QUESTION-2
Your employer, a mid-sized human resources management company, is considering expansion into
related fields, including the acquisition of Temp Force Company, an employment agency that
supplies word processor operators and computer programmers to businesses with temporary
heavy workloads. Your employer is also considering the purchase of Bigger- staff & McDonald
(B&M), a privately held company owned by two friends, each with 5 million shares of stock. B&M
currently has free cash flow of $24 million, which is expected to grow at a constant rate of 5%.
B&M’s financial statements report short-term investments of $100 million, debt of $200 million,
and preferred stock of $50 million. B&M’s weighted average cost of capital (WACC) is 11%.
Answer the following questions.
a. Describe briefly the legal rights and privileges of common stockholders.
b. What is free cash flow (FCF)? What is the weighted average cost of capital? What is the free cash
flow valuation model?
c. Use a pie chart to illustrate the sources that comprise a hypothetical company’s total value.
Using another pie chart, show the claims on a company’s value. How is equity a residual claim?
d. Suppose the free cash flow at Time 1 is expected to grow at a constant rate of gL forever. If gL
WACC, what is a formula for the present value of expected free cash flows when discounted at the
WACC? If the most recent free cash flow is expected to grow at a constant rate of gL forever (and
gL WACC), what is a formula for the present value of expected free cash flows when discounted at
the WACC?
e. Use B&M’s data and the free cash flow valuation model to answer the following questions. (1)
What is its estimated value of operations? (2) What is its estimated total corporate value? (This is
the entity value.) (3) What is its estimated intrinsic value of equity? (4) What is its estimated
intrinsic stock price per share?
f. You have just learned that B&M has undertaken a major expansion that will change its expected
free cash flows to −$10 million in 1 year, $20 million in 2 years, and $35 million in 3 years. After 3
years, free cash flow will grow at a rate of 5%. No new debt or preferred stock was added; the
investment was financed by equity from the owners. Assume the WACC is unchanged at 11% and
that there are still 10 million shares of stock outstanding.
(1) What is the company’s horizon value (i.e., its value of operations at Year 3)? What is its current
value of operations (i.e., at Time 0)?
(2) What is its estimated intrinsic value of equity on a price-per-share basis
g. If B&M undertakes the expansion, what percent of B&M’s value of operations at Year 0 is due to
cash flows from Years 4 and beyond? (Hint: Use the horizon value at t 3 to help answer this
question.)
h. Based on your answer to the previous question, what are two reasons why managers often
emphasize short-term earnings?
i. YouremployeralsoisconsideringtheacquisitionofHatfieldMedicalSupplies.Youhave gathered the
following data regarding Hatfield, with all dollars reported in millions:
(1) most recent sales of $2,000;
(2) most recent total net operating capital, OpCap $1,120;
(3) most recent operating profitability ratio,OP NOPAT Sales 45%;and
(4) most recent capital requirement ratio, CR OpCap Sales 56%. You estimate that the growth rate in
sales from Year 0 to Year 1 will be 10%, from Year 1 to Year 2 will be 8%, from Year 2 to Year 3 will
be 5%, and from Year 3 to Year 4 will be 5%. You also estimate that the long-term growth rate
beyond Year 4 will be 5%. Assume the operating profitability and capital requirement ratios will not
change. Use this information to forecast Hatfield’s sales, net operating profit after taxes (NOPAT),
OpCap, free cash flow, and return on invested capital (ROIC) for Years 1 through 4. Also estimate
the annual growth in free cash flow for Years 2 through 4. The weighted average cost of capital
(WACC) is 9%. How does the ROIC in Year 4 compare with the WACC?
j. What is the horizon value at Year 4? What is the total net operating capital at Year 0? How does
the value of operations compare with the current total net operating capital?
k. What are value drivers? What happens to the ROIC and current value of operations if expected
growth increases by 1 percentage point relative to the original growth rates (including the longterm growth rate)? What can explain this? (Hint: Use Scenario Manager.)
l. Assume growth rates are at their original levels. What happens to the ROIC and current value of
operations if the operating profitability ratio increases to 5.5%? Now assume growth rates and
operating profitability ratios are at their original levels. What happens to the ROIC and current value
of operations if the capital requirement ratio decreases to 51%? Assume growth rates are at their
original levels. What is the impact of simultaneous improvements in operating profitability and
capital requirements? What is the impact of simultaneous improvements in the growth rates,
operating profitability, and capital requirements? (Hint: Use Scenario Manager.)
m. What insight does the free cash flow valuation model provide regarding possible reasons for
market volatility? (Hint: Look at the value of operations for the combinations of ROIC and gL in the
previous questions
n. (1) Write out a formula that can be used to value any dividend-paying stock, regardless of its
dividend pattern.
(2) What is a constant growth stock? How are constant growth stocks valued?
(3) What happens if a company has a constant gL that exceeds its rs? Will many stocks have
expected growth greater than the required rate of return in the short run (i.e., for the next few
years)? In the long run (i.e., forever)?
o. Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on Tbonds) is 7.0%, and that the market risk premium is 5%. What is the required rate of return on the
firm’s stock?
p. Assume that Temp Force is a constant growth company whose last dividend (D0, which was paid
yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6% rate.
(1) What is the firm’s current estimated intrinsic stock price?
(2) What is the stock’s expected value 1 year from now?
(3) What are the expected dividend yield, the expected capital gains yield, and the expected total
return during the first year?
q. Now assume that the stock is currently selling at $30.29. What is its expected rate of return?
r. Now assume that Temp Force’s dividend is expected to experience nonconstant growth of 30%
from Year 0 to Year 1, 25% from Year 1 to Year 2, and 15% from Year 2 to Year 3. After Year 3,
dividends will grow at a constant rate of 6%. What is the stock’s intrinsic value under these
conditions? What are the expected dividend yield and capital gains yield during the first year? What
are the expected dividend yield and capital gains yield during the fourth year (from Year 3 to Year
4)?
s. What is the market multiple method of valuation? What are its strengths and weaknesses?
t. What are the advantages of the free cash flow valuation model relative to the dividend growth
model?
u. What is preferred stock? Suppose a share of preferred stock pays a dividend of $2.10 and
investors require a return of 7%. What is the estimated value of the preferred stock?
I HAVE ATTACHED EXCEL TOOL KIT TO ASSIST WITH THIS QUESTION
A
1
2
3
4
5
B
C
Tool Kit
D
E
F
Chapter 7
Corporate Valuation and Stock Valuation
7-4 Valuing Common Stocks—Introducing the Free Cash Flow (FCF) Valuation Model
6
7 Data for B&B Corporation (Millions)
8
9
Constant free cash flow (FCF) =
$10
10
Weighted average cost of capital (WACC) =
10%
11
Short-term investments =
$2
12
Debt =
$28
13
Preferred stock =
$4
14
Number of shares of common stock =
5
15
16
17 The first step is to estimate the value of operations, which is the present value of all expected free cash flows. Because the FCF's are
18 expected to be constant, this is a perpetuity. The present value of a perpetuity is the cash flow divided by the cost of capital:
19
Value of operations (Vop) = FCF/WACC
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
Value of operations (Vop) =
$100,00 million
B&B's total value is the sum of value of operations and the short-term investments:
Value of operations
+ ST investments
Estimated total intrinsic value
$100
$2
$102
The next step is to estimate the intrinsic value of equity, which is the remaining total value after accounting for the claims of debtholders
and preferred stockholders:
Value of operations
+ ST investments
Estimated total intrinsic value
− All debt
− Preferred stock
Estimated intrinsic value of equity
$100
$2
$102
$28
$4
$70
The final step is to estimate the intrinsic common stock price per share, which is the estimated intrinsic value of equity divided by the
number of shares of common stock:
Value of operations
+ ST investments
Estimated total intrinsic value
− All debt
− Preferred stock
Estimated intrinsic value of equity
÷ Number of shares
Estimated intrinsic stock price =
The figure below shows a summary of the previous calculations.
