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Ch07 Solutions Manual 2015-10-27
Financial Management (Nova Southeastern University)
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Chapter 7
Corporate Valuation and Stock Valuation
ANSWERS TO END-OF-CHAPTER QUESTIONS
7-1
a. A proxy is a document giving one person the authority to act for another, typically the
power to vote shares of common stock. If earnings are poor and stockholders are
dissatisfied, an outside group may solicit the proxies in an effort to overthrow
management and take control of the business, known as a proxy fight. The
preemptive right gives the current shareholders the right to purchase any new shares
issued in proportion to their current holdings. The preemptive right may or may not
be required by state law. When granted, the preemptive right enables current owners
to maintain their proportionate share of ownership and control of the business. It also
prevents the sale of shares at low prices to new stockholders which would dilute the
value of the previously issued shares. Classified stock is sometimes created by a firm
to meet special needs and circumstances. Generally, when special classifications of
stock are used, one type is designated “Class A”, another as “Class B”, and so on.
Class A might be entitled to receive dividends before dividends can be paid on Class
B stock. Class B might have the exclusive right to vote. Founders’ shares are stock
owned by the firm’s founders that have sole voting rights but restricted dividends for
a specified number of years.
b. The free cash flow model defines the total value of a company as the value of
operations plus the value of nonoperating assets.
The value of operations is the present value of all the future expected free cash
flows when discounted at the weighted average cost of capital:

Vop(at time 0)  
FCFt
t
t 1 1  WACC 
.
Nonoperating assets include investments in marketable securities and noncontrolling interests in the stock of other companies, and other financial securities.
c. Constant growth occurs when a firm’s earnings, dividends, and free cash flows grow
at some constant long-term rate. In this situation, the constant growth model can be
used to estimate the present value of the growing cash flows or dividends. For free
cash flows, the present value is:
Answers and Solutions: 7- 1
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Vop (constant growth) =
FCF0 (1  g L )
FCF1
=
WACC  g L
WACC  g L
When applied to dividends, the model is:
D0 (1  g L )
D1
^

P
0=
rs  g L
rs  g L
The horizon date is the last year in a cash flow forecast. Cash flows may grow
unevenly during the forecast period, but are assumed to grow at a constant rate for all
periods after the horizon date.
The horizon value is the value all cash flows beyond the horizon date when
discounted back to the horizon date.
When applied to free cash flows, the horizon value is the value of operations at
the end of the explicit forecast period. It is equal to the present value of all free cash
flows beyond the forecast period, discounted back to the end of the forecast period at
the weighted average cost of capital. Because growth after the horizon is constant, the
constant growth model can be applied at the horizon date:
HVT  Vop(at time T) 
FCFT 1
FCFT (1  g L )
.

WACC  g L
WACC  g L
When applied to dividends, the horizon value is the intrinsic stock price at the end
of the explicit forecast period. It is equal to the present value of all dividends beyond
the forecast period, discounted back to the end of the forecast period at the required
rate of return on stock. Because growth after the horizon is constant, the constant
growth model can be applied at the horizon date:
̂ T = DT+1 = DT (1+gL)
Horizon value for stock = P
rs -gL
rs -gL
d. A multistage model is used when the growth rate is nonconstant for several years
before becoming constant. In this case, the constant growth model is applied at the
end of the forecast horizon when the growth rate has become constant. The total
present value of cash flows is the present value of all cash flows in the forecast
periods plus the present value of the horizon value:
Answers and Solutions: 7 - 2
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T
Vop,0
=
FCF
HV
t
T

 (1  WACC
t
) (1  WACC )T
t 1
When applied to dividends, the present value of dividends is:
^
P
0=
T
D
P̂
 (1  tr ) t  (1  Tr
t 1
s
L)
T
e. Estimated value ( P̂0 ) is the present value of the expected future cash flows. The
market price (P0) is the price at which an asset can be sold.
f. The required rate of return on common stock, denoted by rs, is the minimum
acceptable rate of return considering both its riskiness and the returns available on
other investments. The expected rate of return, denoted by ^rs, is the rate of return
expected on a stockn given its current price and expected future cash flows. If the
stock is in equilibrium, the required rate of return will equal the expected rate of
return. The realized (actual) rate of return, denoted by r̄ s, is the rate of return that was
actually realized at the end of some holding period. Although expected and required
rates of return must always be positive, realized rates of return over some periods
may be negative.
g. The capital gains yield results from changing prices and is calculated as (P1 - P0)/P0,
where P0 is the beginning-of-period price and P1 is the end-of-period price. For a
constant growth stock, the capital gains yield is g, the constant growth rate. The
dividend yield on a stock can be defined as either the end-of-period dividend divided
by the beginning-of-period price, or the ratio of the current dividend to the current
price. Valuation formulas use the former definition. The expected total return, or
expected rate of return, is the expected capital gains yield plus the expected dividend
yield on a stock. The expected total return on a bond is the yield to maturity.
h. Preferred stock is a hybrid--it is similar to bonds in some respects and to common
stock in other respects. Preferred dividends are similar to interest payments on bonds
in that they are fixed in amount and generally must be paid before common stock
dividends can be paid. If the preferred dividend is not earned, the directors can omit
it without throwing the company into bankruptcy. So, although preferred stock has a
fixed payment like bonds, a failure to make this payment will not lead to bankruptcy.
Most preferred stocks entitle their owners to regular fixed dividend payments.
Answers and Solutions: 7- 3
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7-2
True. The value of a share of stock is the PV of its expected future dividends. If the two
investors expect the same future dividend stream, and they agree on the stock’s riskiness,
then they should reach similar conclusions as to the stock’s value.
7-3
A perpetual bond is similar to a no-growth stock and to a share of preferred stock in the
following ways:
1. All three derive their values from a series of cash inflows--coupon payments from the
perpetual bond, and dividends from both types of stock.
2. All three are assumed to have indefinite lives with no maturity value (M) for the
perpetual bond and no capital gains yield for the stocks.
7-4
The first step is to find the value of operations by discounting all expected future free
cash flows at the weighted average cost of capital. The second step is to find the total
corporate value by summing the value of operations, the value of nonoperating assets,
and the value of growth options. The third step is to find the value of equity by
subtracting the value of debt and preferred stock from the total value of the corporation.
The last step is to divide the value of equity by the number of shares of common stock.
Answers and Solutions: 7 - 4
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SOLUTIONS TO END-OF-CHAPTER PROBLEMS
7-1
D0 = $1.50; g1-3 = 5%; gn = 10%; D1 through D5 = ?
D1 = D0(1 + g1) = $1.50(1.05) = $1.5750.
D2 = D0(1 + g1)(1 + g2) = $1.50(1.05)2 = $1.6538.
D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.05)3 = $1.7364.
D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.05)3(1.10) = $1.9101.
D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.05)3(1.10)2 = $2.1011.
7-2
D1 = $1.50; g = 6%; rs = 13%; P̂0 = ?
P̂0 =
D1
rs  g
=
$1.50
= $21.43.
0.13  0.06

