
Answers to questions 1, 3, and 4 will vary according to student’s selections, tastes, and preferences.
4.2 a. Each investment pays a total of $1,000 over the four years.
Solutions to Problems
4.1 The investor would earn income of $2.25 and a capital gain of $52.50 – $45 =$7.50. The total gain is
$9.75 or 21.7%.
4.3 a. Income: $ 2.70
b. Capital gain: $60.00 – $50.00 $10.00
$50.00
4.4 a. Income is the interest income, which is equal to $900 (three payments of $300).
4.5 a. Total return Income Capital gains (or losses) where:
Capital gains (or losses) Ending price – Beginning price
(1) (2) (3) (4) (5)
(1) – (2) (3) (4)
Year
Ending
Price –
Beginning
Price
Capital
Gain
Current
Income
Total
Return
b. Of course, there is no correct answer here, but one might forecast using the arithmetic average or
the average one-year holding period return.
$3.50 $3.70 $.70 $8.60 $6.75 $4.37
+ - + + =
16 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
ii. The average holding period return (HPR):
- +
= =
Ending price Beginning price Current income Total return
HPR Beginning price Beginning price
(1) (2) (3)
Year
Total
Return*
Beginning
Price
(1) (2)
HPR
*From part a.
11.7 11.4 2.0 26.1 16.9
Average HPR 12.8%
5
+ - + +
= =
i. ii.
Forecasts for:
Based on
Arithmetic Average
Based on
Average HPR
c. Students should be made aware of the fact that many other forecasts are possible. One criticism
of taking the simple arithmetic average of the annual dollar return is that one should a rising trend
over time in dollar returns due to inflation. You can see, for example, that the dividend
N i/y PV PMT FV
Div 4 15.02% -1.00 0 1.75
Price 4 10.67% -30.00 0 45
Forecasts
for: Dividends Price
Capital Gain +
Dividend
(We will discuss forecasting returns on specific investments in later chapters.)
4.6 Total return Income plus capital gains
Income 100 ($1.00 $1.20 $1.30) $350
©2017 Pearson Education, Inc.
Chapter 2 Securities Markets and Transactions 17
4.7 a. Using the notation given in the chapter, the risk-free rate of return is:
Rf = r* + IP or 2% +3%
b. The required returns for each investment are calculated as follows:
r1
*r
IP RPior RF RPi
4.9 Holding period return (HPR)
Current income Ending price Beginning price
Beginning price
+ + + + -
= =
=
+ + + + -
= =
=
X
Y
$1.00 $1.20 $0 $2.30 $29.00 $30.00 $3.50
HPR $30.00 $30.00
11.67%
$0 $0 $0 $2.00 $56.00 $50.00 $8.00
HPR 50.00 $50.00
16%
Assuming they are of equal risk, Investment Y would be preferred since it offers the higher return
(16.00% for Y versus 11.67% for X).
4.10 If the first stock is held for 6 months, it will earn 2 quarterly dividends of $0.25 per share and a
If the second stock is held for 1 year, it will earn 4 quarterly dividends of $0.50 and a capital gain
of $3.00 for an annualized holding period return $5.00/$27.00 =18.5%.
4.11 HPR ($50 ($1,000 $950))/$950 $100/$950 10.5%.
4.12 The present value is $4000. The value in 10 years will be $9,000.
a. Using present value, the IRR is calculated as:
A B
1 Year Cash Flow
©2017 Pearson Education, Inc.
18 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
9 7 0
4.13 Using a present value interest factor of 4%:
Spreadsheet solution is shown below
A B
1 Year Cash Flow
Cell B6 shows the amount received from selling the stock plus the year 4 dividend because those
4.14 Interest on the investment in year 5:
Spreadsheet solution is shown below
A B
1 Year Cash Flow
2 0 $ (10,000)
4.15
©2017 Pearson Education, Inc.
Chapter 2 Securities Markets and Transactions 19
Initial Future Calculator
Investment Investment Value Years Solution
A $1,000 $1,200 5 3.71%
4.16 a. Calculator solution (Excel’s IRR function would work equally well.)
4.17 The internal rate of return for these investments is the discount rate that results in the
stream of income equaling the initial investment.
End of Year Investment A Investment B
0 (8,500.00) (9,500.00)
1 2,500.00 2,000.00
4.18 a. Using the same technique as shown in the prior question, we can solve for the internal rate
of return.
End of Year Investment A
©2017 Pearson Education, Inc.
20 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
0 (14,000.00)
b. Elliott should make the proposed investment because the internal rate of return is greater than
the 11% required return. Alternatively, if we find the net present value by discounting cash flows
4.19 Again this problem is most easily solved using Excel’s internal rate of return formula =IRR(range of
cash flows). The IRR is well above the required 9%, so the investment should be accepted.
End of Year Income Stream
$ (1,000)
2017 140
Note that in the first printing of this textbook, the text of this problem indicated that the
4.20 Growth rates are calculated using either Excel or a financial calculator.
Investment
An 2017 – 2013 4
Using a financial calculator,
Bn 2017 –2008 9
©2017 Pearson Education, Inc.
Chapter 2 Securities Markets and Transactions 21
Excel =rate(9,0,-1.50,2.28)
Cn 2017 – 2011 6
Using a financial calculator,
4.21 2016 – 2009 7 years
Using a financial calculator,
4.22 2016 – 2012 4 years
Using a financial calculator,
4.23 a. Investment A, with returns that vary widely—from 1% to 26%—appears to be more risky
than Investment B, whose returns vary from 8% to 16%.
b.
2
1
( )
n
i
s r r
=
= -
å
Standard deviation
CV Average return
=
Investment A:
(1) (2) (3) (4)
Return Average (1) – (2) (3)2
Year r I Return, r ri – r(ri – r)2
2013 19% 12% 7% 49%
22 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