$100
$2
$102
$28
$4
$70
5
$14,00
A
B
C
D
E
F
52
53
54 Figure 7-2
55 B&B Corporation's Sources of Value and Claims on Value (Millions of Dollars except Per Share Data)
56
57 Inputs:
Valuation Analysis
58
Constant free cash flow (FCF) =
$10
Value of operations
59
Weighted average cost of capital (WACC) =
10%
+ ST investments
60
Short-term investments =
$2
Estimated total intrinsic value
61
Debt =
$28
62
Preferred stock =
$4
− Preferred stock
63
Number of shares of common stock =
5
Estimated intrinsic value of equity
64
÷ Number of shares
65
Estimated intrinsic stock price
66
67
68
Sources of Value Short-term
Claims on Value
69
investments =
70
$2
71
72
73
74
Debt = $28
75
76
77
78
79
Estimated equity
Value of
80
value = $70
operations =
81
$100
82
83
84
85
86
87
88
89
7-5 The Constant Growth Model: Valuation when Expected Free Cash Flow Grows at a Constant Rate
90
91 Case 1: The expected free cash flow at t=1 and the expected constant growth rate after t=1 are known.
92
First expected free cash flow (FCF1) =
93
$105
94
95
Weighted average cost of capital (WACC) =
Constant growth rate (gL) =
9%
5%
96
97 When free cash flows are expected to grow at a constant rate, the value of operations is:
98
99
𝐅𝐂𝐅𝟏
100
𝐕𝐨𝐩 =
𝐖𝐀𝐂𝐂 − 𝐠 𝐋
101
102
103
104
A
B
C
D
Value of operations (Vop) = FCF1 / [WACC-gL]
105
Value of operations (Vop) =
E
$2.625
106
107
108 Case 2: Constant growth is expected to begin immediately.
109
Most recent free cash flow (FCF0) =
110
$200
111
112
12%
7%
Weighted average cost of capital (WACC) =
Constant growth rate (gL) =
F
113
114 When free cash flows are expected to grow at a constant rate, the value of operations is:
115
116
𝐅𝐂𝐅𝟎 (𝟏 + 𝐠 𝐋 )
117
𝐕𝐨𝐩 =
𝐖𝐀𝐂𝐂 − 𝐠 𝐋
118
119
120
Value of operations (Vop) = [FCF0(1+gL)]/[WACC-gL]
121
122
Value of operations (Vop) =
$4.280
123
124
125 7-6 The Multi-Stage Model: Valuation when Expected Short-Term Free Cash Flow Grows at a Nonconstant Rate
126
127 Thurman Corporation's expected free cash flows are shown below.
128
129
Year
0
1
2
3
4
130
FCF
−$20
$80
$100
$110
Growth in FCF
131
25%
10%
132
133
134
Free cash flows are expected to grow at a 5% rate starting at Year 4 and to continue growing at a 5% rate for
135
the foreseeable future. We know the free cash flow at Year 4 and we know that FCF grows at a constant rate
136
after Year 4. Therefore, we set the horizon date at Year 4.
137
138
Free cash flow at beginning of the constant growth phase (FCF 4) =
139
$110
140
141
142
143
144
145
146
147
148
149
Weighted average cost of capital (WACC) =
Constant growth rate (gL) =
𝐇𝐕𝟒 = 𝐕𝐨𝐩, 𝐚𝐭 𝟒 =
𝐅𝐂𝐅𝟒 (𝟏 + 𝐠 𝐋 )
𝐖𝐀𝐂𝐂 − 𝐠 𝐋
HV4 = Vop, at 4 = [FCF4 (1+gL)]/ [WACC-gL]
HV4 = Vop, at 4 =
$1.155
150
151
152 Thurman's time line of expected free cash flows and horizon value is shown below.
153
15%
5%
A
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
Year
FCF
Horizon value
B
0
C
1
−$20
D
2
$80
E
3
$100
Present value of HV4 =
$660,375
Present value of free cash flows =
Total value of operations at Year 0, Vop, at t=0 =
$171,745
$832,120
F
4
$110
$1.155
There is more than one correct way to find the present value of the FCFs and the horizon value. For example,
you could find the total cash flows, as shown below, which are equal to the free cash flows except for the last
period, when they are equal to the sum of the free cash flow and the horizon value. (It is as though you
received the FCF at Year 4 and then "sold" the operations and received cash equal to the horizon value.) You
could then find present value of the combined free cash flows and horizon value.
Year
FCF
Horizon value
Combined FCF and HV
0
1
−$20
2
$80
3
$100
−$20,00
$80,00
$100
PV of combined FCF and HV =
Total value of operations at Year 0, Vop, at t=0 =
4
$110
$1.155
$1.265
$832,12
Here is a third way to find the present value of the FCFs and the horizon value. The basic idea is to find the
value of operations at each date. For the last date, the value of operations is the horizon value. For the
previous date, the value of operations is equal to the present value of the sum of the next date's value of
operations and FCF. For example, if you sell the operations immediately after receiving the FCF at Year 3,
then the purchaser would receive the FCF at Year 4 plus the value of operations at Year 4 (which is the
present value of all cash flows beyond Year 4).
Year
FCF
Horizon value
Vop,t =
(FCFt+1 + Vop,t+1)/
(1+WACC)
2018
2019
−$20,00
2020
$80,00
2021
$100,00
2022
$110,00
$1.155
$832,12
$976,94
$1.043,48
$1.100,00
$1.155,00
Optional Material. You may have noticed that we could have defined the horizon date at Year 3 because
we have an estimate of the Year 4 free cash flow, which is expected to grow at a constant rate thereafter.
However, we recommend defining the horizon date as the last date in the forecast period even if growth
becomes constant at or prior to this date because we have found that this leads to fewer errors. But we
illustrate this approach below for the interested reader.
Free cash flow at beginning of the constant growth phase (FCF 4) =
$110
Weighted average cost of capital (WACC) =
15%
A
B
C
205
D
Constant growth rate (gL) =
206
HV3 = Vop, at 3 = FCF4 / [WACC-gL]
207
HV3 = Vop, at 3 =
E
F
5%
$1.100
208
209
210 Thurman's time line of expected free cash flows and horizon value is shown below.
211
212
Year
0
1
2
3
213
FCF
−$20
$80
$100
214
Horizon value
$1.100
215
216
Present value of HV4 =
217
$723,268
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
Present value of free cash flows =
Total value of operations at Year 0, Vop, at t=0 =
$108,852
$832,120
Following is a summary of the steps used in estimating Thurman Corporation's value of operations.
Figure 7-3
Thurman Corporation's Value of Operations (Millions of Dollars)
INPUTS:
gL =
5%
Projections
WACC =
15%
Year
0
1
2
FCF
−$20,00
$80,00
↓
↓
FCF1
FCF2
3
$100,00
↓
FCF3
4
$110,00
↓
FCF4
235
──────
──────
──────
──────
236
237
(1+WACC)1
↓
↓
↓
↓
⟵ ⟵⤶
⟵⟵⟵⟵
⟵⟵⟵⟵
⟵⟵⟵⟵
⟵⟵⟵⟵
(1+WACC)2
↓
↓
↓
↓
↓
(1+WACC)3
↓
↓
↓
↓
↓
↓
⟵⤶
⟵⟵⟵⟵
⟵⟵⟵⟵
(1+WACC)4
↓
↓
↓
↓
↓
↓
↓
⟵⤶
$1.155,000
238
239
240
241
242
243
244
245
−$17,391
$60,491
$65,752
$62,893
$660,375
PVs of FCFs
PV of HV
246
247
Vop =
⟵⤶
⟵⟵⟵⟵
⟵⟵⟵⟵
⟵⟵⟵⟵
↓
$832,12
248
249
250
251
252
253
254
7-7 Application of the FCF Valuation Model to MicroDrive
= ──────
(1+WACC)4
255
256
257
258
259
260
261
262
263
264
265
266
267
268
A
B
C
D
E
We begin with MicroDrive's most recent financial statements and selected additional data.