7-3
P0 = $22; D0 = $1.20; g = 10%; P̂1 = ?; r s= ?
P̂1 = P0(1 + g) = $22(1.10) = $24.20.

rs =
=
7-4
D1
$1.20(1.10)
+g=
+ 0.10
P0
$22

$1.32
+ 0.10 = 16.00%. r s = 16.00%.
$22
Dps = $5.00; Vps = $50; rps = ?
rps =
D ps
v ps
=
$5.00
= 10%.
$50.00
Answers and Solutions: 7- 5
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7-5
0
1
|
2
|
D0 = 2.00
3
|
|
D1
D2
D3
P̂2
Step 1: Calculate the required rate of return on the stock:
rs = rRF + (rM - rRF)b = 7.5% + (4%)1.2 = 12.3%.
Step 2: Calculate the expected dividends:
D0 = $2.00
D1 = $2.00(1.20) = $2.40
D2 = $2.00(1.20)2 = $2.88
D3 = $2.88(1.07) = $3.08
Step 3: Calculate the PV of the expected dividends:
PVDiv = $2.40/(1.123) + $2.88/(1.123)2 = $2.14 + $2.28 = $4.42.
Step 4: Calculate P̂2 :
P̂2 = D3/(rs – g) = $3.08/(0.123 – 0.07) = $58.11.
Step 5: Calculate the PV of P̂2 :
PV = $58.11/(1.123)2 = $46.08.
Step 6: Sum the PVs to obtain the stock’s price:
P̂0 = $4.42 + $46.08 = $50.50.
Alternatively, using a financial calculator, input the following:
CF0 = 0, CF1 = 2.40, and CF2 = 60.99 (2.88 + 58.11) and then enter I/YR = 12.3 to solve
for NPV = $50.50.
Answers and Solutions: 7 - 6
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7-6
Value of operations = Vop = PV of expected future free cash flow
Vop =
FCF (1  g )
$400,000(1.05)
=
= $6,000,000.
WACC  g
0.12  0.05
7-7
The growth rate in FCF from 2018 to 2019 is g = ($750.00-$707.55)/$707.50 = 0.06.
$707.55 (1.06)
HV2019 = VOp at 2019 =
= $15,000.
0.11  0.06
7-8
The problem asks you to determine the constant growth rate, given the following facts:
P0 = $80, D1 = $4, and rs = 14%. Use the constant growth rate formula to calculate g:

D1
+g
P0
$4
0.14 =
+g
$80
g = 0.09 = 9%.
rs=
Answers and Solutions: 7- 7
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7-9
The problem asks you to determine the value of P̂3 , given the following facts: D1 = $3, b
= 0.8, rRF = 5.2%, RPM = 6%, and P0 = $40. Proceed as follows:
Step 1:
Calculate the required rate of return:
rs = rRF + (rM – rRF)b = 5.2% + (6%)0.8 = 10%.
Step 2:
Use the constant growth rate formula to calculate g:

D1
+g
P0
$3
+g
0.10 =
$40
g = 0.025 = 2.5%.
rs
Step 3:
=
Calculate P̂3 :
P̂3 = P0(1 + g)3 = $40(1.025)3 = $43.076 ≈ $43.08.
Alternatively, you could calculate D4 and then use the constant growth rate formula to
solve for P̂3 :
D4 = D1(1 + g)3 = $3.00(1.025)3 = $3.2307.
P̂3 = $3.2307/(0.10 – 0.025) = $43.0756  $43.08.
7-10
Vps = Dps/rps; therefore, rps = Dps/Vps.
a.
b.
c.
d.
7-11
rps = $3.5/$30 = 11.67%.
rps = $3.5/$40 = 8.75%.
rps = $3.5/$50 = 7.00%.
rps = $3.5/$70 = 5.00%.
P̂0 =
D1
D (1  g)
$5.76
$6[1  (0.04)]
= 0
=
=
= $32.00.
rs  g
rs  g
0.14  (0.04)]
0.18
Answers and Solutions: 7 - 8
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7-12
D0 = $1, rS = 7% + 6% = 13%, g1 = 50%, g2 = 25%, gn = 6%.
0
rs = 13%
|
1
2
|
g1 = 50%
1.50
3
|
g2 = 25%
gn = 6%
4
|
|
1.875
1.9875
+ 28.393 = 1.9875/(0.13 – 0.06)
= 30.268
1.327
23.704
$25.03
7-13
Calculate the dividend stream and place them on a time line. Also, calculate the price of
the stock at the end of the nonconstant growth period, and include it, along with the
dividend to be paid at t = 5, as CF5. Then, enter the cash flows as shown on the time line
into the cash flow register, enter the required rate of return as I = 15, and then find the
value of the stock using the NPV calculation. Be sure to enter CF0 = 0, or else your
answer will be incorrect.
D0 = 0; D1 = 0, D2 = 0, D3 = 0.50
D4 = 0.50(1.8) = 0.9; D5 = 0.50(1.8)2 = 1.62; D6 = 0.80(1.8)2(1.07)
= $1.7334.
P̂0 = ?
0 rs = 16% 1
|
2
|
g = 80%
4
3
|
|
0.50
0.32
0.50
9.94
$10.76 = P̂0
g = 7%
6
5
|
0.90
|
1.62
19.26
20.88
|
1.7334
0.16  0.07
P̂5 = D6/(rs – g) = 1.7334/(0.16 – 0.07) = 19.26. This is the price of the stock at the end
of Year 5.
CF0 = 0; CF1-2 = 0; CF3 = 0.5; CF4 = 0.9; CF5 = 20.88; I = 16%.
With these cash flows in the CFLO register, press NPV to get the value of the stock
today: NPV = $10.76.
Answers and Solutions: 7- 9
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7-14
a. Vps =
b. Vps =
7-15
D ps
rps
=
$10
= $125.
0.08
$10
= $83.33.
0.12
a. g = $1.1449/$1.07 – 1.0 = 7%.
Calculator solution:
I/YR = ? I = 7.00%.
Input N = 1, PV = -1.07, PMT = 0, FV = 1.1449,
b. $1.07/$21.40 = 5%.

c. r s= D1/P0 + g = $1.07/$21.40 + 7% = 5% + 7% = 12%.
7-16
a. 1. P̂0 =
$3(1  0.05)
$2.85
=
= $15.83.
0.13  0.05
0.18
2. P̂0 = $3/0.13 = $23.08.
3. P̂0 =
$3(1.05)
$3.15
=
= $39.38.
0.13  0.05
0.08
4. P̂0 =
$3(1.10)
$3.30
=
= $110.00.
0.13  0.10
0.03
b. 1. P̂0 = $3.39/0 = Undefined.
2. P̂0 = $3.45/(-0.02) = -$172.5, which is nonsense.
These results show that the formula does not make sense if the required rate of return
is equal to or less than the expected growth rate.
c. No.
Answers and Solutions: 7 - 10
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7-17
a. HV2 =
$108,000
= $2,700,000.
0.12  0.08
b.
0 WACC = 12%1
2 g = 8%
3
N
|
|
|
|
$80,000
$100,000
$108,000
  
|
$
71,428.57
79,719.39
2,152,423.47
$2,303,571.43
7-18
a. HV3 =
b.
$40 (1.07)
= $713.33.
0.13  0.07
0
WACC = 13%
|
|
2
3
4
|
| g = 7%
|
-20
30
($ 17.70)
23.49
522.10
$527.89
1
N
  
|
40
Vop 3 = 713.33
753.33
c. Total valuet=0 = $527.89 + $10.0 = $537.89.
Value of common equity = $537.89 - $100 = $437.89.
$437.89
= $43.79.
Price per share =
10.0
Answers and Solutions: 7- 11
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7-19
0
g=6%
|
D0 = 1.50
1
2
3
|
|
D1
D2
4
|
D3
P̂3
|
D4
a. D1 = $1.5(1.06) = $1.59. D2 = $1.50(1.06)2 = $1.69. D3 = $1.5(1.06)3 = $1.79.
b. PV = $1.59(0.8850) + $1.69(0.7831) + $1.79(0.6930) = $3.97.
Calculator solution: Input 0, 1.59, 1.69, and 1.79 into the cash flow register, input
I/YR = 13, PV = ? PV = $3.97.
c. $27.05(0.6930) = $18.74.
Calculator solution: Input 0, 0, 0, and 27.05 into the cash flow register, I/YR = 13,
PV = ? PV = $18.74.
d. $18.74 + $3.97 = $22.71 = Maximum price you should pay for the stock. (rounding
differences may give you $22.72.)
e. P̂0 =
D1
D 0 (1  g)
$1.59
=
=
= $22.71.
rs  g
rs  g
0.13  0.06
f. The value of the stock is not dependent upon the holding period. The value
calculated in Parts a through d is the value for a 3-year holding period. It is equal to
the value calculated in Part e except for a small rounding error. Any other holding
period would produce the same value of P̂0 ; that is, P̂0 = $22.71.
Answers and Solutions: 7 - 12
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7-20
a. End of Year:
0 r = 12%1
|
2
|
3
|
4
5
|
|
Dt
D1
D2
D3
D4
D5
D1
|
g = 5%
g = 15%
D0 = 1.75
6
|
D2
D3
D4
D5
D6
= D0(1 + g)t
= $1.75(1.15)1 = $2.01.
= $1.75(1.15)2 = $1.75(1.3225) = $2.31.
= $1.75(1.15)3 = $1.75(1.5209) = $2.66.
= $1.75(1.15)4 = $1.75(1.7490) = $3.06.
= $1.75(1.15)5 = $1.75(2.0114) = $3.52.
b. Step 1
5
PV of dividends =
D
 (1  rt ) t .
t 1
s
PV D1 = $2.01(PVIF12%,1) = $2.01(0.8929) = $1.79
PV D2 = $2.31(PVIF12%,2) = $2.31(0.7972) = $1.84
PV D3 = $2.66(PVIF12%,3) = $2.66(0.7118) = $1.89
PV D4 = $3.06(PVIF12%,4) = $3.06(0.6355) = $1.94
PV D5 = $3.52(PVIF12%,5) = $3.52(0.5674) = $2.00
PV of dividends = $9.46
Step 2
P̂5 
D5 (1  g n )
$3.52(1.05)
$3.70
D6
=
=
= $52.80.

0.12  0.05
0.07
rs  g n
rs  g n
This is the price of the stock 5 years from now. The PV of this price, discounted back
5 years, is as follows:
PV of P̂5 = $52.80(PVIF12%,5) = $52.80(0.5674) = $29.96.
Step 3
The price of the stock today is as follows:
P̂0
= PV dividends Years 1 through 5 + PV of P̂5
= $9.46 + $29.96 = $39.42.
Answers and Solutions: 7- 13
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This problem could also be solved by substituting the proper values into the following
equation:
P̂0 =
5
D 0 (1  g s ) t
t 1
(1  rs ) t

 D6
 
 rs  g n
 1
 
  1  rs
5

 .

Calculator solution: Input 0, 2.01, 2.31, 2.66, 3.06, 56.32 (3.52 + 52.80) into the cash
flow register, input I/YR = 12, PV = ? PV = $39.43.
c. First Year (t = 0)
D1/P0 = $2.01/$39.42
Capital gains yield
Expected total return
= 5.10%
= 6.90%
= 12.00%
Sixth Year (t = 5)
D6/P5 = $3.70/$52.80
Capital gains yield
Expected total return
= 7.00%
= 5.00
= 12.00%
*We know that r is 12%, and the dividend yield is 5.10%; therefore, the capital gains
yield must be 6.90%.
The main points to note here are as follows:
1. The total yield is always 12% (except for rounding errors).
2. The capital gains yield starts relatively high, then declines as the nonconstant
growth period approaches its end. The dividend yield rises.
3. After t = 5, the stock will grow at a 5% rate. The dividend yield will equal 7%,
the capital gains yield will equal 5%, and the total return will be 12%.
Answers and Solutions: 7 - 14
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7-21
a. Part 1. Graphical representation of the problem:
Nonconstant
growth
1
0
|
D0
PVD1
PVD2
PV P̂2
P0
2
3
|
|
D1
(D2 + P̂2 )
Normal
growth
∞
|
|
D3
D∞
D1 = D0(1 + gs) = $2.50(1.30) = $3.25.
D2 = D0(1 + gs)2 = $2.50(1.30)2 = $4.225.
P̂2 =
D (1  g n ) $4.225 (1.06)
D3
= 2
=
= $90.415.
rs  g n
rs  g n
0.12  0.07
P̂0 = PV(D1) + PV(D2) + PV( P̂ )
2
D1
D2
P̂2


2
(1  rs ) (1  rs )
(1  rs ) 2
= $3.25(0.8929) + $4.225(0.7972) + $90.415(0.7972) = $78.35.
=
Calculator solution: Input 0, 3.25, 94.64(4.225 + 90.415) into the cash flow register,
input I/YR = 12, PV = ? PV = $78.35.
Answers and Solutions: 7- 15
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Part 2.
Expected dividend yield: D1/P0 = $3.25/$78.35 = 4.15%.
Capital gains yield: First, find P̂1 which equals the sum of the present values of D2
and P̂2 , discounted for one year.
P̂1 = D2/(1.12) + P̂2 /(1.12) =
$4.225  $90.415
= $84.50.
(1.12) 1
Calculator solution: Input 0, 94.64 (4.225 + 90.415) into the cash flow register, input
I/YR = 12, PV = ? PV = $84.50.
Second, find the capital gains yield:
$84.50  $78.35
P̂1  P0
=
= 7.85%.
$78.35
P0
Dividend yield = 4.15%
Capital gains yield = 7.85
12.00% = rs.
b. Due to the longer period of supernormal growth, the value of the stock will be higher
for each year. Although the total return will remain the same, rs = 12%, the
distribution between dividend yield and capital gains yield will differ: The dividend
yield will start off lower and the capital gains yield will start off higher for the 5-year
nonconstant growth condition, relative to the 2-year nonconstant growth state. The
dividend yield will increase and the capital gains yield will decline over the 5-year
period until dividend yield = 5% and capital gains yield = 7%.
c. Throughout the nonconstant growth period, the total yield will be 12%, but the
dividend yield is relatively low during the early years of the nonconstant growth
period and the capital gains yield is relatively high. As we near the end of the
nonconstant growth period, the capital gains yield declines and the dividend yield
rises. After the nonconstant growth period has ended, the capital gains yield will
equal gn = 7%. The total yield must equal rs = 12%, so the dividend yield must equal
12% - 7% = 5%.
Answers and Solutions: 7 - 16
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d. Some investors need cash dividends (retired people) while others would prefer
growth. Also, investors must pay taxes each year on the dividends received during
the year, while taxes on capital gains can be delayed until the gain is actually realized.
Answers and Solutions: 7- 17
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SOLUTION TO SPREADSHEET PROBLEMS
7-22
The detailed solution for the spreadsheet problem, Ch07 P22 Build a Model
Solution.xlsx, is available at the textbook’s Web site.
7-23
The detailed solution for the spreadsheet problem, Ch07 P23 Build a Model
Solution.xlsx, is available at the textbook’s Web site.
7-24
The detailed solution for the spreadsheet problem, Ch07 P24 Build a Model
Solution.xlsx, is available at the textbook’s Web site.
Answers and Solutions: 7 - 18
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MINI CASE
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 Biggerstaff & 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.
Answer: The common stockholders are the owners of a corporation, and as such, they have
certain rights and privileges as described below.
1. Ownership implies control. Thus, a firm’s common stockholders have the right to
elect its firm’s directors, who in turn elect the officers who manage the business.
2. Common stockholders often have the right, called the preemptive right, to
purchase any additional shares sold by the firm. In some states, the preemptive
right is automatically included in every corporate charter; in others, it is necessary
to insert it specifically into the charter.
b.
What is free cash flow (FCF)? What is the weighted average cost of capital?
What is the free cash flow valuation model?
Answer: Free cash flow (FCF) is the cash flow available for distribution to all of a company’s
investors. FCF is generated by a company’s operations.
The weighted average cost of capital (WACC) is the overall rate of return required by
all of the company’s investors. The PV of their expected future free cash flows,
discounted at the WACC, is the value of operations. This is the essence of the FCF
valuation model.
Mini Case: 7 - 19
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
Vop =
FCF
t
 (1  WACC
)t
t 1
Nonoperating assets are marketable securities and ownership of non-controlling
interest in another company. The value of nonoperating assets usually is very close to
figure that is reported on balance sheets.
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?
Answer: Total corporate value is sum of value of operations and value of nonoperating assets.
Some company’s also have growth options, but assume they are negligible for this
company. Debt holders have first claim. Preferred stockholders have the next claim.
Any remaining value belongs to stockholders.
Mini Case: 7 - 20
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d.
1. Suppose the free cash flow at Time 1 is expected to grow at a constant rate of g L
forever. If gL < WACC, what is a formula for the present value of expected free
cash flows when discounted at the WACC?
Answer:
Vop 
d.
FCF1
WACC  g L 
2. 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?
Answer:
Vop 
e.
FCF0 (1  g L )
WACC  g L 
1. Use B&M’s data and the free cash flow valuation model to answer the following
questions. What is its estimated value of operations?
Answer:
e.
FCF0 (1  g L )
WACC  g L 
Vop 
24 (1  0.05)
 420
0.11  0.05
2. What is its estimated total corporate value? (This is the entity value.)
Answer:
e.
Vop 
Total corporate value = Vop + Short-term investments.
= $420 + $100
= $520 million
3. What is its estimated intrinsic value of equity?
Answer:
Intrinsic value of equity = Total value- Debt - Pref.
Mini Case: 7 - 21
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= $520 - $200 - $50
= $270 million
e.
4. What is its estimated intrinsic stock price per share?
Answer:
f.
Intrinsic stock price per share = Value of equity / Number of shares
= $270 / 10 - $200 - $50
= $27.00
1. 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 were 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. What is its horizon value
(i.e., its value of operations at year three)? What is its current value of
operations (i.e., at time zero)?
Answer:
Year
FCF
0
1
2
3
4
−$10
$20
$35
FCF3(1+0.05)
5
FCF4(1+ 0.05) FCFt(1+ 0.05)
HV3  Vop,3 
HV3 = V op,3 =
…t
FCF3 (1  g L )
WACC  g L
35 (1  0.05)
= $612.50
0.11  0.05
Mini Case: 7 - 22
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Year
0
FCF
PV of FCF in explicit forecast
PV of HV is the PV of FCF beyond
the explicit forecast
1
2
3
FCF1
←฀
FCF2
←฀
FCF3
←฀
←฀
HV3
←฀
←฀
0 WACC = 11% 1
2
3
|
|
|
|
-10
$ -9.009
16.232
25.592
447.855
$480.67 = Value of operations
f.
20
4
5
…t
FCF3(1+gL)
←฀
FCF4(1+gL)
←฀
FCFt(1+gL)
←฀
gL = 5%
4
|
N
  
|
35
Vop 3 = 612.5 = 35 (1  0.05)
0.11  0.05
2. What is its value of equity on a price per share basis?
Answer:
Value of operations
+ Value of nonoperating assets
Total estimated value of firm
− Debt
− Preferred stock
Estimated value of equity
÷ Number of shares
Estimated stock price per share =
$480.67
100.00
$580.67
200.00
50.00
$330.67
10.00
$33.07
Mini Case: 7 - 23
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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.
Answer: First, calculate the present value of the horizon value. Then divide the present value
of the horizon value by the Year 0 value of operations. This will show what percent
of value is due to cash flows occurring 4 or more years in the future.
Vop,0 = $480.67
HV3 = $612.50
PV of HV3 = $612.50/(1+0.11)3 = $447.855
Percent of value due to cash flows from Year 4 and beyond:
% due to long-term = (PV of HV3) / Vop,0 = $447.855 / $480.67 = 0.93 = 93%
h.
Based on your answer to the previous question, what are two reasons why
managers often emphasize short-term earnings?
Answer: 1. Changes in quarterly earnings can signal changes future in cash flows. This would
affect the current stock price.
2. Managers often have bonuses tied to quarterly earnings, so they have incentive to
manage earnings.
Mini Case: 7 - 24
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i.
Your employer also is considering the acquistion of Hatfield Medical Supplies.
You have 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 = 4.5%; 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?
Answer:
The operating items are forecast as follows: Sales1 = $2,000(1+0.10) = $2,200;
NOPAT1 = $2,200(0.045) = $99; and OpCap1 = $2,200(0.56) = $1,232. The operating
items for the other years are forecast in a similar manner.
Actual
Scenario:
No Change
Sales
0
1
2
3
4
$2,000
$2,200
$2,376
$2,495
$2,620
$99
$107
$112
$117.879
$1,120 $1,232
$1,331
$1,397.088
$1,466.942
−$13
$8.36
$45.738
$48.025
-164%
447.1%
5.0%
8.0%
8.0%
8.0%
NOPAT
OpCap
Forecast
FCF
Growth in FCF
ROIC
8.0%
8.0%
The ROIC4 is 8% and the WACC is 9%. This means that ROIC < WACC/(1+gL) at
the horizon: 0.08 < 9%/(1 + 0.05) = 0.0857. Therefore, we expect that the value of
operations at Year 4 (i.e., the horizon value at Year 4) should be less than the total net
operating capital at Year 4, OpCap4.
Mini Case: 7 - 25
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j.
What is the horizon value at Year 4? What is the value of operations at Year 0?
How does the value of operations compare with the current total net operating
capital?
Answer:
$48.025(1 + 0.05)
FCF4 (1 + g L )
=
= $1,260.65
(0.09 − 0.05)
(WACC − g L )
HV4
$1,260.65
PV of HV4 = (1+WACC)
= (1+0.09)4 = $893.08
4
HV4 =
PV of FCF =
PV of FCF =
FCF2
FCF3
FCF4
FCF1
+
+
+
2
3
1
(1+WACC)
(1+WACC)
(1+WACC)4
(1+WACC)
−$13
$8.36
$45.738
$48.025
+ (1+0.09)2 + (1+0.09)3 + (1+0.09)4
(1+0.09)1
PV of FCF = $64.45
The value of operations is the sum of the PV of the horizon value plus the PVs of the
FCFs:
Value of Operations:
Present value of HV
+ Present value of FCF
$893.08
$64.45
Value of operations ≈
$958
Notice that the value of operations at Year 4 (i.e., the horizon value, HV4) is
$1,260.65 and that the total net operation capital at Year 4 (OpCap4 from Part i) is
$1,466.94. In other words, the value of operations is less than the total net operating
capital. This is because ROIC4 < WACC/(1+gL) at the horizon: 0.08 < 9%/(1 + 0.05)
= 0.0857.
Also, at Year 0, the most recent total net operating capital, OpCap0 = $1,120. Note
that the value of operations at Year 0 is $958, and this is less than the OpCap0. Thus,
the low ROIC relative to the WACC causes the value of operations to be less than the
total net operating capital.
Mini Case: 7 - 26
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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 long-term growth rate)? What can explain
this? Hint: Use Scenario Manager.
Answer: Value drivers are the inputs to the FCF valuation model that managers are able to
influence: sales growth rates, operating profitability, capital requirements, and cost of
capital.
Scenario
g0,1
g1,2
g2,3
g3,4
gL
OP
CR
ROIC
Current value of operations
WACC
WACC/(1+WACC)
No Change
10%
8%
5%
5%
5%
4.5%
56.0%
8.0%
$958
9.00%
8.26%
Improve Growth
11%
9%
6%
6%
6%
4.5%
56.0%
8.0%
$933
9.00%
8.26%
Higher growth causes Vop,0 to fall. ROIC must be greater than WACC/(1+WACC) for
growth to add value.
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.
Mini Case: 7 - 27
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Answer: .
Scenario
g0,1
g1,2
g2,3
g3,4
gL
OP
CR
ROIC
Current value of operations
WACC
WACC/(1+WACC)
No Change
10%
8%
5%
5%
5%
4.5%
56.0%
8.0%
$958
9.00%
8.26%
Improve OP
10%
8%
5%
5%
5%
5.5%
56.0%
9.8%
$1,523
9.00%
8.26%
The improvement in operating profitability increases the ROIC, which increases the value of
operations.
Scenario
g0,1
g1,2
g2,3
g3,4
gL
OP
CR
ROIC
Current value of operations
WACC
WACC/(1+WACC)
No Change
10%
8%
5%
5%
5%
4.5%
56.0%
8.0%
$958
9.00%
8.26%
Improve CR
10%
8%
5%
5%
5%
4.5%
51.0%
8.8%
$1,191
9.00%
8.26%
The improvement in capital requirements increases the ROIC, which increases the value of
operations.
Mini Case: 7 - 28
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Scenario
g0,1
g1,2
g2,3
g3,4
gL
OP
CR
ROIC
Current value of operations
WACC
WACC/(1+WACC)
No Change
10%
8%
5%
5%
5%
4.5%
56.0%
8.0%
$958
9.00%
8.26%
Improve OP and CR
10%
8%
5%
5%
5%
5.5%
51.0%
10.8%
$1,756
9.00%
8.26%
The improvements in operating profitability and capital requirements increased the ROIC, so
growth now adds substantial value.
Scenario
g0,1
g1,2
g2,3
g3,4
gL
OP
CR
ROIC
Current value of operations
WACC
WACC/(1+WACC)
No Change
10%
8%
5%
5%
5%
4.5%
56.0%
8.0%
$958
9.00%
8.26%
Improve All
11%
9%
6%
6%
6%
5.5%
51.0%
10.8%
$2,008
9.00%
8.26%
The improvements in operating profitability increased the ROIC, so growth now adds substantial
value.
Mini Case: 7 - 29
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m.
What insight does the free cash flow valuation model give provide us about
possible reasons for market volatility? Hint: Look at the value of operations for
the combinations of ROIC and gL in the previous questions.
Answer: .
gL
5%
6%
ROIC
8.8%
9.8%
$1,191
$1,523
$1,247
$1,694
8.0%
$958
$933
10.8%
$1,756
$2,008
Small changes in ROIC and growth cause large changes in value. Similarly, small
changes in the cost of capital (WACC) cause large changes in value. As new
information arrives, investors continually update their estimates of operating
profitability, capital requirements, growth, risk, and interest rates. If stock prices
aren’t volatile, then this means there isn’t a good flow of information
n.
1. Write out a formula that can be used to value any dividend-paying stock,
regardless of its dividend pattern
Answer: The value of any stock is the present value of its expected dividend stream:
P̂0 =
D1
(1  rs ) t

D2
(1  rs )

D3
(1  rs ) 3

D
(1  rs ) 
.
However, some stocks have dividend growth patterns which allow them to be valued
using short-cut formulas.
Mini Case: 7 - 30
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n.
2. What is a constant growth stock? How are constant growth stocks valued?
Answer: A constant growth stock is one whose dividends are expected to grow at a constant
rate forever. “Constant growth” means that the best estimate of the future growth rate
is some constant number, not that we really expect growth to be the same each and
every year. Many companies have dividends which are expected to grow steadily
into the foreseeable future, and such companies are valued as constant growth stocks.
For a constant growth stock:
D1 = D0(1 + gL), D2 = D1(1 + gL) = D0(1 + gL)2, and so on.
With this regular dividend pattern, the general stock valuation model can be
simplified to the following very important equation:
P̂0 =
D1
D (1  g L )
= 0
.
rs  g L
rs  g L
This is the well-known “Gordon,” or “constant-growth” model for valuing stocks.
Here D1, is the next expected dividend, which is assumed to be paid 1 year from now,
rs is the required rate of return on the stock, and g is the constant growth rate.
n.
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)?
Answer: The model is derived mathematically, and the derivation requires that rs > gL. If gL is
greater than rs, the model gives a negative stock price, which is nonsensical. The
model simply cannot be used unless (1) rs > gL, (2) gL is expected to be constant, and
(3) gL can reasonably be expected to continue indefinitely.
Stocks may have periods of nonconstant growth, where g > rs; however, this
growth rate cannot be sustained indefinitely. In the long-run, gL < rs.
Mini Case: 7 - 31
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o.
Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the
yield on T-bonds) is 7%, and that the market risk premium is 5%. What is the
required rate of return on the firm’s stock?
Answer: Here we use the SML to calculate temp force’s required rate of return:
rs = rRF + (rM – rRF)bTemp Force = 7% + (12% – 7%)(1.2)
= 7% + (5%)(1.2) = 7% + 6% = 13%.
p.
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 stock price?
Answer: We could extend the time line on out forever, find the value of Temp Force’s
dividends for every year on out into the future, and then the PV of each dividend,
discounted at r = 13%. For example, the PV of D1 is $1.76106; the PV of D2 is
$1.75973; and so forth. Note that the dividend payments increase with time, but as
long as rs > gL, the present values decrease with time. If we extended the graph on
out forever and then summed the PVs of the dividends, we would have the value of
the stock. However, since the stock is growing at a constant rate, its value can be
estimated using the constant growth model:
P̂0 =
D1
rs  g L
D1 = D0 (1+gL) = $2.00 (1.06) = $2.12
P̂0 =
D1
$2.12
$2.12
=
=
= $30.29.
rs  g
0.13  0.06
0.07
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p.
2. What is the stock’s expected value one year from now?
Answer: After one year, D1 will have been paid, so the expected dividend stream will then be
D2, D3, D4, and so on. Thus, the expected value one year from now is $32.10:
P̂1 =
D2
( rs  g L )
D2 = D1 (1+gL) = $2.12(1.06) = 2.2472
P̂1 =
D2
$2.2472
$2.2472
=
=
= $32.10.
( rs  g L )
(0.13  0.06)
0.07
Mini Case: 7 - 33
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p.
3. What are the expected dividend yield, the capital gains yield, and the total
return during the first year?
Answer: The expected dividend yield in any year n is
Dividend Yield =
Dn
$2.12
P̂n 1 0.13  0.06
Expected Dividend Yield at Time 0 =
D1
P̂0
=
$2.12
= 7%
$30.29
While the expected capital gains yield is
Capital Gains Yield =
Expected Capital Gains Yield at Time 0 =
( P̂n  P̂n 1 )
P̂n 1
$1.81
( P̂n  P̂n 1 ) $32.10  $30.29
=
=
= 6%
$30.29
$30.29
P̂n 1
Alternatively,
Capital Gains Yield = rs – Dividend Yield = 13% − 7% = 6%
The total yield is comprised of the dividend yield and the capital gains yield.
Dividend yield = 7.0%
Capital gains yield = 6.0%
Total return = 13.0%
q.
Now assume that the stock is currently selling at $30.29. What is its expected
rate of return?
