12_fsav2e_sm_final_05.20

Module 12

Cost of Capital and Valuation Basics

QUESTIONS

Q12-1. Finding the present value of a bond consists of finding the present value of all future cash flows and determining the discount (effective) rate. A bond may have a lump-sum (face value of the bond) and an annuity (coupon payments) component. Multiplying the coupon rate by the face amount of the bond will yield the coupon payments. The appropriate present value factors can be determined one of two ways. The first is to find the present value factors using the appropriate present value tables. The second method computes the present value factors. Using the tables, the present value of the face value of the bond can be found by multiplying the face value of the bond by the present value factor for lump sums (found in the present value tables using the appropriate number of periods and the effective rate). The appropriate annuity multiplication factor (for the appropriate number of periods and annuity effective rate) can also be found on the annuity present value table. The coupon payment is then multiplied by this annuity multiplication factor. The present value of the face value of the bond and coupon payments can then be added together to find the present value of the bond.

Alternatively, the present value factors can be computed. The present value factor for the face value of the bond can be computed as 1/ (1+r)n where r is the effective (discount) rate and n represents the number of periods. The coupon payments can be treated as a series of lump-sums. The factor for each coupon payment can be found by using the lump sum formula (1/ (1+r)n). Summing the product from multiplying each payment by the appropriate present value factor will also yield the present value of the bond.

Q12-2. A bond consists of a finite series of payments. The payments are stipulated on the face of the bond. The bond will have, at most, two payment streams; the face value of the bond and (often) the coupon payments.

A company can be valued using the dividend discount model. However, with the going concern assumption, the dividends may be considered as a perpetuity or a growing perpetuity. The final dividend payment is unknown and must be estimated. All of these cash flows must be discounted by the cost of equity capital.

Q12-3. The company’s market beta (β) is a statistical coefficient that provides an estimation of a company’s stock price volatility (sensitivity) relative to the market. The company’s market beta is estimated from a regression of a company’s stock returns (dependent variable) on a market index of returns

©Cambridge Business Publishers, 2010

Solutions Manual, Module 12 12-1

(independent variable) over a reasonable period of time (often the previous 60 months). The market index of returns represents the returns from a portfolio of all risky assets (a market index like the S&P 500 can be used as a proxy for the market portfolio). By definition, the market has a beta of one. A beta of 0.5 (2.0) implies that a stock’s volatility is approximately half of (double) the market return. A beta of 1.0 implies that the stock’s volatility will approximate that of the market.

Q12-4. Beta is a backward looking risk estimate. It assumes that the risk factor will not change in the future. It does not account for company changes or economy wide changes that may affect the company’s risk relative to the market. It also does not account for other risk factors.

Q12-5. The company’s stock price represents the price utilized in the most recent trade. The intrinsic value represents the company’s value estimated using insights gained from financial statement analysis and the company’s fundamentals (dividends and other payoffs). The dividend discount model, using estimated future dividends and the cost of equity capital, is one means to estimate the intrinsic value of a company’s stock.

Q12-6. The cost of debt capital is the product of two components. The first is the average borrowing rate and the second is one minus the marginal tax rate. The average borrowing rate and marginal tax rates can generally be estimated from the notes to the financial statement. One less the marginal tax rate represents the cost of debt after the tax savings from the interest expense is taken into account.

Q12-7. The market premium is the difference between the expected return on the market and the expected risk-free rate.

The cost of equity capital can be estimated from the expected risk-free rate, the expected market premium, and beta. The market’s expected return, or cost of equity capital, can be computed by adding the product of beta and the market premium to the risk-free rate.

Q12-8. The cost of capital represents the return the investor must receive in order to invest in a risky asset. The investor must recover two costs (1) the foregone interest from investing in this asset (time value of money) and (2) the risk the investor incurs for investing in this asset.

Q12-9. A series of payments are considered an annuity when they (1) are equal payments, (2) over equal time periods, (3) with a constant discount rate.

