Chapter 12: Basics of Valuation
Problem 1
a. False. We can use it to value the firm by looking at the dividends that will be paid after the high growth period ends.
b. False. There is no builtin conservatism in the model. The value generated depends on the assumptions made regarding the growth rate and the required rate of return on equity.
c.False. This will be true if the stock market drop is not supported by a change in the fundamentals.
d. True. Portfolios of stocks that are undervalued using the dividend discount model seem to earn excess returns over long time periods.
e. True. The model is biased towards these stocks because of its emphasis on dividends.
Problem 2
The cost of equity = .0625+0.9(.055) = 11.2%
; Solving, we find g = 6.46%
Problem 3
a. This would suggest a higher growth rate
b. This would also suggest a higher growth rate, since the nominal growth = real growth rate + inflation rate.
c. The stable growth rate would not be affected, but the length of the highgrowth period would be greater.
d. The stable growth rate would not be affected, but the growth rate in the highgrowth period would probably go up.
Problem 4
The expected rate of return on equity after 1998 = 0.0625 + 1.1(0.055) = 12.3%
The dividends from 1993 onwards can be estimated as:
Year 
1993 
1994 
1995 
1996 
1997 
1998 
1999 
Earnings 
2.1 
2.415 
2.78 
3.19 
3.67 
4.22 
4.48 
Dividends 
0.69 
0.794 
0.913 
1.048 
1.206 
1.387 
2.91 
PV of dividends 
0.70 
0.70 
0.70 
0.70 
0.70 
a. The price as of 1998 = 2.91/(.123.06) = $46.19
b. The required rate of return upto 1998 = .0625+1.4(0.055) = 13.95%. The dividends upto 1998 are discounted using this rate. The current price = 5(0.70) + 46.19/(1.1395)^{5} = $27.54.
Problem 5
a. The payout ratio = 0.42/1.50 = 28% for 1993. The retention ratio = 10.28 = 72%. The Return on capital = EBIT(1tax rate)/Book Value of Assets = (300.8)(10.385)/(7.6+160) = 10.71%.
The return on equity = 30/160 = 18.75%
Hence, the estimated growth rate in earnings = 0.72(.1875) = 13.5%
b. If the growth rate approaches 6% after 1998, and the return on assets approaches the industry average of 12.5%, then the payout ratio must approach = 1  g/[ROA + D/E (ROA  i (1tax rate))] = = 1  .06/(.125+.25(.125  .07(1.385)) = 58.76%.
c. The expected beta after 1998 is related to the leverage ratio at that time. The current unlevered beta = 0.85/(1+(10.385)(0.05)) = 0.82. If the firm’s leverage ratio approaches the industry average, and the unlevered beta remains constant, the levered beta will become 0.82(1+(10.385)(0.25)) = 0.95.
d. The required rate of return at that point would be 0.07 + 0.95(0.055) = 12.23%, assuming that the best estimate of the Tbond rate in 1998 is 0.07. The stock price at that time would then be 1.5(1.135)^{5}(1.06)(0.5876)/(0.12230.06) = $28.25.
e. The required rate of return at this time = 0.07 + 0.85(0.055) = 11.68%
Year 
1993 
1994 
1995 
1996 
1997 
1998 
1999 
Earnings 
1.5 
1.61565 
1.740217 
1.874387 
2.018903 
2.17456 
2.305034 
Dividends 
0.42 
0.452382 
0.487261 
0.524828 
0.565293 
0.608877 
1.198617 
Present value of dividends 
0.405687 
0.391863 
0.378509 
0.36561 
0.353151 
Value per share using the Gordon Growth model = $1.50(1.06)(0.5876)/(.1223  .06) = $15.00
Value Per Share With No Growth = $1.50(0.5876)/.1223 = $7.21
Value of Extraordinary Growth = $18.47  $15.00 = $3.47
Value of Stable Growth = $15.00  $7.21 = $7.79
Problem 6.
Stage 
Year 
Growth rate in earnings 
Payout ratio 
Earnings 
Dividends 
Beta 
Rate of return on equity 
1993 
3.95 
0.68 

