Chapter 9 Problem 15
Actual
2014
2015 2016 2017 2018 2019
Income statement
Net sales 1,996$ 2,267$ 2,508$ 2,827$ 3,138$ 3,571$
Cost of sales 644 742 830 959 1,087 1,241
Gross income 1,352 1,525 1,678 1,868 2,051 2,330
Depreciation 492 785 1,061 1,301 1,009 917
Interest expense 171 178 191 175 142 110
Operating expenses 212 239 270 306 334 374
Net income before tax 477 323 156 86 566 929
Provision for taxes 186 126 61 34 221 363
Net income after tax 291$ 197$ 95$ 52$ 345$ 566$
Balance sheet
Cash and securities 358 413$ 462$ 545$ 618$ 704$
Accounts receivable 208 236 267 309 354 405
Inventory 399 463 541 629 739 864
Other current assets 156 122 142 167 212 206
Total current assets 1,121 1,234 1,412 1,650 1,923 2,179
Gross property and equipment 4,180 5,149 6,410 7,449 8,200 9,016
Accumulated depreciation 868 1,654 2,714 4,015 5,024 5,941
Net property and equipment 3,312 3,495 3,696 3,434 3,176 3,075
Goodwill 1,069 1,069 1,069 1,069 1,069 1,069
Total assets 5,502 5,798 6,177 6,153 6,168 6,323
Accounts payable 104 77 91 110 117 135
Short-term debt 335 482 842 814 585 393
Current portion long-term debt 41 140 165 200 223 267
Accrued expenses 86 97 120 134 174 168
Total current liabilities 566 796 1,218 1,258 1,099 963
Long-term debt 1,694 1,554 1,389 1,189 966 699
Deferred taxes 335 344 370 454 505 496
Shareholders’ equity 2,907 3,104 3,200 3,252 3,598 4,165
Total liabilities and equity 5,502$ 5,798$ 6,177$ 6,153$ 6,168$ 6,323$
a. Estimate Fractal’s free cash flow from 2015 through 2019.
In early 2015, Integrated Communiciations, Ltd. was interested in acquiring Fractal Antenna Systems, Inc., a
privately–held company producing compact antennae. As a first step in deciding what price to bid for Fractal,
Integrated’s finance department has prepared a five-year financial projection for the company assuming an
acquisition. Use this projection and Fractal’s 2014 actual financial figures to answer the questions below.
b. Estimate the present value of Fractal’s free cash flow for the years 2015 – 2019. Integrated’s WACC is 8.0
percent. Fractal’s WACC is 11.5 percent, and the average of the two companies’ WACCs, weighted by sales,
is 8.2 percent.
Fractal Antenna Systems, Inc.
5-year Financial Projection
($ millions)
j. Which of the three estimated maximum acquisition prices in question (i) above do you think is least reliable?
g. Estimate Fractal’s value at the end of 2014 assuming that at year-end 2019 the company‘s equity is worth 15
times earnings after tax and its debt is worth book value.
h. Based on your answer to (g) above, what is the maximum acquisition price Integrated should pay to
acquire Fractal’s equity?
i. Assuming Fractal has 60 million shares outstanding, what maximum acquisition price per share is
consistent with each of the three estimated values of equity determined in (d), (f) and (h)?
c. Estimate Fractal’s value at the end of 2014 assuming it is worth the book value of its assets at the end of
2019.
d. Based on your answer to (c) above, what is the maximum acquisition price Integrated should pay to
acquire Fractal’s equity?
e. Estimate Fractal’s value at the end of 2014 assuming in the years after 2019 the company‘s free cash flow
grows 4 percent per year in perpetuity.
f. Based on your answer to (e) above, what is the maximum acquisition price Integrated should pay to
acquire Fractal’s equity?
Chapter 9 Problem 15 Suggested Answers
Actual
2014
2015 2016 2017 2018 2019
Income statement
Net sales 1,996$ 2,267$ 2,508$ 2,827$ 3,138$ 3,571$
Cost of sales 644 742 830 959 1,087 1,241
Gross income 1,352 1,525 1,678 1,868 2,051 2,330
Depreciation 492 785 1,061 1,301 1,009 917
Interest expense 171 178 191 175 142 110
Operating expenses 212 239 270 306 334 374
Net income before tax 477 323 156 86 566 929
Provision for taxes 186 126 61 34 221 363
Net income after tax 291$ 197$ 95$ 52$ 345$ 566$
Balance sheet
Cash and securities 358 413$ 462$ 545$ 618$ 704$
Accounts receivable 208 236 267 309 354 405
Inventory 399 463 541 629 739 864
Other current assets 156 122 142 167 212 206
Total current assets 1,121 1,234 1,412 1,650 1,923 2,179
Gross property and equipment 4,180 5,149 6,410 7,449 8,200 9,016
Accumulated depreciation 868 1,654 2,714 4,015 5,024 5,941
Net property and equipment 3,312 3,495 3,696 3,434 3,176 3,075
Goodwill 1,069 1,069 1,069 1,069 1,069 1,069
Total assets 5,502 5,798 6,177 6,153 6,168 6,323
Accounts payable 104 77 91 110 117 135
Short-term debt 335 482 842 814 585 393
Current portion long-term debt 41 140 165 200 223 267
Accrued expenses 86 97 120 134 174 168
Total current liabilities 566 796 1,218 1,258 1,099 963
Long-term debt 1,694 1,554 1,389 1,189 966 699
Deferred taxes 335 344 370 454 505 496
Shareholders’ equity 2,907 3,104 3,200 3,252 3,598 4,165
Total liabilities and equity 5,502$ 5,798$ 6,177$ 6,153$ 6,168$ 6,323$
a. Estimate Fractal’s free cash flow from 2015 through 2019.