Answer: The constant growth model can be rearranged to this form:
r̂s =
D1
g.
P0
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Here the current price of the stock is known, and we solve for the expected return.
For Temp Force:
r.
r̂s = $2.12/$30.29 + 0.060 = 0.070 + 0.060 = 13%.
Now assume that Temp Force’s dividend is expected to experience nonconstant
growth of 30% from Year 0 to Year 1, 20% from Year 1 to Year 2, and 10%
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)?
Answer: Temp Force is no longer a constant growth stock, so the constant growth model is not
applicable. Note, however, that the stock is expected to become a constant growth
stock in 3 years. Thus, it has a nonconstant growth period followed by constant
growth. The easiest way to value such nonconstant growth stocks is to set the
situation up on a time line as shown below:
0
|
rs = 13% 1
g = 30%
2.3009
2.5452
2.5903
39.2246
46.6610
2
|
3
|
4
|
g = 25%
2.6000
3.2500
|
g = 15%
3.7375
P̂3 = $56.5971 =
gL = 6%
3.9618
3.9618
0.13  0.06
Simply enter $2 and multiply by (1.30) to get D1 = $2.60; multiply that result by 1.25
to get D2 = $3.25, multiply that result by 1.15 to get D3 = $3.7375 and multiply that
result by 1.06 to get D4 = $3.9618. Then recognize that after year 3, Temp Force
becomes a constant growth stock, and at that point P̂3 can be found using the constant
growth model. P̂3 is the present value as of t = 3 of the dividends in year 4 and
beyond.
With the cash flows for D1, D2, D3, and P̂3 shown on the time line, we discount
each value back to year 0, and the sum of these four PVs is the intrinsic value of the
^
stock today, P
0 = $46.6610 ≈ $46.66.
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The dividend yield and the capital gains yield are:
Dividend yield =
$2.600
= 0.0557 ≈ 5.6%.
$46.66
Capital gains yield = 13.00% - 5.6% = 7.4%.
During the nonconstant growth period, the dividend yields and capital gains yields are
not constant, and the capital gains yield does not equal g. However, after year 3, the
stock becomes a constant growth stock, with gL = capital gains yield = 6.0% and
dividend yield = 13.0% - 6.0% = 7.0%.
s.
What is the market multiple method of valuation? What are its strengths and
weaknesses?
Answer: Analysts often use the P/E multiple (the price per share divided by the earnings per
share) or the P/CF multiple (price per share divided by cash flow per share, which is
the earnings per share plus the dividends per share) to value stocks. For example,
estimate the average P/E ratio of comparable firms. This is the P/E multiple. Multiply
this average P/E ratio by the expected earnings of the company to estimate its stock
price. The entity value (V) is the market value of equity (# shares of stock multiplied
by the price per share) plus the value of debt. Pick a measure, such as EBITDA, sales,
customers, eyeballs, etc. Calculate the average entity ratio for a sample of comparable
firms. For example, V/EBITDA, V/customers. Then find the entity value of the firm
in question. For example, multiply the firm’s sales by the V/sales multiple, or
multiply the firm’s # of customers by the V/customers ratio. The result is the total
value of the firm. Subtract the firm’s debt to get the total value of equity. Divide by
the number of shares to get the price per share. There are problems with market
multiple analysis. (1) It is often hard to find comparable firms. (2) The average ratio
for the sample of comparable firms often has a wide range. For example, the average
P/E ratio might be 20, but the range could be from 10 to 50. How do you know
whether your firm should be compared to the low, average, or high performers?
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t.
What are the advantages of the free cash flow valuation model relative to the
dividend growth model?
Answer: You can apply FCF model in more situations, such as privately held companies,
divisions of companies, and companies that pay zero (or very low) dividends.
However, the FCF model requires forecasted financial statements to estimate FCF.
u.
Answer:
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?
Vps 
D ps
rps

$2.10
 $30.00
0.07
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