Figure 7-4
MicroDrive’s Most Recent Financial Statements (Millions, Except for Per Share Data)
INCOME STATEMENTS
BALANCE SHEETS
2015
2016 Assets
Net sales
$ 4.760
$ 5.000
Cash
$
COGS (excl. depr.)
3.560
3.800
ST Investments
Depreciation
170
200 Accounts receivable
Other operating expenses
480
500 Inventories
EBIT
$
550
$
500
Total CA
$
Interest expense
100
120 Net PP&E
Pre-tax earnings
$
450
$
380
Total assets
$
269 Taxes (40%)
270 NI before pref. div.
271 Preferred div.
272 Net income
273
274
275
276
277
278
279
280
281
Other Data
Common dividends
Addition to RE
Tax rate
Shares of common stock
Price per share
$
$
180
270
8
262
$48
$214
40%
50
$40,00
$
$
152
228 Liabilities and Equity
8 Accounts payable
220 Accruals
$50
$170
40%
50
$27,00
Notes payable
Total CL
Long-term bonds
Total liabilities
Preferred stock
Common stock
Retained earnings
Total common equity
Total liabs. & equity
$
2015
60
40
380
820
1.300
1.700
3.000
190
280
130
600
1.000
$ 1.600
100
500
800
$ 1.300
$ 3.000
$
F
$
$
$
$
$
$
2016
50
0
500
1.000
1.550
2.000
3.550
200
300
280
780
1.200
1.980
100
500
970
1.470
3.550
$
$
Weighted average
10,50%
10,97%
282 cost of capital (WACC)
283
284
285 The first step is to calculate the key performance measures that determine free cash flows.
286
287 Figure 7-5
288 Key Performance Measures for MicroDrive (Millions of Dollars)
289
MicroDrive
290
2015
2016
291 Calculating Net Operating Profit after Taxes (NOPAT)
292
NOPAT = EBIT(1 − T)
$330
$300
293 Calculating Net Operating Working Capital (NOWC)
294
Operating current assets
$1.260
$1.550
295 − Operating current liabilities
$470
$500
296
NOWC
$790
$1.050
297 Calculating Total Net Operating Capital (OpCap)
298
NOWC
$790
$1.050
299 + Net PP&E
$1.700
$2.000
300
OpCap
$2.490
$3.050
301
Investment in operating capital
$560
302 Calculating Free Cash Flow (FCF)
303 FCF = NOPAT – Investment in operating capital
−$260
304 Calculating Return on Invested Capital (ROIC)
305
ROIC = NOPAT/Total net operating capital
13,25%
9,84%
306 Calculating the Operating Profitability Ratio (OP)
307
OP = NOPAT/Sales
6,93%
6,00%
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
A
B
C
Calculating the Capital Requirement Ratio (CR)
CR = (Total net operating capital)/Sales
D
E
52,31%
F
61,00%
The next step is to forecast sales, NOPAT, and total net operating capital. We do this by estimating future sales' growth rates, operating
profitability ratios, and capital requirement ratios, as shown in Panel A in the Figure below.
Yearly sales are forecast by letting the previous year's sales increase by the forecasted sales growth rate. Operating profitability and
total net operating capital in a forecasted year are assumed to be proportional to sales in that year.
Figure 7-6
MicroDrive's Forecast of Operations for the Selected Scenario (Millions of Dollars, Except for Per Share Data)
Status Quo
Industry
MicroDrive
MicroDrive
Panel A:
Actual
Actual
Forecast
Operating Ratios
2016
2015
2016
2017
2018
g = Sales growth rate
15%
5%
10%
8%
OP = NOPAT/Sales
6,92%
6,9%
6%
6%
6%
CR = OpCap/Sales
46,0%
52,3%
61%
61%
61%
Tax rate
40%
40%
40%
40%
40%
Panel B:
Actual
Forecast
Operating Items
2016
2017
2018
Net sales
$5.000
$5.500
$5.940
Net operating profit after taxes
$300
$330
$356
Total net operating capital (OpCap)
$3.050
$3.355
$3.623
FCF = NOPAT – Investment in OpCap
−$260
$25
$88
Growth in FCF
252%
ROIC = NOPAT/OpCap
9,84%
9,84%
9,84%
Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations.
The next step is to estimate the horizon value and the value of operations, beginning with the horizon value.
Free cash flow at beginning of the constant growth phase (FCF 2021) =
$216,892
Weighted average cost of capital (WACC) =
Constant growth rate (gL) =
10,97%
5%
𝐇𝐕𝟐𝟎𝟐𝟏 = 𝐕𝐨𝐩, 𝟐𝟎𝟐𝟏 =
𝐅𝐂𝐅𝟐𝟎𝟐𝟏 (𝟏 + 𝐠 𝐋 )
𝐖𝐀𝐂𝐂 − 𝐠 𝐋
HV2021 = Vop, 2021 = [FCF2021 (1+gL)]/ [WACC-gL]
HV2021 = Vop, 2021 =
$3.814,678
358
359
360 MicroDrive's time line of expected free cash flows and horizon value is shown below.
A
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
Year
FCF
Horizon value
B
C
D
E
F
2016
2017
$25,000
2018
$88,000
2019
$127,710
2020
$206,564
Present value of HV =
Present value of free cash flows =
Total value of operations at Year 0, Vop, at t=0 =
The figure below shows a summary of these calculations.
Figure 7-7
MicroDrive Inc.'s Value of Operations (Millions of Dollars)
INPUTS:
Scenario:
gL =
5%
WACC =
10,97%
Year
2016
2017
2018
FCF
$25,000
$88,000
↓
↓
FCF2017
FCF2018
──────
383
384
395
396
PVs of FCFs
PV of HV
$22,529
$71,461
$93,456
$136,217
$128,889
$2.266,887
Status Quo
Projections
2019
$127,710
↓
FCF2019
──────
1
385
386
387
388
389
390
391
392
393
394
$2.266,887
$452,552
$2.719,439
(1+WACC)
↓
↓
↓
↓
⟵⤶
⟵⟵⟵⟵
⟵⟵⟵⟵
⟵⟵⟵⟵
⟵⟵⟵⟵
⟵⟵⟵⟵
(1+WACC)
↓
↓
↓
↓
↓
2020
$206,564
↓
FCF2020
──────
2
⟵⤶
⟵⟵⟵⟵
⟵⟵⟵⟵
⟵⟵⟵⟵
⟵⟵⟵⟵
──────
3
(1+WACC)
(1+WACC)4
↓
↓
↓
↓
↓
↓
↓
↓
↓
↓
↓
↓
⟵⤶
↓
⟵⟵⟵⟵
⟵⤶
⟵⟵⟵⟵ ⟵⟵⟵⟵
⟵⟵⟵⟵ ⟵⟵⟵⟵
↓
Vop = $2.719,44
397
398
Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations.
399
400
401
402
403 Estimating MicroDrive's Intrinsic Stock Price per Share
404
405
Value of operations =
$2.719,44
406
Weighted average cost of capital (WACC) =
10,97%
407
Short-term investments =
$0
408
Short-term debt (notes payable) =
$280
409
Long-term debt (bonds) =
$1.200
410
Preferred stock =
$100
411
Number of shares of common stock =
50
A
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
B
C
D
E
F
MicroDrive's total value is the sum of value of operations and the short-term investments:
Value of operations
+ ST investments
Estimated total intrinsic value
$2.719,44
$0
$2.719,44
The next step is to estimate the intrinsic value of equity, which is the remaining total value after accounting for the claims of debtholders
and preferred stockholders:
Value of operations
+ ST investments
Estimated total intrinsic value
− All debt
− Preferred stock
Estimated intrinsic value of equity
$2.719
$0
$2.719,44
$1.480
$100
$1.139,44
The final step is to estimate the intrinsic common stock price per share, which is the estimated intrinsic value of equity divided by the
number of shares of common stock:
Value of operations
+ ST investments
Estimated total intrinsic value
− All debt
− Preferred stock
Estimated intrinsic value of equity
÷ Number of shares
Estimated intrinsic stock price =
$2.719,44
$0
$2.719,44
$1.480
$100
$1.139,44
50
$22,79
The figure below shows a summary of the previous calculations.
Figure 7-8
MicroDrive Inc.'s Intrinsic Stock Price (Millions, Except for Per Share Data)
INPUTS:
gL =
5%
WACC =
10,97%
Year =
2017
2018
2019
Projected FCF =
$25
$88,0
$127,71
448
449
450
2020
2021
451
$206,564
$216,892
452
453 Horizon Value:
Value of operations
454
+ ST investments
𝐅𝐂𝐅𝟐𝟎𝟐𝟏 (𝟏+𝐠 𝐋 )
𝐇𝐕𝟐𝟎𝟐𝟏 =
455
=
$3.815
Estimated total intrinsic value
(𝐖𝐀𝐂𝐂 − 𝐠 𝐋 )
456
− All debt
457 Value of Operations:
− Preferred stock
458
Present value of HV $2.266,89
Estimated intrinsic value of equity
459
+ Present value of FCF $452,55
÷ Number of shares
460
Value of operations = $2.719,44
Estimated intrinsic stock price =
461
462
Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all calculations.
463
464
A
B
C
D
E
F
465
466 7-8 Do Stock Prices Reflect Long-Term or Short-Term Cash Flows?
467
468
Managers often claim that stock prices are "short-term" in nature in the sense that they reflect what is happening in the near-term and
469
ignore the long-term. We can use MicroDrive's results to shed light on this claim.
470
471
472
We previously estimated MicroDrive's current value of operations. We also estimated MicroDrive's horizon value at Year 5 and
473 calculated its present value. If we divide the present value of the horizon value, we can estimate how much of MicrDrive's value is due to
cash flows occurring beyond Year 5. In other words, we can determine how much of MicroDrive's value is due to long-term cash flows
474
and how much is due to short-term cash flows.
475
476
Inputs:
477
478
479
480
481
482
483
484
485
486
487
Weighted average cost of capital =
Horizon year =
Horizon value at Year 5 (HV5) =
10,97%
5
$3.814,678
Value of operations at Year 0 (Vop,0) =
$2.719,439
Present value of the horizon value =
Value of operations at Year 0 =
$2.266,887
$2.719,439
Analysis:
Results:
Percent of current value due to long-term cash flows (i.e., PV of HV 5) =
488
489
Percent of current value due to short-term cash flows =
490
491 For most stocks, the percentage of the current price that is due to long-term cash flows is over 80%.
83%
17%
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
7-9 Using the Free Cash Flow Valuation Model to Identify Value Drivers
We can use the free cash flow valuation model we developed previously for MicroDrive to determine how the inputs (sales growth,
operating profitability, and capital requirements) affect the value of operations and intrinsic stock price. It is very easy to do this in Excel
by using the Scenario Manager feature. Following is an explantion of how to use this feature.
The Scenario Manager allows you to specify values for particular cells and then save those values as a "scenario." If you later change the
values in the cells, perhaps to see the impact that the change has on an output, the Scenario Manager allows you to restore the saved
scenario without having to re-input the original values. You can create numerous different scenarios, and you can even have the Scenario
Manager create a summary that shows the values of the input cells and the values of the output cells for each scenario that you created.
To create a scenario, go to the Data tab in the menu, look in the Data Tools section for What-If Analysis, and then select Scenario
Manager. This will open a dialog box that shows seven existing scenarios. If you select the button for "Add…", you will get another dialog
box asking you to give the scenario a name and to specify the "Changing cells." The "Changing cells" are the cells with values that you
want the Scenario Manager to save. For example, we want to save the values for MicroDrive's estimated sales growth rates, operating
profitabiltiy ratio, and capital requirement ratio.
To create a scenario, go to the Data tab in the menu, look in the Data Tools section for What-If Analysis, and then select Scenario
Manager. This will open a dialog box that shows seven existing scenarios. If you select the button for "Add…", you will get another dialog
box asking you to give the scenario a name and to specify the "Changing cells." The "Changing cells" are the cells with values that you
want the Scenario Manager to save. For example, we want to save the values for MicroDrive's estimated sales growth rates, operating
profitabiltiy ratio,
and capital requirement
ratio.
A
B
C
D
E
F
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
After specifying the "Changing cells", click "Ok" and you will get a new dialog box asking you to input the values into the changing cells
that you want for this scenario. There will already be values shown, which are the values currently in those cells. So if you have already
put the values into the cells in the Excel workbook, you won't have to re-enter them in the dialog box, you can simply click "Ok" and you
will have created a new scenario.
The original dialog box gives you several options, including adding a scenario, deleting a scenario, and editing a scenario. It also give you
the option to run a "Summary." If you select the "Summary" button, you get a dialog box asking you to specify some "Results" cells. For
example, we specified the cells in this worksheet that have the value of operations, the intrinsic stock price, and the return on invested
capital for the last year in the forecast horizon.
After selecting the "Results" cells, you can click "Ok" and the Scenario Manager will create a new worksheet named "Scenario Summary".
This new sheet contains the name of each scenario, the values in the "Changing cells", and the values in the "Results cells. We copied the
information from the "Scenario Summary" into the table below and then formatted the table to make it a bit more reader-friendy.
Figure 7-9
Value Drivers for MicroDrive Inc. (Millions, Except for Per Share Data)
(1)
Status Quo
(2)
Higher Sales Growth
(Only)
Scenario
(3)
Higher
(4)
Operating Better Capital
Profitabilit
Utilization
y (Only)
(Only)
Inputs
545
546
547
548
Sales growth in 1st year
Sales growth in 2nd year
Sales growth in 3rd year
Long-term sales growth (gL)
10%
8%
7%
5%
11%
9%
8%
6%
10%
8%
7%
5%
10%
8%
7%
5%
549
550
Operating profitability (OP)
Capital requirement (CR)
Weighted average cost
of capital (WACC)
6%
61%
6%
61%
7%
61%
6%
52%
10,97%
10,97%
10,97%
10,97%
$2.719
$22,79
$2.713
$22,67
$3.682
$42,04
$3.576
$39,91
551
552
Results
Value of operations
Intrinsic stock price
Return on invested
capital (ROIC)
553
554
555
9,84%
9,84%
11,48%
556
557
558 To better understand why growth doesn't always add value, we can express the horizon value as:
559
560
561
562
L
T
op(at HorizonYear T )
T
563
V
11,54%
(1+ g )ROIC − WACC
= OpCap 1+
WACC − g L
564
565
566
567
568
569
570
571
572
573
574
575
(1+ g L )ROICT − WACC
V
=
OpCap
T 1+
A op(at HorizonYear
B T)
C
D
E
F
WACC − g L
If the numerator in the fraction in brackes, (1+gL) ROIC − WACC, is negative, then the value of operations will be less than the total net
operation capital, OpCapT. If ROIC < WACC/(1+WACC), then growth hurts value. The 2-way data table below show the difference between
the value operations and the amount of operating capital for different combinations of growth and ROIC. For input values, we use values
similar to those of MicroDrive's at the horizon.
OpCap =
gL =
576
577
578
579
580
ROIC =
WACC =
581
Vop − OpCap =
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
9,84%
10,97%
Output from equation above in yellow.
$3.815
-$460
A Two-Way Data Table Showing How Combinations of Growth and ROIC Affect the Value of Operations Minus
the Value of Operating Capital
Combinations of growth and ROIC that have Vop < OpCap are shown in pink. Notice that for very low values of ROIC, such as the first row
with ROIC = 9.7%, growth reduces value (you can see this by looking across the row. For very high values of ROIC, such as the last row
with ROIC = 11%, growth adds value. For other combinations, it depends on the relative values of growth, ROIC, and WACC.
gL
ROIC
582
583
584
585
586
587
588
589
590
591
592
593
Vop =
Input Values (Base Case)
$4.274
5,0%
−$460
9,70%
9,80%
9,84%
9,90%
10,00%
10,10%
10,20%
10,30%
10,40%
10,50%
10,60%
10,70%
10,80%
10,90%
11,00%
0,0%
-$495
-$456
-$442
-$417
-$378
-$339
-$300
-$261
-$222
-$183
-$144
-$105
-$66
-$27
$12
2,5%
-$519
-$467
-$448
-$415
-$363
-$312
-$260
-$208
-$156
-$105
-$53
-$1
$50
$102
$154
613 7-11 Valuing Common Stocks with the Dividend Growth Model
614
615 The Discounted Dividend Approach
5,0%
-$562
-$487
-$460
-$412
-$337
-$261
-$186
-$111
-$36
$39
$115
$190
$265
$340
$415
7,5%
-$668
-$536
-$488
-$403
-$271
-$139
-$6
$126
$259
$391
$524
$656
$788
$921
$1.053
A
616
617
618
619
620
621
622
623
624
625
B
E
D1
D2
+
( 1 + rs )
( 1 + rs )
+
Valuing a Constant Growth Stock
In the constant growth model, we assume that the dividend and stock will grow forever at a constant growth rate. Naturally, assuming a consta
growth rate for the rest of eternity is a rather bold assumption. However, considering the implications of imperfect information, information
asymmetry, and general uncertainty, the assumption of constant growth is often reasonable. It is reasonable to guess that a given stock will
experience ups and downs throughout its life. By assuming constant growth, we are trying to find the average of the good times and the bad ti
and we assume that we will see both scenarios over the firm's life. In addition to a constant growth rate, we also need the estimated long-term
required return for the stock, and it too must be constant. If these variables are constant, our price equation for common stock simplifies to th
following expression:
D1
( rs – g L )
Generally speaking, the long-run growth rate of a firm is likely to fall between 5% and 8% a year.
Example: Value of a Constant Growth Stock
A firm just paid a $1.15 dividend and its dividend is expected to grow at a constant rate of 8%. What is its stock price, assuming it has a requir
return of 13.4%?
654
655
656
D0 =
657
gL =
8%
658
659
rs =
13,4%
P0 =
$1,15
D1
( rs – g L )
661
662
663
664
. . . .
2
The dividend stream theoretically extends on out forever, i.e., to N = infinity. Obviously, it would not be feasible to deal with an infinite stream
dividends, but fortunately, a relatively simple equation has been developed that can be used to find the PV of the dividend stream, provided it
growing at a constant rate.
645 P0 =
660
F
Here is the basic dividend valuation equation:
627
646
647
648
649
650
651
652
653
D
The value of any financial asset is the present value of the future cash flows provided by the asset. When an investor buys a share of stock, he o
typically expects to receive cash in the form of dividends and then, eventually, to sell the stock and to receive cash from the sale. However, the
price the first investor receives is dependent upon the dividends the next investor expects to earn, and so on for different generations of inves
Thus, the stock's value ultimately depends on the cash dividends the company is expected to provide and the discount rate used to find the pre
value of those dividends.
626 P0 =
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
C
P0 =
$23,00
=
D0 (1 + gL) =
( rs – g L )
A
B
C
D
E
F
665
666
667 Expected Rate of Return on a Constant Growth Stock
668
669 Using the constant growth equation introduced earlier, we can re-work the equation to solve for r s. In doing so, we are now solving for an expe
670 return. The expression we are left is:
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
D1
𝐫ො =
gL
+
P0
This expression tells us that the expected return on a stock comprises two components. First, it consists of the expected dividend yield, which
simply the next expected dividend divided by the current price. The second component of the expected return is the expected capital gains yie
The expected capital gains yield is the expected annual price appreciation of the stock, and is given by g L. This shows us the dual role of gL in t
constant growth rate model. Not only does g indicate expected dividend growth, but it is also the expected stock price growth rate.
Example: Expected Rate of Return on a Constant Growth Stock
You buy a stock for $23, and you expect the next annual dividend to be $1.242. Furthermore, you expect the dividend to grow at a constant rat
8%. What is the expected rate of return on the stock, and what is the dividend yield of the stock?
Inputs:
689
P0
$23,00
690
D1
$1,242
691
692
693
gL
8%
𝐫ො =
13,40%
694
695
Dividend yield =
5,40%
696
697
698 What is the expected price of this stock in 1 year?
699
700 Application of Constant Growth Model at t=1
701
D2
702 P1 =
( rs – g L )
703
704
705
D2 =
1,34136
P1 =
$24,84
706
707
708
709 Valuing Nonconstant Growth Stocks
710
711
712 For many companies, it is unreasonable to assume that they grow at a constant growth rate. Hence, valuation for these companies proves a lit
713 more complicated. The valuation process, in this case, requires us to estimate the short-run nonconstant growth rate and predict future divid
Then, we must estimate a constant long-term growth rate at which the firm is expected to grow. Generally, we assume that after a certain poin
time, all firms begin to grow at a rather constant rate. Of course, the difficulty in this framework is estimating the short-term growth rate, how
the short-term growth will hold, and the long-term growth rate.
For many companies, it is unreasonable to assume that they grow at a constant growth rate. Hence, valuation for these companies proves a lit
more complicated.
The valuation B
process, in this
to estimate the short-run
nonconstant
A
C case, requires us D
E
F growth rate and predict future divid
714 Then, we must estimate a constant long-term growth rate at which the firm is expected to grow. Generally, we assume that after a certain poin
715 time, all firms begin to grow at a rather constant rate. Of course, the difficulty in this framework is estimating the short-term growth rate, how
716 the short-term growth will hold, and the long-term growth rate.
717
718
719
720 Figure 7-10
721 Illustrative Dividend Growth at Different Rates
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
$2,65
$1,65
Constant Growth: 8%
$1,15
Zero Growth
$0,65
Declining Growth:
8%
0
1
2
3
4
5
Specifically, we will predict as many future dividends as we can and discount them back to the present. Then we will treat all dividends to be
received after the convention of constant growth rate with the Gordon constant growth model described above. The point in time when the
dividend begins to grow constantly is called the horizon date. When we calculate the constant growth dividends, we solve for the horizon valu
(also called a terminal value or a continuing value) as of the horizon date. The horizon value can be summarized as:
751 HVT =
752
753
754
755
756
757
758
759
760
761
762
763
764
Long-Term Growth:
8%
$2,15
737
738
739
740
741
742
743
744
745
746
747
748
749
750
End of Nonconstant
Growth Period
PT =
DT+1
=
( rs – g L )
DT (1 + g)
( rs – g L )
This condition holds true, where T is the horizon date. The horizon value can be described as the expected value of the stock at the time perio
corresponding to the horizon date.
A company's stock just paid a $1.15 dividend, which is expected to grow at 30% the first year, 20% the second year, and 10% the third year. Af
three years the dividend is expected to grow constantly at 8% forever. The stock's required return is 13.4%; what is the price of the stock tod
Figure 7-11
Process for Finding the Value of a Nonconstant Growth Stock
INPUTS:
A
D0 =
B
$1,15
C
D
Last dividend the company paid.
766
rs =
13,4%
Stockholders' required return.
767
g0,1 =
30%
Growth rate for Year 1 only.
768
g1,2 =
20%
Growth rate for Year 2 only.
769
g2,3 =
770
771
772
773
774
gL =
10%
8%
Growth rate for Year 3 only.
Constant long-run growth rate for all years after Year 3.
765
Year
Growth rate
Dividend
Dt
775
776
777
0
D0
$1,15
778
779
782
783
784
785
786
787
788
789
3
10%
D2(1+g1,2)
$1,495
↓
D1
$1,794
↓
D2
$1,973
↓
D3
──────
──────
──────
2
(1+rs)
↓
↓
↓
↓
↓
PVs of Dividends
𝟑
PV of 𝐏
790
791
Projections
2
20%
D1(1+g1,2)
(1+rs)
781
⟵⤶
$27,065 ⟵⟵⟵⟵
⟵⟵⟵⟵
Vop =
$31,13
⟵⟵⟵⟵
⟶∞
8%
𝟑
HV3 = 𝐏
3
(1+rs)
↓
↓
↓
↓
↓
↓
$1,318 ⟵⤶
$1,395 ⟵⟵⟵⟵
$1,353 ⟵⟵⟵⟵
↓
F
1
30%
D0(1+g0,1)
1
780
E
↓
↓
↓
↓
↓
↓
↓
⟵⤶
↓
D3(1+gL)
───────
(rs− gL)
𝟑 =
𝐏
𝟑 =
𝐏
𝟑 =
𝐏
↓
$2,131
5,400%
↓
$39,468
$39,468
= ──────
⟵⟵⟵⟵
(1+0.134)3
792
793 Note: Numbers in the figure are shown as rounded for clarity in reporting. However unrounded values are used for all
794 calculations.
795
796
797 7-12 Market Multiple Analysis
798
799 Use the following data in the market multiple approach to estimate the stock price per share.
800
801
Forecasted earnings per share (EPS) =
$7,70
802
Average peer price/earnings (P/E) ratio =
12
803
804
Estimated stock price:
$92,40
805
806
807
808 7-14 Preferred Stock
809
810
Consider an issue of preferred stock that pays an $8 dividend and has a required return of 8%. What is the value of this preferred stock?
811
812
813
814
815
A
Vps =
B
Dps
C
÷
D
rps
=
$8,00
÷
8,00%
=
$100,00
E
F
816
817
818
Some preferred stock has a maturity date. Consider a firm whose preferred stock matures in 50 years, pays a $8 annual dividend, has a par va
819
of $100, and has a required return of 6%. What is the price of this preferred stock?
820
821
822
823 Years to Maturity (N):
824 Annual Dividend (PMT):
825 Par value (FV):
826 Required return, rd (I/YR):
50
$8
$100
6%
827
828
829
Vps =
$131,52
G
1
2
H
10/27/2015
3
4
5
6
7
8
9
10
11
12
13
14
15
16
xpected free cash flows.
17 Because the FCF's are
cash flow divided by the
18 cost of capital:
19
20
21
22
23
24
25
26
27
28
value after accounting
29for the claims of debtholders
30
31
32
33
34
35
36
37
38
estimated intrinsic value
39 of equity divided by the
40
41
42
43
44
45
46
47
48
49
50
51
I
J
K
L
M
N
G
H
52
53
54
55
56
57
Value
58of operations
$100
+ 59
ST investments
$2
Estimated total60
intrinsic value
$102
61
− All debt
$28
− 62
Preferred stock
$4
Estimated intrinsic63
value of equity
$70
÷ Number
64
of shares
5
Estimated intrinsic
65 stock price
$14,00
66
67
68
69
70
71
72
73
74$28
75
76
77
78
Preferred stock = $4
79
80
81
82
83
84
85
86
87
88
h Flow Grows at a89
Constant Rate
90
91
92
93
94
95
is:
96
97
98
99
100
101
102
103
I
J
K
L
M
N
Data for Pie Charts
Short-term investments =
Value of operations =
Total =
$2
$100
$102
Debt =
Preferred stock =
Estimated equity value =
Total =
$28
$4
$70
$102
G
H
104
105
106
107
108
109
110
111
112
is:
113
114
115
116
117
118
119
120
121
122
123
124
ee Cash Flow Grows
125 at a Nonconstant Rate
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
I
J
K
L
M
N
G
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
H
I
J
K
L
M
N
G
H
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
of operations.
220
221
222
223
224
225
226
227
228
229
230
231
232 ⟶ ⟶ ⟶ ↴
↓
233
HV = Vop(t=4)
234
↓
235
FCF4(1+gL)
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
─────────
(WACC− g L)
↓
$115,500
10,00%
↓
$1.155,000
↓
⟵⟵⟵⤶
I
J
K
L
M
N
G
data.
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
Industry
2016
15,04%
6,92%
H
I
J
K
L
M
N
G
H
308
309
46,00%
310
311
312
313
by estimating future sales'
314 growth rates, operating
below.
315
316
317
ed sales growth rate. Operating
profitability and
318
es in that year.
319
320
321
322
323
324MicroDrive
325 Forecast
326
2019
2020
327
7%
5%
328
6%
6%
329
61%
61%
330
40%
40%
331 Forecast
332
2019
2020
333
$6.356
$6.674
334
$381
$400
335
$3.877
$4.071
336
$128
$207
337
45,1%
61,7%
338
9,84%
9,84%
339
340
unrounded values are used for all calculations.
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
I
2021
5%
6%
61%
40%
2021
#######
#######
#######
#######
5,0%
9,84%
J
K
L
M
N
ons
G
361
362
2021
363 $216,892
364 $3.814,678
365
366
367
368
369
H
I
370
371
372
373
374
375
376
377
378
379
2021
380 $216,892
381
↓
FCF2021
382
383 ──────
384 (1+WACC)5
↓
385
386
↓
↓
387
388
↓
↓
389
↓
390
391
↓
392
↓
393 ⟵⤶
394 $3.814,678
⟶
↴
↓
↓
HV = Vop(2021)
↓
FCF2021(1+gL)
─────────
(WACC− g L)
↓
$227,736
0,0597
↓
$3.814,678
↓
⟵⟵⤶
395 = ──────
5
396 (1+WACC)
397
398
unrounded values are used for all calculations.
399
400
401
402
403
404
405
406
407
408
409
410
411
J
K
L
M
N
G
H
412
ents:
413
414
415
416
417
418
value after accounting
419
for the claims of debtholders
420
421
422
423
424
425
426
427
428
estimated intrinsic value
429 of equity divided by the
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
$2.719
454
$0
455
$2.719
456
$1.480
457
$100
458
$1.139
459
50
460
$22,79
461
462
unrounded values are used for all calculations.
463
464
I
J
K
L
M
N
G
H
465
466
467
468
ey reflect what is happening in the near-term and
469
470
471
472
d MicroDrive's horizon value at Year 5 and
an estimate how much
of MicrDrive's value is due to
473
MicroDrive's value is due to long-term cash flows
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
ve to determine how the inputs (sales growth,
497
ntrinsic stock price. It is very easy to do this in Excel
498
eature.
499
500
501
those values as a "scenario."
If you later change the
502
enario Manager allows
you to restore the saved
503
erent scenarios, and 504
you can even have the Scenario
the output cells for each
505scenario that you created.
506
507
508
r What-If Analysis, and
then select Scenario
509
t the button for "Add…",
510you will get another dialog
hanging cells" are the
cells with values that you
511
oDrive's estimated sales
512 growth rates, operating
513
I
J
K
L
M
N
r What-If Analysis, and then select Scenario
t the button for "Add…", you will get another dialog
hanging cells" are the cells with values that you
oDrive's estimated sales growth rates, operating
G
H
I
514
515
516
ing you to input the values into the changing cells
517
lues currently in those cells. So if you have already
518
n the dialog box, you can simply click "Ok" and you
519
520
521
522
ng a scenario, and editing a scenario. It also give you
523
ox asking you to specify some "Results" cells. For
524
he intrinsic stock price, and the return on invested
525
526
527
528
reate a new worksheet
named "Scenario Summary".
529
, and the values in the530
"Results cells. We copied the
he table to make it a bit
531more reader-friendy.
532
533
534
535
536
537
Scenario
538
539
(7)
540
(5)
(6)
Improve
541 Improve
Improve
Growth,
542 Growth and Growth and
OP, and
543
OP
CR
CR
544
J
K
L
M
Additional information not in textbook
(8)
Status Quo
(9)
but Lower Better OP and
WACC
CR
545
546
547
548
11%
9%
8%
6%
11%
9%
8%
6%
11%
9%
8%
6%
10%
8%
7%
5%
10%
8%
7%
5%
549
550
7%
61%
6%
52%
7%
52%
6%
61%
7%
52%
551
552
10,97%
10,97%
10,97%
9,50%
10,97%
553
554
$3.880
$46,00
$3.751
$43,42
$4.918
$66,76
$3.690
$42,19
$4.538
$59,16
555
556
557
558
559
560
561
562
563
11,48%
11,54%
13,46%
9,84%
13,46%
ROICT − WACC
WACC − g L
N
ROICT − WACC
G
WACC − g L 564
H
565
566
567
value of operations will be less than the total net
568
2-way data table below show the difference between
569
of growth and ROIC. For input values, we use values
570
571
572
573
574
575
576
577
578
579
580
581
582
583
ct the Value of Operations
Minus
584
585
586
587
at for very low values of ROIC, such as the first row
588
For very high values of ROIC, such as the last row
589
ive values of growth, ROIC, and WACC.
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
9,5%
-$1.013
-$695
-$580
-$377
-$58
$260
$579
$897
$1.215
$1.534
$1.852
$2.171
$2.489
$2.807
$3.126
I
J
K
L
M
N
G
H
I
616
617
by the asset. When an investor buys a share of stock, he or she
618
the stock and to receive cash from the sale. However, the
619
pects to earn, and so on for different generations of investors.
620
ected to provide and the discount rate used to find the present
621
622
623
624
625
626
DN
627
( 1 + rs ) N
628
sly, it would not be feasible
to deal with an infinite stream of
629
be used to find the PV630
of the dividend stream, provided it is
631
632
633
634
635
er at a constant growth
636rate. Naturally, assuming a constant
g the implications of imperfect
information, information
637
onable. It is reasonable
638 to guess that a given stock will
trying to find the average
639 of the good times and the bad times,
nstant growth rate, we
640also need the estimated long-term
tant, our price equation
641for common stock simplifies to the
642
643
644
645
646
647
d 8% a year.
648
649
650
651
te of 8%. What is its 652
stock price, assuming it has a required
653
654
655
656
657
658
659
660
$1,2420
661
662
0,0540
663
664
J
K
L
M
N
G
H
I
665
666
667
668
to solve for r s. In doing
669so, we are now solving for an expected
670
671
672
673
674
675
ts. First, it consists of676
the expected dividend yield, which is
ent of the expected return
677 is the expected capital gains yield.
k, and is given by g L. 678
This shows us the dual role of gL in the
it is also the expected679
stock price growth rate.
680
681
682
683
684
ermore, you expect the dividend to grow at a constant rate of
685
of the stock?
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
h rate. Hence, valuation
712 for these companies proves a little
ort-run nonconstant 713
growth rate and predict future dividends.
ed to grow. Generally, we assume that after a certain point of
framework is estimating the short-term growth rate, how long
J
K
L
M
N
h rate. Hence, valuation for these companies proves a little
ort-run nonconstant growth rate
G and predictHfuture dividends.
I
J
K
L
M
N
ed to grow. Generally,
we assume that after a certain point of
714
framework is estimating
715 the short-term growth rate, how long
716
717
718
719
720
721
Data for figure:
Growth Rates
722
Year
Declining Zero
Constant
Nonconstant
723
1
-8%
0%
8%
30%
724
2
-8%
0%
8%
20%
725
Term Growth:
3
-8%
0%
8%
10%
726
8%
4
-8%
0%
8%
8%
727
5
-8%
0%
8%
8%
728
Dividend
729
Year
Declining Growth:
Zero Growth
-8%
Constant Growth:
Long-Term
8%
Growth: 8%
730 Growth: 8%
Constant
0
$1,15
$1,15
$1,15
$1,15
731
1
$1,06
$1,15
$1,24
$1,50
732
2
$0,97
$1,15
$1,34
$1,79
733
3
$0,90
$1,15
$1,45
$1,97
734
Zero Growth
4
$0,82
$1,15
$1,56
$2,13
735
736 Growth: 5
$0,76
$1,15
$1,69
$2,30
Declining
737
8%
738
739
740
741
742
743
ack to the present. Then
744we will treat all dividends to be
th model described above.
745 The point in time when the
constant growth dividends,
we solve for the horizon value
746
on value can be summarized
as:
747
748
749
750
751
752
753
cribed as the expected
value of the stock at the time period
754
755
756
757
rst year, 20% the second year, and 10% the third year. After
758
equired return is 13.4%; what is the price of the stock today?
759
760
761
762
763
764
G
H
765
766
767
768
769
770
771
772
773
774
775
776
777
𝟑
HV3 =778
779
↓
780D3(1+gL)
───────
781
782(rs− gL)
783
↓
$2,131
784
5,400%
785
786
↓
$39,468
787
788 ↓
789
𝟑
𝐏
790 = ──────
791
(1+rs)3
792
unrounded values are793
used for all
794
795
796
er share.
797
798
799
800
801
802
803
804
805
806
807
808
809
810
urn of 8%. What is the value of this preferred stock?
811
812
I
J
K
L
M
N
G
H
I
813
814
815
816
817
818
atures in 50 years, pays a $8 annual dividend, has a par value
819
820
821
822
823
824
825
826
827
828
829
J
K
L
M
N
O
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
P
Q
R
S
T
U
O
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
P
Q
R
S
T
U
O
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
P
Q
R
S
T
U
O
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
P
Q
R
S
T
U
O
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
P
Q
R
S
T
U
O
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
P
Q
R
S
T
U
O
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
P
Q
R
S
T
U
O
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
P
Q
R
S
T
U
O
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
P
Q
R
S
T
U
O
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
P
Q
R
S
T
U
O
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
P
Q
R
S
T
U
O
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
P
Q
R
S
T
U
O
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
P
Q
R
S
T
U
O
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
P
Q
R
S
T
U
O
P
Q
R
S
T
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
Year
Declining Growth:
Zero
-8%
Growth
Constant Growth:
Long-Term
8% Growth: 8%
0
1,1500
1,1500
1,1500
1,1500
1
1,0580
1,1500
1,2420
1,4950
2
0,9734
1,1500
1,3414
1,7940
3
0,8955
1,1500
1,4487
1,9734
4
0,8239
1,1500
1,5646
2,1313
5
0,7579
1,1500
1,6897
2,3018
U
Scenario Summary
Current Values:
Changing Cells:
$A$324 Status Quo
Status Quo
$F$327
8%
$G$327
7%
$H$327
5%
$E$327
10%
$E$328
6%
$E$329
61%
$C$282
10,97%
Result Cells:
$B$396
$2.719,44
$G$460
$22,79
$I$338
9,84%
Notes: Current Values column represents values of changing cells at
time Scenario Summary Report was created. Changing cells for each
scenario are highlighted in gray.
Status Quo
Higher Growth (Only)
Higher Growth (Only)
8%
7%
5%
10%
6%
61%
10,97%
9%
8%
6%
11%
6%
61%
10,97%
$2.719,44
$22,79
9,84%
$2.713,27
$22,67
9,84%
Higher OP (Only)
Higher OP (Only)
Better CR (Only)
Better CR (Only)
Improve Growth and OP
Improve Growth and OP
Improve Growth and CR
Improve Growth and CR
8%
7%
5%
10%
7%
61%
10,97%
8%
7%
5%
10%
6%
52%
10,97%
9%
8%
6%
11%
7%
61%
10,97%
9%
8%
6%
11%
6%
52%
10,97%
$3.681,78
$42,04
11,48%
$3.575,63
$39,91
11,54%
$3.879,93
$46,00
11,48%
$3.751,25
$43,42
11,54%
Improve Growth, OP, and CR
Lower WACC (Only)
Improve Growth, OP, and CR Lower WACC (Only)
9%
8%
6%
11%
7%
52%
10,97%
$4.917,91
$66,76
13,46%
Better OP and CR
Better OP and CR
8%
7%
5%
10%
6%
61%
9,50%
8%
7%
5%
10%
7%
52%
10,97%
$3.689,71
$42,19
9,84%
$4.537,97
$59,16
13,46%
SECTION 7-4
SOLUTIONS TO SELF-TEST
A company expects a constant FCF of $240 million per year forever. If the WACC is 12%, what is the value of
operations?
Expected FCF
WACC
$240
12%
Vop =
$2.000,00
A company has a current value of operations of $800 million. The company has $100 million in short-term
investments. If the company has $400 million in debt and has 10 million shares outstanding, what is the price per
share?
Vop
$800
ST investments
Total value
Debt
Value of equity
Number of shares
Price per share
$100
$900
$400
$500
10
$50,00
SECTION 7-5
SOLUTIONS TO SELF-TEST
A company expects to have a FCF in 1 year of $300, which is expected to grow at a constant rate of 3% forever. If the
WACC is 11%, what is the value of operations?
Expected FCF1 =
$330
Expected gL =
3%
WACC =
11%
Vop =
$4.125
A company's most recent free cash flow was $270. The company expects to have a FCF in 1 year of $300, which is
expected to grow at a constant rate of 3% forever. If the WACC is 11%, what is the value of operations?
Expected FCF1 =
$300
Expected gL =
3%
WACC =
11%
Notice that the FCF of $270 at t = 0 is irrelevant to the value of operations, because it occurred in the past. The value
of operations depends only on the future free cash flows.
Vop =
$3.750
A company's most recent free cash flow was $600 and is expected to grow at a constant rate of 4% forever. If the
WACC is 10%, what is the value of operations?
FCF0 =
$600
Expected gL =
4%
WACC =
10%
Vop =
$10.400
SECTION 7-6
SOLUTIONS TO SELF-TEST
A company expects to have a FCF at Year 10 of $600, which is expected to grow at a constant rate of 8% thereafter. If
the WACC is 8%, what is the value of operations at Year 10, HV 10?
Expected FCF12 =
$600
Expected gL =
4%
WACC =
8%
Vop =
$15.600
A company expects a FCF of −$10 million at Year 1 and a FCF of $20 million at Year 2. FCF is expected to grow at a 5%
rate after Year 2. If the WACC is 10%, what is the horizon value of operations; i.e., V op(Year 2)? What is the current
value of operations; i.e., Vop(Year 0)?
Long-term growth rate
WACC
5%
10%
Year
1
FCF1
Expected FCF
-$10,00
Vop(Year 2)
2
FCF2
$20,00
$420,00
PV of expected FCF
PV of expected Vop(Year 2)
$7,44
$347,11
Vop(Year 0)
$354,55
SECTION 7-7
SOLUTIONS TO SELF-TEST
Cathey Corporation currently has sales of $1,000, which are expected to grow by 10% from Year 0 to Year 1 and by 4% from Year 1
to Year 2. The company currently has and operating profitability (OP) ratio of 7% and a capital requirement (CR) ratio of 50% and
expects to maintain these ratios at their current levels. The current level of operating capital is $510. Use these inputs to forecast
free cash flow (FCF) for Years 1 and 2. Hint: You must first forecast sales, net operating profit after taxes (NOPAT), and total net
operating capital (OpCap) for each year.
Sales0 =
g0,1 =
g1,2 =
$1.000
10%
4%
OP = NOPAT/Sales =
CR = OpCap/Sales =
OpCap0 =
7%
50%
$510
Year
Growth rate in sales
Sales
NOPAT
OpCap
Investment in OpCap
FCF
Growth in FCF
0
$1.000
$510
1
10%
$1.100,00
$77,00
$550,00
$40,00
$37,00
2
4%
$1.144,00
$80,08
$572,00
$22,00
$58,08
57,0%
3
4%
$1.189,76
$83,28
$594,88
$22,88
$60,40
4,0%
Cathey Corporation has a 12% weighted average cost of capital. Cathey's free cash flows, estimated in the previous question, are
expected to grow at 4% beginning at Year 2 and continuing for the foreseeable future. What is the horizon value (use Year 2 for the
horizon)? What is the current value of operations?
Long-term growth rate
WACC
4%
12%
Year
1
FCF1
Expected FCF
$37,00
HV2 = Vop(Year 2)
2
FCF2
$58,08
$755,04
PV of expected FCF
PV of expected HV(Year 2)
$79,34
$601,91
Vop(Year 0)
$681,25
Cathey Corporation has $80 in short-term investments, $20 in short-term debt, $140 in long-term debt, $30 in preferred stock, and
10 shares of common stock outstanding. Use the value of operations from the previous question to estimate the intrinsic common
stock price per share.
Vop =
ST investments =
ST debt =
Long-term debt =
Preferred stock =
$681,25
$80,00
$20,00
$140,00
$30,00
Number of shares =
10
Vop
$681,25
ST investments
Value of equity
Number of shares
$80,00
$761,25
$160,00
$30,00
$571,25
10,00
Price per share
$57,13
Total value
All debt
Preferred stock
SECTION 7-11
SOLUTIONS TO SELF-TEST
If D1 = $3.00, P0 = $50, and the expected P at t=1 is equal to $52, what are the stock’s expected dividend yield, capital gains yield, and
total return for the coming year?
D1
$3,00
P0
$50,00
Expected P1
$52,00
Exp. dividend yield
Exp. capital gains yield
Exp. total return
6,0% =B6/B7
4,0% =(B8-B7)/B7
10,0% =C10+C11
A stock is expected to pay a dividend of $2 at the end of the year. The required rate of return is r s = 12%. What would the stock’s price
be if the growth rate were 4%?
D1
$2,00
gL
4%
rs
12%
Stock price
$25,00
A stock is expected to pay a dividend of $2 at the end of the year. The required rate of return is r s = 12%. What would the stock’s price
be if the growth rate were 0%?
D1
$2,00
gL
0%
rs
12%
Stock price
$16,67
If D0 = $4.00, rs = 9%, and g = 5% for a constant growth stock, what are the stock’s expected dividend yield and
capital gains yield for the coming year?
D0
$4,00
gL
5%
rs
9%
Expected D1
$4,20
Stock price
$105,00
Expected dividend yield
4,00%
Expected capital gains yield
5,00%
Alternatively, you know that the capital gains yield is equal to the growth rate.
Expected capital gains yield = growth rate =
5,00%
Because the total return is rs, the dividend yield is rs minus the capital gains yield:
Expected dividend yield =
4,00%
Suppose D0 = $5.00 and rs = 10%. The expected growth rate from Year 0 to Year 1 (g 0 to 1) = 20%, the expected
growth rate from Year 1 to Year 2 (g1 to 2) = 10%, and the constant rate beyond Year 2 is g L = 5%. What are the
expected dividends for Year 1 and Year 2? What is the expected horizon value price at Year 2? What is the
expected price at Time 0?
D0
$5,00
g0 to 1
20%
g1 to 2
10%
gL
5%
rs
10%
Year
1
D1
Expected dividends
2
D2
$6,00
Expected HVP,2
$6,60
$138,60
PV of expected dividends
PV of expected HVP,2
$10,91
$114,55
Expected price at Time 0
$125,45
SECTION 7-12
SOLUTIONS TO SELF-TEST
Dodd Corporation is a private company that earned $4.00 per share for the most recent year. If the average P/E ratio of a group of
comparable public companies is 11, what is an estimate of Dodd's stock value on a per share basis?
Earnings per share =
Average comparable P/E ratio =
$4,00
11,0
Estimated price per share =
$44,00
The company in the previous question, Dodd Corporation, has 100,000 shares of common stock owned by its founder. Dodd owes
$1,300,000 to its bank. Dodd has 11,400 customers. If the average ratio of total entity value to customers is $500 for a group of comparable
public companies, what is Dodd's estimated total entity value? What is its estimated stock value on a per share basis?
Number of shares =
Debt =
Number of customers =
100.000
$1.300.000
11.400
Average comparable ratio of
total entity value to number of customers =
$500
Estimated entity value =
− Debt
Intrinsic equity value
÷ Number of shares
$5.700.000
$1.300.000
4.400.000
100.000
Estimated price per share =
$44,00
io of a group of
der. Dodd owes
or a group of comparable
is?
SECTION 7-14
SOLUTIONS TO SELF-TEST
A preferred stock has an annual dividend of $5. The required return is 8%. What is the V ps?
Dps
rps
Vps
$5,00
8%
$62,50
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