# P7-5. LG 4: Common Stock Valuation–Zero Growth: Po = D1 ¸ ks

```P7-5.
LG 4: Common Stock Valuation–Zero Growth: Po  D1  ks
Basic
Po \$2.40  0.12
Po \$20
(b) Po \$2.40  0.20
Po \$12
(c) As perceived risk increases, the required rate of return also increases, causing the stock
price to fall.
(a)
P7-6.
LG 4: Common Stock Valuation–Zero Growth
Intermediate
Value of stock when purchased 
\$5.00
 \$31.25
0.16
\$5.00
 \$41.67
0.12
Sally’s capital gain is \$10.42 (\$41.67  \$31.25).
Value of stock when sold 
P7-10. LG 4: Common Stock Value–Constant Growth: Po  D1  (ks  g)
Intermediate
Computation of growth rate:
FV  PV  (1  k)n
\$2.87  \$2.25  (1  k)5
\$2.87  \$2.25  FVIFk%,5
1.276  FVIFk%,5
g
 k at 5%
P7-15. LG 5: Free Cash Flow Valuation
Challenge
(a) The value of the total firm is accomplished in three steps.
(1) Calculate the present value of FCF from 2012 to infinity.
FCF 
\$390,000(1.03) \$401,700

 \$5,021,250
0.11  0.03
0.08
(2) Add the present value of the cash flow obtained in (1) to the cash flow for 2011.
FCF2011  \$5,021,250  390,000  \$5,411,250
(3) Find the present value of the cash flows for 2004 through 2008.
Year
2007
2008
2009
2010
2011
FCF
PVIF11%,n
PV
\$200,000
0.901
\$180,200
250,000
0.812
203,000
310,000
0.731
226,610
350,000
0.659
230,650
5,411,250
0.593
3,208,871
Value of entire company, Vc  \$4,049,331
(b) Calculate the value of the common stock.
VS  VC  VD  VP
VS  \$4,049,331  \$1,500,000  \$400,000  \$2,191,331
\$2,191,331
 \$10.96
(c) Value per share 
200,000
P7-16. LG 5: Using the Free Cash Flow Valuation Model to Price an IPO
Challenge
(a) The value of the firm’s common stock is accomplished in four steps.
(1) Calculate the present value of FCF from 2011 to infinity.
FCF 
\$1,100,000(1.02) \$1,122,000

 \$18,700,000
0.08  0.02
0.06
(2) Add the present value of the cash flow obtained in (1) to the cash flow for 2010.
FCF2010  \$18,700,000  1,100,000  \$19,800,000
(3) Find the present value of the cash flows for 2004 through 2007.
Year
2007
2008
2009
2010
FCF
PVIF11%,n
PV
\$700,000
0.926
\$648,200
800,000
0.857
685,600
950,000
0.794
754,300
19,800,000
0.735
14,533,000
Value of entire company, Vc  \$16,621,100
(4) Calculate the value of the common stock using equation 7.8.
VS  VC  VD  VP
VS  \$16,621,100  \$2,700,000  \$1,000,000  \$12,921,100
\$12,921,100
 \$11.75
Value per share 
1,100,000
(b) Based on this analysis the IPO price of the stock is over valued by \$0.75 (\$12.50 
\$11.75) and you should not buy the stock.
(c) The value of the firm’s common stock is accomplished in four steps.
(1) Calculate the present value of FCF from 2011 to infinity.
FCF 
\$1,100,000(1.03) \$1,133,000

 \$22,660,000
0.08  0.03
0.05
(2) Add the present value of the cash flow obtained in (1) to the cash flow for 2010.
FCF2010  \$22,660,000  1,100,000  \$23,760,000
(3) Find the present value of the cash flows for 2004 through 2007.
Year
2007
2008
2009
2010
FCF
PVIF11%,n
PV
\$700,000
0.926
\$648,200
800,000
0.857
685,600
950,000
0.794
754,300
23,760,000
0.735
17,463,000
Value of entire company, Vc  \$19,551,700
```