Earnings before interest and taxes 501 347 261 708 1,039
Tax rate 39.0% 39.1% 39.5% 39.0% 39.1%
EBIT(1-tax rate) 306 211 158 432 633
Depreciation 785 1,061 1,301 1,009 917
Capital expenditures 969 1,261 1,039 751 816
Working capital 931 1,060 1,201 1,406 1,632 1,876
Change in working capital 129 141 205 226 244
Free cash flow (7)$ (130)$ 215$ 464$ 490$
Fractal Antenna Systems, Inc.
5-year Financial Projection
($ millions)
b. Estimate the present value of Fractal’s free cash flow for the years 2012 – 2016. Integrated’s WACC is 8.0
percent. Fractal’s WACC is 11.5 percent, and the average of the two companies’ WACCs, weighted by sales,
is 8.2 percent.
PV@ 11.5% {FCF, 2015-2019} = $628.24
Terminal value in 2019 6,323.00
Present value of terminal value at 11.5%
3,669.01
Estimated firm value 4,297.25$
Estimated firm value 4,297.25
Existing interest-bearing debt 2,070.00
Estimated value of equity 2,227.25$
Terminal value in 2019 6,794.92
Present value of terminal value at 11.5%
3,942.85
Estimated firm value 4,571.09$
Estimated firm value 4,571.09
Existing interest-bearing debt 2,070.00
Estimated value of equity 2,501.09$
Value of equity in 2019 8,490.00
Value of debt in 2019 1,359.00
Value of firm in 2019 9,849.00
Present value of firm in 2019 at 11.5% 5,715.02
Estimated firm value 6,343.26$
Estimated firm value 6,343.26
Existing interest-bearing debt 2,070.00
Estimated value of equity 4,273.26$
(d) (f) (h)
d. Based on your answer to (c) above, what is the maximum acquisition price Integrated should pay to
acquire Fractal’s equity?
e. Estimate Fractal’s value at the end of 2014 assuming in the years after 2019 the company’s free cash flow
grows 4 percent per year in perpetuity.
f. Based on your answer to (e) above, what is the maximum acquisition price Integrated should pay to
acquire Fractal’s equity?
g. Estimate Fractal’s value at the end of 2014 assuming that at year-end 2016 the company’s equity is worth
15 times earnings after tax and its debt is worth book value.
h. Based on your answer to (g) above, what is the maximum acquisition price Integrated should pay to
acquire Fractal’s equity?
i. Assuming Fractal has 60 million shares outstanding, what maximum acquisition price per share is
consistent with each of the three estimated values of equity determined in (d), (f) and (h)?
c. Estimate Fractal’s value at the end of 2014 assuming it is worth the book value of its assets at the end of
2019.
The fundamental principle is that the discount rate should reflect the risks of the cash flows discounted. Here, the
cash flows are Fractal’s, so Fractal’s WACC is the appropriate discount rate. Some argue incorrectly that because
Fractal will disappear in the merger, the cash flows will become Integrated’s, so Integrated‘s WACC is the
we call them.
Estimated value of equity 2,227.25 2,501.09 4,273.26
Number of shares outstanding 60.00 60.00 60.00
Estimated value per share 37.12$ 41.68$ 71.22$
j. Which of the three estimated maximum acquisition prices in question (i) above do you think is least
reliable?
The value estimated in part (d) assumes a terminal value for Fractal in 2019 equal to the book value of assets.
Book value of assets is often a serious under-estimate of a company‘s market value. Hence, this is my candidate
for least reliable estimate.