Q12-10. A perpetuity represents an annuity that lasts forever. The present value factor of a perpetuity can be computed as 1/r where r represents the appropriate discount rate. The present value of a perpetuity is computed as the product of the present value factor of a perpetuity and the perpetuity payment.

Q12-11. The present value factor of a growing perpetuity can be computed as 1/(r-g) where r represents the appropriate discount rate and g represents the growth rate. This is often called the Gordon Growth Model. The present value of a growing perpetuity can be computed as the product of the present value factor and the perpetuity payment.


Financial Statement Analysis & Valuation, 2nd Edition12-2

MINI EXERCISES

M 12-12 (20 minutes)

Years 1 2 3 4 5

Cash flows, 10% coupon rate...... $100.00 $100.00 $100.00 $100.00 $1,100.00

Present value factor, 8% rate.......0.925926 0.857339 0.793832 0.73503 0.680583

Present value of cash flows......... $92.59 $85.73 $79.38 $73.50 $748.64

Present value computation:Year 1.......................................$ 92.59Year 2....................................... 85.73Year 3....................................... 79.38Year 4....................................... 73.50Year 5....................................... 748.64 Present value of bond............$1,079.85


Years 1 2 3

Cash flows, 8% coupon rate.. $400.00 $400.00 $5,400.00

Present value factor, 9% rate 0.917431 0.84168 0.772183

Present value of cash flows. . $366.97 $336.67 $4,169.79

Present value computation:Year 1....................................... $ 366.97Year 2....................................... 336.67Year 3....................................... 4,169.79Present value of bond............ $4,873.43


5% + [0.8 x (8% - 5%)] = 7.4%




5% – [0.8 x (8% - 5%)] = 2.6%


P0 = $10.00D1 = $0.25P1 = $10.50

The expected cost of capital is 7.5%.


P0 = $15.00D1 = $1.00r = 10%

The expected price at the end of period 1 is $15.50.




6% x (1-35%) = 3.9%


($80/$1,600) x (1-35%) = 3.25%







We know that:

Substituting:

Solving for re: Cost of equity capital = 5%





EXERCISES

E 12-26 (20 minutes)

a. Average borrowing cost = Interest expense / Average debt outstanding = $307 million / [($5 billion + $4.9 billion)/2] = 6.2%

b. Cost of debt capital = Average borrowing cost x (1 - Tax rate)= 6.2% x (1-35%)= 4%


a. A beta of 0.32 indicates that Kellogg’s stock is less volatile than the market index. This means that for each 1% increase in the market return, Kellogg’s stock tends to move only 0.32%.

b. Using the CAPM model as explained in this module, we get:Cost of equity = 4.6% + [0.32 x 5%]

= 6.2%


a. Total market capitalization= $50.06 x (418.515339 shares – 20.817930 shares) = $19.9 billion

b. The weighted average cost of capital can be estimated as follows:




a. A beta of 0.99 implies that TOUSA’s stock has roughly the same level of volatility as the market index (in this case the S&P 500). That is, TOUSA’s stock price will move at about the same percentage rate as the market overall.

b. Calculating the weighted average cost of capital requires estimating the cost of debt capital and the cost of equity capital.

The cost of debt capital can be estimated from Equation 12.4.

The expected cost of equity capital can be estimated from the CAPM in Equation 12.1.

The expected weighted average cost of capital can be estimated from Equation 12.5.




a. Using the DDM model with a constant perpetuity, we get:

Price estimate = Dividends per share / Cost of equity capital= $1.24/0.062= $20

b. The estimated price ($20) is substantially lower than its recent market price of $50.50. This means that the market participants expect Kellogg to enjoy both positive future growth and increases in its dividend per share beyond the current $1.24.


Using the DDM with an increasing perpetuity, we get:

Price estimate = Dividends per share / (Cost of equity capital – Growth)$50.50 = $1.24 / (6.2% - Growth)

This relation implies that the expected growth rate = 3.8%.




[Instructor note: In late 2007, TOUSA was being traded at about $0.14 per share.]

a.

b.

c.




The terminal dividend is an estimate of an investment’s future worth when the investment in that asset is terminated.

Because the current payout ratio ($0.06) is so small the estimate of the terminal dividend plays a significant role in the intrinsic value computation. It appears that the estimates of a perpetuity or a 4% growth in dividends do not meet the market’s perception of the terminal value.


To verify this solution, plug the growth rate into the Gordon growth model:



PROBLEMS

P 12-35 (40 minutes)

Computation of common shares outstanding as of June 30, 2007:

Common shares issued............................................................ 3,989.7 million

Number of treasury shares....................................................... 857.8 million

Number of common shares outstanding................................. 3,131.9 million

Computation of P&G’s market capitalization as of June 30, 2007:

Market capitalization = Stock price x Number of shares outstanding= $67.25 x 3,131.9 million= $210.62 billion




a. Average before-tax borrowing cost equals = $1.5 billion / $22.1 billion= 6.8%

Cost of debt capital = 6.8% x (1 - 35%)= 4.4%

b. A beta of 2.12 means that Sprint Nextel’s stock price tends to be volatile compared to the market index. Specifically, each 1% move in the market price index, on average, is expected to yield a 2.12% change in Sprint’s stock price.

c. Cost of equity capital = 4.6% + (2.12 x 5%)= 15.2%

The 15.2% cost of equity capital indicates that investors demand a high return for investing in highly volatile stocks such as Sprint Nextel.

d. Weighted average cost of capital computation:




a. Its 2007 balance sheet only reports the number of shares issued, not the number of shares outstanding. Thus, we need to look at the statement of retained earnings to identify the number of shares outstanding, which is 509,034,801.

We then multiply this number by the stock price, $76.55, to yield its market capitalization as follows:

Market capitalization = Stock price x Number of shares outstanding= $76.55 x 509,034,801= $38.97 billion

b. Its book value of long-term debt is reported on the balance sheet. We see that the current portion of long-term debt equals $138.1 million. Thus, adding this amount to the long-term debt number in the non-current liability section of $3,221.9 million, we get the book value of long-term debt:

$3,221.9 million + $138.1 million = $3,360.0 million

c. The market value of Colgate-Palmolive’s debt, according to Yahoo.Finance.com, is computed by subtracting the market capitalization from the total enterprise value:

Market value of debt = Total enterprise value – Market capitalization $3.52 billion = $42.49 billion – $38.97 billion

d. The difference in the estimates computed in parts c and d can be due to several reasons—some of which follow:i. Yahoo.Finance.com might include other liabilities, such as lease

obligations, in the calculation of debt.ii. The market price of Colgate-Palmolive’s debt changed in value on

December 31, 2007.iii. The market value and book value of debt differs due to accounting

usage of historical cost.



P 12-37 (concluded)

e. Cost of debt capital = 5.6% x (1-35%) = 3.6%

f. Cost of equity capital = 4.6% + (0.46 x 5%) = 6.9%

g. Weighted average cost of capital:




a.

b. Estimate of re given price and dividends per share.

c. The 2.47% estimated cost of equity capital seems low. The rf has historically fluctuated around 4% to 6%, and the 2.47% cost of equity capital would be below the expected risk-free rate. This would imply that the investment has a negative beta.




a.

b. When assuming that the dividends will continue as a perpetuity the intrinsic value per share is (the DDM uses the cost of equity capital as the denominator):

IV = $0.36 / 0.081IV = $4.44

c. Using the Gordon growth DDM:

This 7.77% growth seems high. It emphasizes one of the weaknesses in DDM. That is, when estimating intrinsic value using DDM, a tremendous amount of weight is placed on the dividends beyond the forecast horizon (the so called terminal dividend). Moreover, forecasting the terminal dividend is difficult.




