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142 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
8.16 a. Valuation using the DVM:
Intrinsic value
D
1
r-g=D0(1+g)
r-g
Buggies-Are-Us:
Intrinsic value
$2.25(1 + 0) $22.50
0.10 0 =
-
Steady Freddie, Inc.:
Intrinsic value
$2.25(1 0.06) $2.385 $59.63
0.10 0.06 0.04
+= =
-
Gang Buster Group:
Step 1: Present value of dividends using a required rate of return of 10%:
Year Dividends Present Value
Step 2: Price of stock at the end of year 4:
P4=D5
r-g=D4(1+g)
r-g
=$3.60(1+0.06)
0.10 -0.06 =$3.82
0.04 =$95.50
Step 3: Present value of the stock price = $95.40 / (1.10) 4 = $65.16
Step 4: Value of stock $9.52 (Step 1) + $65.16 (Step 3) $74.68
b. The intrinsic value of Gang Busters is $74.68, compared to $59.63 for Steady Freddie and $22.50 for
Buggies-Are-Us. The difference in the values is caused by the difference in dividend growth rates.
8.17
a. Free cash flow = Net Income + Depreciation-Increase in Working Capital – Capital Investment =
©2017 Pearson Education, Inc.
143 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
8.18.To solve this problem, first compute future sales, profits, dividends, and share price.
Future sales:
Future profits:
Future EPS:
Future dividends:
Future share price:
Now we can find the stock’s intrinsic value, approximate yield, and HPRs.
a. Intrinsic value/justified price:
Intrinsic value Present value of future dividends and share price
($.80 0.833) ($0.88 0.694) ($26.40 0.694)
$19.60
=
= ´ + ´ + ´
=
b. Calculate the IRR by taking an initial outflow of $15, followed by an inflow one year later of $0.80
and an inflow two years later of $25.48 ($0.88 dividend plus $24.60 selling price for stock). Using a
calculator or Excel’s IRR function you obtain an IRR of 37.55%
c. Holding period returns:
$0.80 $24.00 $15.00
HPR (year 1) 65.3%
$15.00
$0.88 $26.40 $24.00
HPR (year 2) 13.7%
$24.00
+ -
= =
+ -
= =
8.19 (i) CAPM:
Required rate of return Risk-free rate + [Stock’s beta (Market return – Risk-free rate)]
5% [1.80 (11% 5%)]
Chapter 8 Stock Valuation 144
(ii) The first step in valuing the stock is projecting the dividend payments for the next four years:
Next calculate the present value of each dividend by discounting each payment at 15.8% for the
Next, calculate the PV value as of the end of year 4 of all dividends paid in year 5 and beyond (this would
Now we need to know the present value as of today of this stream of dividends. Simply discount $75.67
8.20 (i) Find the growth rate in dividends:
ROE Firm's retention rate,
1 Dividend payout ratio
0.20 (1 0.4)
0.12 or 12%
g rr
rr
g
g
= ´
= -
= ´ -
=
(ii) Use the constant growth rate dividend model:
Value of the stock in four years
4(1 )D g
k g
+
-
$3.00(1.12)
0.15 0.12-
$112.00
(iii) Value of stock today = $112/1.154 = $64.04
8.21 In order to value this company, you first need to determine the firm’s ROE, then the growth rate in
dividends, and finally the dividend payment.
(i) ROE
Net income $3,750,000 0.15 or 15%
Total equity value $25,000,000
= =
(ii) Growth rate ROE rr
(iii) Dividend EPS payment ratio
©2017 Pearson Education, Inc.
145 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Value of the stock
D0(1+g)
r-g=$2.00(1.09)
0.12 -0.09
$72.67
8.22 a. Using the P/E approach:
Stock price EPS P/E ratio ( Market P/E Relative P/E)
$4.00 (18.5 1.25)
$4.00 (23.125)
$92.50
= ´ = ´
= ´ ´
=
=
b. ($110 – $87.50)/$87.50 25.7%
8.23 Using the P/E approach to value the stock:
Value of the stock EPS P/E
1.25(2.75) 30
$103.125
= ´
= ´
=
8.24 The most logical approach based on the data presented is to value the stock based on a multiple of sales.
Market values are fairly consistent at 10% of sales, so a good estimate would be $1 per share. If, however,
Newco is expected to grow much faster than its competitors, then the price should be adjusted upward for
the growth.
8.25 Amazing.com 4.5
To find the value of a share, multiply the sales per share by the average price-to-sales ratio:
Solutions to Case Problems
Case 8.1 Chris Looks for a Way to Invest His Newfound Wealth
This case allows the student to estimate the future price and approximate yield of a stock. With this
information, the student must analyze the risk and recommend whether or not the stock is a good investment.
a. 1.
($ in millions)
Year
1 2 3
2. Estimated price (year 3) Estimated P/E Estimated EPS
©2017 Pearson Education, Inc.
Chapter 8 Stock Valuation 146
40 $4 $160
3. To calculate the expected return, use Excel’s IRR function, listing the $70 price as a current outflow,
4. Chris faces a considerable amount of both intrinsic and market risk. Chris must consider the
5. Because Chris expects the stock to provide a return of almost 32%, he should decide whether this
b. 1. Chris has adopted a speculative investment strategy, and it may not meet his investment needs. He
has no need for current income, but he does need a store of value and capital appreciation. The
2. One might suggest he put a large part of his earnings into more “conservative” (but still appealing)
3. Yes, there are many foreign stocks and nation funds that offer substantial growth opportunities and
Case 8.2 An Analysis of a High-Flying Stock
This case enables the student to generate future earnings and per share performance; in addition, the student is
a. Average growth rate:
Years Growth Rate
Arithmetic average
0.333+0.25+0.296 +0.358 +0.296
5=30.7%
©2017 Pearson Education, Inc.
147 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Note: With more advanced students, the compound annual rate may be introduced here as an alternative
precise measure. Here the two measures produce very similar average returns, but when the annual rates
1. Using a growth rate of 30.7%, we have:
2. Earnings in 2017 Sales Profit margin
Chapter 8 Stock Valuation 148
2. If HP’s actual market price at the time was $73, one interpretation would be that investors expect slower
3. If HP paid out all of its earnings as dividends and consequently entered a zero growth steady state, its
©2017 Pearson Education, Inc.