Chapter 9 Problem 16
Harley-Davidson Inc. 2004 ($ millions)
Net income 889.77$
Number of common shares, millions 294.31
Earnings before interest and tax 1,506.16$
Tax rate 35.0%
Book value of equity 3,218.47$
Book value interest-bearing debt 1,295.44$
Total Sales 5,320.45$
Total Assets 5,483.29$
Harley– Arctic Polaris Marine Winnebago
Davidson Cat Brunswick Industries Products Industries
Comparison of Timberland with Comparable Companies:
Growth Rates, Financial Risks, Size, Returns
5-year growth rate in sales (%) 15.5 6.2 4.1 6.1 15.5 10.8
5-year growth rate in eps (%) 28.1 11.1 47.1 15.9 25.1 17.2
Interest coverage ratio (x) 60.9 * 8.9 85.1 * *
Total liabilities to assets (%) 0.4 0.3 0.6 0.5 0.2 0.5
Total assets ($ millions) 5,483 286 4,346 793 110 395
Indicators of Value
Price/earnings (x) 16.9 17.8 27.8 28.6 18.6
MV firm/EBIT(1-tax rate) (x) 17.3 19.4 24.3 29.0 17.6
MV equity/BV equity (x) 2.8 2.8 8.0 7.7 6.5
MV firm/BV firm (x) 2.8 2.3 7.7 7.7 6.5
Price/sales (x) 0.8 0.9 1.6 2.7 1.2
MV firm/sales (x) 0.8 1.1 1.7 2.7 1.2
* These companies have little or no interest-bearing debt outstanding.
Harley-Davidson Inc. produces motorcycles, motorcycle parts and related accessories and merchandise in the United States and internationally. It is headquartered in Milwaukee,
Wisconsin. Use the following information on Harley-Davidson and five other similar companies to value Harley-Davidson as of December 31, 2004.
Chapter 9 Problem 16 Suggested Answers
Harley-Davidson Inc. 2004 ($ millions)
Net income 889.77$
Number of common shares, millions 294.31
Earnings before interest and tax 1,402.30$
Tax rate 35.5%
Book value of equity 3,218.47$
Book value interest-bearing debt 1,295.44$
Total Sales 5,320.45$
Total Assets 5,483.29$
Harley- Arctic Polaris Marine Winnebago
Davidson Cat Brunswick Industries Products Industries Median Mean
Comparison of Timberland with Comparable Companies:
Growth Rates, Financial Risks, Size, Returns
5-year growth rate in sales (%) 15.5 6.2 4.1 6.1 15.5 10.8 6.2 8.5
5-year growth rate in eps (%) 28.1 11.1 47.1 15.9 25.1 17.2 17.2 23.3
Interest coverage ratio (x) 60.9 * 8.9 85.1 * * 47.0 47.0
Total liabilities to assets (%) 0.4 0.3 0.6 0.5 0.2 0.5 0.5 0.4
Total assets ($ millions) 5,483 286 4,346 793 110 395 395.0 1,186.0
Indicators of Value
Price/earnings (x) 16.9 17.8 27.8 28.6 18.6 18.6 21.9
MV firm/EBIT(1-tax rate) (x) 17.3 19.4 24.3 29.0 17.6 19.4 21.5
MV equity/BV equity (x) 2.8 2.8 8.0 7.7 6.5 6.5 5.6
MV firm/BV firm (x) 2.8 2.3 7.7 7.7 6.5 6.5 5.4
Price/sales (x) 0.8 0.9 1.6 2.7 1.2 1.2 1.4
MV firm/sales (x) 0.8 1.1 1.7 2.7 1.2 1.2 1.5
Excluding
Here are my estimates. In coming to these estimates, I judged that Harley-Davidson (HOG) exhibits average financial risk relative to its peers, but an above-average five-
year growth rate in sales. All of the companies have modest financial leverage, and HOG is representative of the other companies. The company’s above average sales
growth suggests to me that its indicator of value for the first two (income-based) ratios should be above the average value for the comparable firms. A figure about 5
percent above the sample average looks about right. I use a slightly lower than average ratio for the market to book ratios for HOG to be conservative, as I feel that
HOG may be more capital intensive than its peers. Lastly, HOG’s brand name and recognition should result in higher profit margins, thus I choose above average ratios
for the sales based ratios.
Harley-Davidson:
The median and mean values for Harley-Davidson’s peers are appended to the table above.
Price/earnings 23.0 X
MV firm/EBIT(1 – tax rate) 23.0 X
MV equity/BV equity 5.6 X
MV firm/BV firm 5.0 X
Price/sales (x) 3.0 X
MV firm/sales (x) 3.0 X
Price/earnings $ 69.53
MV firm/EBIT(1 – tax rate) $ 66.28
MV equity/BV equity $ 61.24
MV firm/BV firm $ 72.28
Price/sales $ 54.23
MV firm/sales $ 49.83
Average implied value $ 62.23
My best guess of a fair price for Harley-Davidson’s shares at year-end 1998 is $67.00. I place more weight on the earnings-related values, as income is more closely
related to cash flows than sales or book values. The actual price of HOG on the valuation date is $60.75 per share, so my estimate is about 10 percent high. So is HOG
undervalued? Well… not according to the market. Shares of HOG fell during 2005, closing at 51.49 per share on Dec.31, 2005. It is important to remember that these
values are estimates and only as good as the assumptions behind them.
Here are my estimated indicators of value for Harley-Davidson Inc.:
The implied value of HOG common stock per share for each indicator of value is: