Chapter 10
Valuation
P10-1.
Using the CAPM model, we can calculate ABC’s required rate of return as follows:
rf = 0.053 (US Treasury Bills)
rm - rf = 0.094 (Market risk premium)
= 0.54
r = rf + (rm - rf) = 0.053 + 0.54(0.094) = 0.1038
No-growth dividend discount model:
P0 = / D / = / 1.50 / = $14.46r / 0.1038
With the current market price of $18, ABC’s stock seems to be overvalued. Therefore, we would not recommend purchase.
P10-2.
One begins by using the CAPM model to calculate Furniware’s required rate of return:
rf = 0.055 (Long-term Government Bond)
rm = 0.133 (Large Company Stocks)
= 1.25
r = rf + (rm - rf) = 0.055 + 1.25(0.133 – 0.055) = 0.1525
The constant-growth dividend discount model is then used to arrive at a valuation:
P0 = / D0(1 + g) / = / 1.65(1+ 0.05) / = $16.90r - g / 0.1525 - 0.05
The fair value of Furniware’s stock according to the constant-growth dividend discount model is $16.90 per share.
P10-3.
Furniware’s required rate of return remains the same, r = 0.1525.
The next step is to calculate the sustainable growth rate of its earnings:
ROE = 0.155
Payout Rate = 0.6
g = ROE(1 - PayoutRate) = 0.155(1 – 0.6) = 0.062
Using the constant-growth dividend discount model to arrive at a valuation:
P0 = / D0(1 + g) / = / 1.65(1 + 0.062) / = $19.36r - g / 0.1525 - 0.062
With the additional information pertinent to Furniware’s sustainable growth rate, the fair value of its stock according to the constant-growth dividend discount model is $19.36 per share. As a result of an increase in the estimate of Furniware’s growth rate, the fair value of the stock increased.
P10-4.
Under the constant-growth model:
P0 = / D0(1 + g)r – g
or, equivalently,
g = / P0r – D0 / = / 22.5x0.156 – 0.80 / = 11.63%P0 + D0 / 22.5 + 0.80
The current stock price implies a constant growth rate of somewhat less than 12%.
An estimate of Partners’ sustainable growth rate can be computed as follows:
ROE = 0.215
PayoutRate = 0.4
g = ROE(1 - PayoutRate) = 0.215(1 – 0.4) = 0.129
The sustainable growth rate of 12.9% is somewhat higher than the growth rate implied in current stock price. This difference suggests that the Partners’ stock is undervalued. The fair stock price, which can be derived from the sustainable growth rate, reveals the magnitude of the undervaluation:
P0 = / D0(1 + g) / = / 0.80(1 + 0.129) / = $33.45r - g / 0.156 – 0.129
Partners’ stock price is currently underpriced by $10.95 or 48%.
P10-5.
To calculate the company’s growth rates:
g = ROE(1 – PayoutRate)
Short-term: gshort = 0.30(1 – 0.20) = 0.240
Long-term: glong = 0.18(1 – 0.60) = 0.072
Calculate investors’ required rate of return:
rf = 0.051 (Long-term Government Bond)
rm - rf = 0.085
= 1.25
r = rf + (rm - rf) = 0.051 + 1.25(0.085) = 0.1573
Meyers’ EPS and dividends for the next four years:
Current earnings E0 = $2.25. If payout rate remains the same, earnings will increase at the same rate as dividends.
Year / 1 / 2 / 3 / 4EPS / $2.79 / $3.46 / $4.29 / $4.60
Dividends / $0.56 / $0.69 / $0.86 / $2.76
Using the constant-growth, dividend discount model:
P3 = / D4 / = / 2.76 / = $32.36r - glong / 0.1573 - 0.072
Therefore,
P0 = / D1 / + / D2 / + / D3 / + / P31 + r / (1 + r)2 / (1 + r)3 / (1 + r)3
= / 0.56 / + / 0.69 / + / 0.86 / + / 32.36
1.1573 / (1.1573)2 / (1.1573)3 / (1.1573)3
= / 0.4839 / + / 0.5152 / + / 0.5548 / + / 20.8771
= / $22.43
Meyers’ fair stock price is $22.43.
P10-6.
Calculate the required rate of return with CAPM model:
rf = 0.055 (long-term government bonds)
rm - rf = 0.085 (market risk premium)
= 1.55
r = rf + (rm - rf) = 0.055 + 1.55(0.085) = 0.1868
Fair stock price with H-model:
H = 7/2 = 3.5
gshort = 0.185
glong = 0.136
D0 = $0.25
r = 0.1868
P0 = / D0(1 + glong) + D0(H)(gshort - glong) / = / 0.25(1.136) + 0.25(3.5)(0.185 – 0.136)r - glong / 0.1868 - 0.136
= $6.43
The fair stock price using the H-model is $6.43.
P10-7.
Choice B is correct.
The geometric mean return will always be less than or equal to the arithmetic return from a stock by nature of the respective computations of each of these performance metrics. Moreover, the geometric return will be closer to the arithmetic return when the variability of annual returns is lower. Thus, only statement B is correct.
P10-8.
Value (in thousands) Percentage
Book Value of Debt (D)$14,500 48.33%
Market Value of Equity (E)$15,500 51.67%
(1,000 thousand shares @ $15.50)
Total Capital (V)$30,000100.00%
Pre-tax Cost of Debt
rD = 0.075 (interest rate on debt)
Cost of Equity (using CAPM)
rf = 0.053 (20-year Government Bonds)
rm – rf = 0.085 (Market risk premium)
= 1.15
rE = rf + (rm - rf) = 0.053 + 1.15(0.085) = 0.1508
Weighted Average Cost of Capital
T = 0.33
= 0.4833(1 – 0.33)0.075 + 0.5167x0.1508 = 0.1022
P10-9.
When a firm floats a new issue of long-term debt to buy back a portion of its outstanding shares, it may increase its earnings per share. However, as more debt is floated, equityholders’ residual cash flow is more volatile. Therefore, a decrease in the P/E ratio is caused by an increase in r; that is, the firm has borne more risk than it had previously. The P/E ratio contracted to compensate for the added risk.
P10-10.
Required rate of return using CAPM:
rf = 0.055 (Long-term Government Bonds)
rm = 0.125 (Market risk premium)
= 1.45
r = rf + (rm - rf) = 0.055 + 1.45(0.125 – 0.055) = 0.1565
Residual income approach:
B = $18.00
ROE = 0.205
g = ROE(1 - PayoutRate) = 0.205(1 – 0.40) = 0.1230
= 18.00 + 26.06 = $44.06
P10-11.
Choice D is correct. The underlying assumption of all discounted cash flow models is the “going-concern” assumption. Discounting expected future dividends, free cash flows, or any other cash flows to their present values to produce the fair price is only meaningful if the company is going to stay in the business as an independent entity. If there is evidence that the company does not plan to retain its current operating structure, then estimates of expected future cash flows would not have much meaning, and discounted cash flow models will not be very illuminating.
Market-based models, as discussed in the text, are directly linked to the dividend discount model. In fact, they are simplified dividend discount models. The going-concern assumption is still critical to those models. Because the management is considering liquidation, asset-based models that derive the firm’s worth from the recoverable value of its assets are more appropriate.
Case 10-1
SBC Communications – For What It’s Worth
- Dividends grew from $0.975 per share in 1999 to $1.025 in 2001, for an annual growth rate of approximately 2.5%. As a percentage of net income, dividends rose from 41% in 1999 to 48% in 2000. Thus, the growth in dividends per share was derived from increasing the payout ratio rather than growth in net income. Return on Average Equity (NI/SE) was 7,242/0.5(32,491+30,463) or 23% in 2001. Assuming a 50% payout ratio, the sustainable growth rate is 23%(50%) or 11.5%. The 2.5% actual growth in dividends appears quite sustainable.
- The current year dividend is $1.025. At a 2.5% growth rate, next year’s dividend will be $1.05. We estimate the cost of equity as 5.5% + (0.5)(5.0%) = 8.0%. Thus, the current DDM predicted value is P = 1.05/(0.08 – 0.025) = $19.09, or about half the current share price. Assuming the 11.5% sustainable growth rate would be impossible, since the growth rate is higher than the cost of equity. However, if we assume a Beta of 1.0 and reduce the estimated sustainable growth to 10% we can get the following: D1 = 1.025(1.1) = 1.1275. r = 5.5% + 5.0% = 11.5%. P = 1.1275/(0.115 – 0.10) = $75.17, or about twice the current price. Thus, the dividend discount approach yields a dubious fair value estimate ranging from 50% to 200% of the current share price.
Current Sales (Exclude Wireless) / $45,753 / Assuming 5% growth:
Sales Growth Rate (Exclude Wireless) / ~2.5% / 5.0%
Forecasted Sales / 46,897 / 48,041
Average Operating Margin (All) / ~22.5% / ~22.5%
Forecasted Operating Profit / 10,552 / 10,809
Tax Rate / ~38% / ~38%
Forecasted After-tax Profit / 6,542 / 6,702
Add Depreciation and Amortization / 9,077 / 9,077
Working Capital/Sales Ratio / (27%) / (27%)
Incremental Working Capital Requirements / 333 / 618
Average CapEx/Sales Ratio / ~23.5% / ~23.5%
Forecasted CapEx / (11,021) / (11,290)
Forecasted Free Cash Flow / 4,931 / 5,107
Value / % of Cap / Cost / Contrib.
To WACC
Book value of debt (short and long) / 26,166 / 17.25% / 6.2% / 1.07%
Market value of equity / 125,734 / 82.75% / 8.0% / 6.62%
Total capital / 151,900 / 100.00% / 7.69%
To calculate the DCF value, we take next year’s FCF of $4,931 and discount it at 5.19% (7.69% – 2.5% growth): 4,931/0.0519 = 95,009. From the firm value we deduct debt to arrive at a 68,843 equity value, or $20.26 per share – much less than the current $37 market price. Based on 5% growth, we get 5,107/0.0269 = 189,851 in firm value, 163,685 in equity value and a stock price of $48.17 – 30% higher than the current price.
- Discounted cash flow models are highly sensitive to the estimated growth rate, which is a subjective measure.