Growth 
1994 
0.16 
0.172152 
4.582 
0.7888 
1.25 
0.13125 
Growth 
1995 
0.16 
0.172152 
5.31512 
0.915008 
1.25 
1.13125 
Growth 
1996 
0.16 
0.172152 
6.165539 
1.061409 
1.25 
0.13125 
Growth 
1997 
0.16 
0.172152 
7.152025 
1.231235 
1.25 
0.13125 
Growth 
1998 
0.16 
0.172152 
8.29635 
1.428232 
1.25 
0.13125 
Transition 
1999 
0.14 
0.257722 
9.457838 
2.437489 
1.2 
0.1285 
Transition 
2000 
0.12 
0.343291 
10.59278 
3.636407 
1.15 
0.12575 
Transition 
2001 
0.1 
0.428861 
11.65206 
4.99711 
1.1 
0.123 
Transition 
2002 
0.08 
0.51443 
12.58422 
6.473706 
1.05 
0.12025 
Stable 
2003 
0.06 
0.6 
13.33927 
8.003565 
1 
0.1175 
Stable 
2004 
0.06 
0.6 
14.13963 
8.483779 
1 
0.1175 
The share price at the end of 2003 = 8.48/(.1175  .06) = $147.48
The share value today (at the end of 1993) equals the present value of all the dividends plus the present value of the share price at the end of 2003 = 12.77 + PV(Share price in 2003) = $ 57.36.
PV of price in 10 years = $147.48/(1.13125)^{5} (1.1285)(1.12575)(1.123)1.12025)(1.1175)
Problem 7
a. The required rate of return on equity = 0.0625 + 1.05(0.055) = 12.025%
The DPS for 1993 is 1.70. Hence the price using the dividend discount model = 1.70(1.07)/(.120250.07) = 36.20.
b. The current debt to capital ratio = 1600/(160x51+1600) = 0.1639
The FCFE per share for 1993 = Net Income + (1d )(Capital Expenditures  Depreciation) + (1d )D Working Capital) = 3.20  (10.1639)(475315)/160 =$2.36.
The estimated growth rate is the same. Hence the price per share = 2.36*1.07/(.120250.07) = $50.20.
c. The difference between the two prices is the value of control, or the additional value that could be realized if the firm were better run. Assuming that the probability of takeover is high, I would use the price based on the FCFE. However, if there were a lot of legal constraints on a takeover, the price based on dividends would be more appropriate.
Problem 8
Required rate of return on equity = 0.065 + 1(0.055) = 0.12
a. If Capital expenditures offset depreciation in stable growth
Year 
EPS 
Cap Exp 
Depr 
D WC 
FCFE 
Term Price 
1 
$2.71 
$2.60 
$1.30 
$0.05 
$1.64 

2 
$3.13 
$3.00 
$1.50 
$0.05 
$1.89 

3 
$3.62 
$3.47 
$1.73 
$0.05 
$2.19 

4 
$4.18 
$4.00 
$2.00 
$0.06 
$2.54 

5 
$4.83 
$4.62 
$2.31 
$0.06 
$2.93 
$84.74 
6 
$5.12 
$4.90 
$4.90 
$0.04 
$5.08 
Present Value of FCFE for next 5 years = $ 7.71
Present Value of Terminal Price = $ 84.74/1.12^{5} = $ 48.10
Total Value per share = $ 55.91
b. If Cap Expenditures continue to be twice depreciation in stable growth
Year 
EPS 
Cap Exp 
Depr 
D WC 
FCFE 
Term Price 
1 
$2.71 
$2.60 
$1.30 
$0.05 
$1.64 

2 
$3.13 
$3.00 
$1.50 
$0.05 
$1.89 

3 
$3.62 
$3.47 
$1.73 
$0.05 
$2.19 

4 
$4.18 
$4.00 
$2.00 
$0.06 
$2.54 

5 
$4.83 
$4.62 
$2.31 
$0.06 
$2.93 
$52.09 
6 
$5.12 
$4.90 
$2.45 
$0.04 
$3.13 
PV(FCFE upto 1998) = 7.81
PV of Terminal Price = $ 29.56
Value per Share = $ 37.36
Since the debt ratio is lower, the firm should have a lower beta and cost of equity.
Year 
EPS 
Cap Exp 
Depr 
Chg WC 
FCFE 
Term Price 
1 
$2.71 
$2.60 
$1.30 
$0.05 
$1.43 

2 
$3.13 
$3.00 
$1.50 
$0.05 
$1.66 

3 
$3.62 
$3.47 
$1.73 
$0.05 
$1.92 

4 
$4.18 
$4.00 
$2.00 
$0.06 
$2.23 

5 
$4.83 
$4.62 
$2.31 
$0.06 
$2.58 
$45.85 
6 
$5.12 
$4.90 
$2.45 
$0.04 
$2.75 
If we used the same beta, the value of equity would be:
Present Value Per Share = 1.43/1.12 + 1.66/1.12^{2} + 1.92/1.12^{3} + 2.23/1.12^{4} + (2.58 + 45.85)/1.12^{5} = $32.87
Problem 9
a.
Year 
EPS 
Cap Ex 
Deprec'n 
Ch. WC 
FCFE 
Terminal Price 
1 
$2.30 
$0.68 
$0.33 
$0.45 
$1.57 

2 
$2.63 
$0.78 
$0.37 
$0.48 
$1.82 

3 
$2.99 
$0.89 
$0.42 
$0.51 
$2.11 

4 
$3.41 
$1.01 
$0.48 
$0.54 
$2.45 

5 
$3.89 
$1.16 
$0.55 
$0.57 
$2.83 
$61.32 
6 
$4.16 
$0.88 
$0.59 
$0.20 
$3.71 
Net capital expenditures (Cap Ex  Depreciation) and working capital change is offset partially by debt (10%). The balance comes from equity. For instance, in year 1  

FCFE = $2.30  ($0.68  $0.33) * (1  0.10)  $0.45 * (1  0.10) = $1.57) 

b. Terminal Price = $3.71/ (.1305  .07) = $61.32 

c. Present Value Per Share = 1.57/1.136 + 1.82/1.136^{2} + 2.11/1.136^{3} + 2.45/1.136^{4} + (2.83 + 52.69)/1.136^{5} = $39.61 
Problem 10
a. 

Year 
1 
2 
3 
4 
5 

Earnings 
$0.66 
$0.77 
$0.90 
$1.05 
$1.23 

(CapExDeprec'n) * (1) 
$0.05 
$0.06 
$0.07 
$0.08 
$0.10 

D Working Capital * (1) 
$0.27 
$0.31 
$0.37 
$0.43 
$0.50 

FCFE 
$0.34 
$0.39 
$0.46 
$0.54 
$0.63 

Present Value 
$0.29 
$0.30 
$0.30 
$0.31 
$0.31 

Transition Period 

Year 
6 
7 
8 
9 
10 

Growth Rate 
14.60% 
12.20% 
9.80% 
7.40% 
5.00% 

Cumulated Growth 
14.60% 
28.58% 
41.18% 
51.63% 
59.21% 

Earnings 
$1.41 
$1.58 
$1.73 
$1.86 
$1.95 

(CapExDeprec'n) * (1) 
$0.11 
$0.13 
$0.14 
$0.15 
$0.16 

D Working Capital * (1) 
$0.45 
$0.39 
$0.30 
$0.22 
$0.13 

FCFE 
$0.84 
$1.07 
$1.29 
$1.50 
$1.67 

Beta 
1.38 
1.31 
1.24 
1.17 
1.1 

Cost of Equity 
14.59% 
14.21% 
13.82% 
13.44% 
13.05% 

Present Value 
$0.37 
$0.41 
$0.43 
$0.44 
$0.43 

Since the cost of equity changes each year after year 6, discounting has to be done at the cumulated cost of equity. 

Stable Growth Phase 

Growth Rate: Stable Phase = 
5.00% 

FCFE in Terminal Year = 
$1.92 

Cost of Equity in Stable Phase = 
13.05% 

Price at the End of Growth Phase = 
$23.79 

PV of FCFE in High Growth Phase = 
$1.51 

Present Value of FCFE in Transition Phase = 
$2.08 

Present Value of Terminal Price = 
$6.20 

Value of the Stock = 
$9.79 
Year 
1 
2 
3 
4 
5 

Earnings 
$0.66 
$0.77 
$0.90 
$1.05 
$1.23 

(CapExDeprec'n)* (1) 
$0.05 
$0.06 
$0.07 
$0.08 
$0.10 

D Working Capital * (1) 
$0.27 
$0.31 
$0.37 
$0.43 
$0.50 

FCFE 
$0.34 
$0.39 
$0.46 
$0.54 
$0.63 

Present Value 
$0.29 
$0.30 
$0.30 
$0.31 
$0.31 

Transition Period (up to ten years) 

Year 
6 
7 
8 
9 
10 

Growth Rate 
14.60% 
12.20% 
9.80% 
7.40% 
5.00% 

Cumulated Growth 
14.60% 
28.58% 
41.18% 
51.63% 
59.21% 

Earnings 
$1.41 
$1.58 
$1.73 
$1.86 
$1.95 

(CapExDeprec'n)*(1) 
$0.11 
$0.13 
$0.14 
$0.15 
$0.16 

D Working Capital *(1) 
$0.50 
$0.48 
$0.43 
$0.36 
$0.26 

FCFE 
$0.79 
$0.97 
$1.16 
$1.35 
$1.54 

Beta 
1.38 
1.31 
1.24 
1.17 
1.1 

Cost of Equity 
14.59% 
14.21% 
13.82% 
13.44% 
13.05% 

Present Value 
$0.34 
$0.37 
$0.39 
$0.40 
$0.40 

Stable Growth Phase 

Growth Rate in Stable Phase = 
5.00% 

FCFE in Terminal Year = 
$1.78 

Cost of Equity in Stable Phase = 
13.05% 

Price at the End of Growth Phase = 
$22.09 

PV of FCFE in High Growth Phase = 
$1.51 

Present Value of FCFE in Transition Phase = 
$1.90 

Present Value of Terminal Price = 
$5.76 

Value of the Stock = 
$9.17 
10.c. If the beta remains at 1.45 forever, but all other quantities are as in part a), then we have the same FCFE, but the following numbers will differ:
Year 
1 
2 
3 
4 
5 

Earnings 
$0.66 
$0.77 
$0.90 
$1.05 
$1.23 

(CapExDeprec'n) * (1) 
$0.05 
$0.06 
$0.07 
$0.08 
$0.10 

D Working Capital * (1) 
$0.27 
$0.31 
$0.37 
$0.43 
$0.50 

FCFE 
$0.34 
$0.39 
$0.46 
$0.54 
$0.63 

Present Value 
$0.29 
$0.30 
$0.30 
$0.31 
$0.31 

Transition Period (up to ten years) 

Year 
6 
7 
8 
9 
10 

Growth Rate 
14.60% 
12.20% 
9.80% 
7.40% 
5.00% 

Cumulated Growth 
14.60% 
28.58% 
41.18% 
51.63% 
59.21% 

Earnings 
$1.41 
$1.58 
$1.73 
$1.86 
$1.95 

(CapExDeprec'n) * (1) 
$0.11 
$0.13 
$0.14 
$0.15 
$0.16 

D Working Capital * (1) 
$0.45 
$0.39 
$0.30 
$0.22 
$0.13 

FCFE 
$0.84 
$1.07 
$1.29 
$1.50 
$1.67 

Beta 
1.45 
1.45 
1.45 
1.45 
1.45 

Cost of Equity 
14.98% 
14.98% 
14.98% 
14.98% 
14.98% 

Present Value 
$0.36 
$0.40 
$0.42 
$0.43 
$0.41 

Stable Growth Phase 

Growth Rate in Stable Phase = 
5.00% 

FCFE in Terminal Year = 
$1.92 

Cost Of Equity in Stable Phase = 
14.98% 

Price at End of Growth Phase = 
$19.19 

PV of FCFE In High Growth Phase = 
$1.51 

Present Value of FCFE in Transition Phase = 
$2.03 

Present Value of Terminal Price = 
$4.75 

Value of the Stock = 
$8.29 
Problem 11
a.
Year 
1 
2 
3 
4 
5 

Earnings 
$1.02 
$1.22 
$1.47 
$1.76 
$2.12 

(CapExDeprec'n)* (1) 
$0.00 
$0.00 
$0.00 
$0.00 
$0.00 

D Working Capital * (1) 
$0.85 
$1.02 
$1.22 
$1.47 
$1.76 

FCFE 
$0.17 
$0.20 
$0.24 
$0.29 
$0.35 

Present Value 
$0.15 
$0.16 
$0.17 
$0.18 
$0.19 

Year 
6 
7 
8 

Growth Rate 
15.00% 
10.00% 
5.00% 

Cumulated Growth 
15.00% 
26.50% 
32.83% 

Earnings 
$2.43 
$2.68 
$2.81 

(CapExDeprec'n)*(1) 
0 
$0.00 
$0.00 

D Working Capital *(1) 
$1.59 
$1.22 
$0.67 

FCFE 
$0.85 
$1.46 
$2.14 

Beta 
1.1 
1.1 
1.1 

Cost of Equity 
13.05% 
13.05% 
13.05% 

Present Value 
$0.41 
$0.62 
$0.80 

Stable Growth Phase 

Growth Rate in Stable Phase = 5.00% 

FCFE in Terminal Year = $2.25 

Cost of Equity in Stable Phase = 13.05% 

Price at the End of Growth Phase = $27.92 

PV of FCFE in High Growth Phase = $0.85 

Present Value of FCFE in Transition Phase = $1.83 

Present Value of Terminal Price = 
$10.46 

Value of the Stock = 
$13.14 
b. This would increase your working capital requirements, but the easier credit terms may also increase revenues. The net effect can be positive or negative.
c. Working capital is a high proportion of FCFE, and as such, the stock price estimate is likely to be very sensitive to changes in the working capital assumptions.
Problem 12.
A. Both models should have the same value, as long as a higher growth rate in earnings is used in the dividend discount model to reflect the growth created by the interest earned, and a lower beta to reflect the reduction in risk.
B. The dividend discount model will overstate the true value, because it will not reflect the dilution that is inherent in the issue of new stock.
C. Both models should provide the same value.
D. Since acquisition, with the intent of diversifying, implies that the firm is paying too much (i.e., negative net present value), the dividend discount model will provide a lower value than the FCFE model.
E. If the firm is overlevered to begin with, and borrows more money, there will be a loss of value from the overleverage. The FCFE model will reflect this lost value, and will thus provide a lower estimate of value than the dividend discount model.
Problem 13
a. From the information given, we can work out the following information:
EBITDA 
2483.125 
Depreciation 
960 
EBIT 
1523.125 
Interest 
320 
EBT 
1203.125 
Taxes 
433.125 
Net Income 
770 
Hence Free Cash Flow to the Firm = EBIT(1tax rate) +Depreciation  Capital Expenditures  Change in Working Capital = 1523.125(10.36) + 960  1200 = $734.8m.
b. The value of the equity = 200m. x $60 = $12b. The value of the debt = $4b. Hence, the value of the firm at the end of 1993 = $16b.
Reinvestment Rate = (1200960)/(1523.125(1.3) )= 10.09%
Expected Growth Rate in Operating Income = 10.83% (.1009) = 1.09%
The required rate of return on equity = 7% + 1.05(5.5%) = 12.775%; the cost of debt aftertax = 8%(10.36) = 5.12; the WACC = (4/16)(5.12) + (12/16)(12.775) = 10.86%. Assuming that the firm can grow at 1% a year forever, the value of the firm at the end of 1993 would be 734.8*1.0109/(.1086.0109) = $7,527 Million.
The value of equity would then be$3,527 million., with a pershare price of $ 17.63.
Problem 14
a., b. From the information given, we can compute the following:
Yr 
EBITDA 
Deprec'n 
EBIT 
EBIT 
Cap 
WC 
FCFF 
Term 
(1t) 
Exp. 
Value 

0 
$1,290 
$400 
$890 
$534 
$450 
$82 
$402 

1 
$1,413 
$438 
$975 
$585 
$493 
$90 
$440 

2 
$1,547 
$480 
$1,067 
$640 
$540 
$98 
$482 

3 
$1,694 
$525 
$1,169 
$701 
$591 
$108 
$528 

4 
$1,855 
$575 
$1,280 
$768 
$647 
$118 
$578 

5 
$2,031 
$630 
$1,401 
$841 
$708 
$129 
$633 
$14,326 
Terminal Yr 
$2,112 
$655 
$1,457 
$875 
$655 
$60 
$815 
The WACC in 1993 can be computed as 9.37%, using the cost of equity of 13.05% based on the current beta of 1.1.
Given the current beta and the current D/E ratio of 3200/3968, the unlevered beta = 0.74. If we assume that the operations of the firm do not change until after 1988, we can infer that the WACC for the firm is constant until 1998. After 1998, the stock beta changes to 0.74(1+(10.4)0.5) = 0.96 implying a cost of equity of 12.29% for 1999 and beyond. This is turn can be used to compute a WACC of 9.69%.
WACC after year 5 = 12.29% (2/3) + 7.5% (1.4) (1/3) = 9.69%
We can discount the FCFF to the firm from 1994 to 1998 at the WACC of 9.37, and thereafter at the rate of 9.69%. This yields the following:
Value of the Firm = 440/1.0937 + 482/1.0937^{2} + 528/1.0937^{3} + 578/1.0937^{4} + (633 + 14957)/1.0937^{5} = $11,172 

b. Value of Equity in the Firm = ($11172  Market Value of Debt) = 11172  3200 =$7,972 

Value Per Share = $7972/62 = 
$128.57 
The shares are grossly underpriced.
Problem 15
a. The after tax cost of debt is 7.5(10.4) = 4.5%, while the cost of equity = 7 + 1.15(0.55) = 13.325%. Using a debt ratio of 20%, we find that the cost of capital for the health division = (.2)(4.5) + (0.8)13.325 = 11.56%
b.
Year 
Deprec'n 
EBIT 
EBIT(1t) 
Cap Ex 
FCFF 
Term Val 
0 
$350 
$560 
$336 
$420 
$266 

1 
$364 
$594 
$356 
$437 
$283 

2 
$379 
$629 
$378 
$454 
$302 

3 
$394 
$667 
$400 
$472 
$321 

4 
$409 
$707 
$424 
$491 
$342 

5 
$426 
$749 
$450 
$511 
$364 
$5,021 
TY 
$443.04 
$778.96 
$468 
$531.44 
$379.60 
Value of the Division = 283/1.1156 + 302/1.1156^{2} + 321/1.1156^{3} + 342/1.1156^{4} + (364 + 5021)/1.1156^{5} = $ 4,021 million
c. If the acquirer perceives some synergy between its existing business and the health division, it might be willing to pay more. Also, if the health division is currently mismanaged or if there are currently negative synergies, then an acquirer who hopes to improve on this situation might be willling to pay more.
Problem 16
PE = Payout (1+g)/(rg) = 0.4417(1.06)/(.12775.06) = 6.91
b. The actual P/E ratio of 10 implies a price of $24. This implies a growth rate of g, where 1.06(1.06)/(.12775g) = 24. Hence g = 8%.
Problem 17
a. The average P/E ratio = 13.2, while the median P/E ratio = 12.25, which is the average of the 7^{th} ranking and 8^{th} ranking firm’s P/E ratios. The fact that the mean and the median are relatively close to each other means that there is no appreciable skewness: there are no great extreme values. We can, therefore, interpret either number as a means of the market’s valuation of earnings
b. This would be true if Thiokol’s riskiness were equal or less than that of the industry, on average. Another reason for Thiokol to have a lower P/E ratio even with no underpricing is if it were a low growth stock, say, because of a high payout ratio.
c. These kinds of differences can be controlled for using the regression approach. Using this approach, the second to last column gives us the estimated P/E ratios based on the payout ratio, risk and growth. The last column, which represents the difference between the actual P/E ratio and the estimated P/E ratio gives us an estimate of relative under or overvaluation. Positive values imply overvaluation, while negative values imply undervaluation:
P/E = 2.33 + 35.74 Growth Rate + 11.97 Beta + 2.90 Payout Ratio
Company 
Actual P/E 
Expected Growth 
Beta 
Payout 
Estimated P/E ratio 
Difference 
Thiokol 
8.7 
5.5 
0.95 
15 
11.44 
2.74 
Northrop 
9.5 
9 
1.05 
47 
14.82 
5.32 
Lockheed Corp. 
10.2 
9.5 
0.85 
37 
12.31 
2.11 
United Industrial 
10.4 
4.5 
0.7 
50 
9.11 
1.29 
Martin Marietta 
11 
8 
0.85 
22 
11.34 
0.34 
Grumman 
11.4 
10.5 
0.8 
37 
12.07 
0.67 
Raytheon 
12.1 
9.5 
0.75 
28 
10.85 
1.25 
Logicon 
12.4 
14 
0.85 
11 
13.17 
0.77 
Loral Corporation 
13.3 
16.5 
0.75 
23 
13.21 
0.09 
Rockwell 
13.9 
11.5 
1 
38 
14.85 
0.95 
General Dynamics 
15.5 
11.5 
1.25 
40 
17.90 
2.40 
GM Hughes 
16.5 
13 
0.85 
41 
13.68 
2.82 
Boeing 
17.3 
3.5 
1.1 
28 
12.90 
4.40 
McDonnell Doug. 
22.6 
13 
1.15 
37 
17.15 
5.45 
Problem 18
a. The current payout ratio = 2/4 = 0.5. Assume that this ratio will be kept constant. The return on equity = 4/40 = 10%. If we use the Gordon growth model, the price is estimated at 2(1.06)/(.11675.06) = $37.36. The price/book value ratio = 37.36/40 = 0.934. Alternatively, use the formula directly:
PBV = .10*.5*1.06/(.11675.06) = 0.934
b. The actual share price is $60. We can use this to solve for the value of g in the equation 60 = 2(1+g)/(.11675g). Solving, we find g = 8%. If g = 8%, then we need a Return on Equity, such that .08 = .5(Return on Equity); i.e. the required Return on Equity = 16%. This approach focuses on the price element in the price/book value ratio, since book value is an accounting quantity and is not necessarily directly related to market pricing.
Problem 19
a. The average Price/Book Value ratio = 1.66. I wouldn’t necessarily use this ratio to price the new issue because of the heterogeneity amongst these firms. In particular, even though most of the firms have zero payout ratios like our firm, nevertheless, some of them have high payout ratios, such as Browning Ferris and SafetyKleen. Growth rates also vary quite a bit. These factors affect the Market Value to Book Value ratio.
b. I would regress the Price/Book Value ratio on the other factors and use to come up with a ratio that’s more appropriate for our company. I would also use the data on the debt/equity ratios of the companies to estimate a beta for our company and use that to price it as well. I would use this as an additional input to price the new issue. I would expect that our firm having a lower payout ratio and a higher growth rate than the average would also have a higher Price/Book Value ratio. The lower beta also suggests a higher price to bookvalue ratio.
Problem 20
a. The price can be estimated as 1.12(1.06)/(.07+.9(.055).06)) = $19.95. Hence the price/sales multiple = 19.95/122 = 0.1635. Alternatively,
PS= .02 * 0.4571 * (1.06)/(.1195  .06) = 0.163
Where the profit margin = 2.45/122 = 2%
b. If the stock is trading at $34, then the pricesales multiple is 34/122 = 0.2787. If this price is correct, then the earnings per share would have to increase (assuming that the payout ratio remains constant). We would need to have dividends this year of D(1.06) /(.07+.9(.055).06)) = $34, or D = 1.90. Hence, we would need earnings of (2.45/1.12)1.90 = $4.17 per share. With sales of $122, this implies a profit margin of 4.17/122 = 3.42%
Problem 21
Yes. There are several reasons why Walgreen might have a high Price to Sales ratio and still be fairly priced; however, they don’t seem to apply here. One reason might be that the firm expects higher sales in the future. However, Walgreen’s expected growth rate of 13.5% is less than the average of the firms, which is 14.5. Furthermore, the payout ratio is higher than the average for the sample (22.3). On the other hand, the firm’s beta is higher than the average for the sample (0.9) and so is the firm’s profit margin of 2.7 relative to 1.9. However, on balance, the firm does seem to be overpriced, at least compared with firms such as Arbor Drugs, which has a higher profit margin, a lower payout ratio and a higher expected growth rate.