a. Cost of equity capital = 4.6% + (0.7 x 5%) = 8.1%

b. Intrinsic value = $1.41 / 0.081 = $17.41

c. Given the historical growth in P&G’s business, especially its acquisition of Gillette, it is unreasonable to expect P&G’s business, as well as dividends, to stop growing after 2007. Hence, using the DDM model with a constant perpetuity would likely underestimate P&G’s intrinsic value.

d. Comparing the two growth rates for sales (20.2% versus 4.4%), the latter one is more reasonable. The 20.2% rate would overestimate the growth rate because the 2005 sales number does not include sales from Gillette.

When using a sales growth rate of 4.4%, we can estimate P&G’s intrinsic value using the Gordon Growth model as follows:

e. We can use the Gordon growth model to infer the market’s expected growth rate as follows:

Solving for the growth rate, we get growth equal to 5.5%. Thus, investors seem to expect P&G to grow at a faster rate than the historical number of 4.4%. This difference likely reflects investors’ expected synergy between P&G and Gillette.




a. Total book value of preferred stocks at the end of fiscal year 2006$3,100 million = $25,000 per share x 124,000 shares

Total book value of preferred stocks at the end of fiscal year 2005$1,750 million = $25,000 per share x 70,000 shares

b. The cost of preferred equity capital is computed as

.

During the year 2006, Goldman Sachs declared a total of $139 million preferred stock dividends. And, the average amount of preferred stock outstanding is $2,425 million, computed as ($3,100 mil. + $1,750 mil.)/2. Consequently, the cost of preferred equity capital is 5.7%, computed as

.

c. A common method to compute WACC when a company has outstanding preferred stock is to apply the following formula from the textbook:

Alternatively, some analysts choose to treat preferred stock as part of debt capital. In this case, the market value (or book value) of preferred stock is added to the amount of debt capital (net), and any dividends on preferred stock are included in net interest expenses. We must remember that dividends on preferred stocks are not tax deductible. This alternative method of computing WACC yields the same result as above.




a.

b.

Using the Gordon growth DDM:



DISCUSSION POINTS

D 12-43 (50 minutes)

a. $1,843 million in interest expense, per AT&T’s income statement.

b. At December 31, 2006:Interest-bearing debt = Long-term debt + Debt maturing within one year $59,796 million = $50,063 million + $9,733 million

At December 31, 2005:Interest-bearing debt = Long-term debt + Debt maturing within one year $30,570 million = $26,115 million + $4,455 million

c. Pretax cost of debt capital = Interest expense / Average interest-bearing debt

Importantly, see that AT&T had a substantial increase in debt on December 29, 2006, when AT&T acquired BellSouth and AT&T Mobility. Therefore, given that this acquisition occurred within 2 days of year-end, we decide to use the amount of debt from December 31, 2005, as the denominator in the calculation of pretax cost of debt capital.

Pretax cost of debt capital

NOTE: Students can get different results depending on the numerator used for this computation—this will then carry over to part e.

d.

NOTE: Some students will want to use the 35% statutory rate—this will then carry over to part e.

e. After-tax cost of debt capital = Pretax cost of debt capital x (1- Marginal tax rate)

4.08% = 6.03% x (1 - 32.40%)




a. AT&T’s beta is 1.01, which is close to 1. A market beta of nearly 1.0 implies that the stock of AT&T, on average, moves with changes in market prices.

b. The expected cost of equity capital can be estimated from the CAPM in Equation 12.1.

c. Using the information in Footnote 8, we can use the book value of debt as a proxy for the intrinsic value of debt in the formula for WACC. Thus, the total amount of long-term debt (including debt maturing within one year) equals $59,796 million, computed as $50,063 million + $9,733 million.

AT&T’s balance sheet shows that as of December 31, 2006, it had 6,495 million shares issued. However, 256 million of those shares are in treasury. Accordingly, the total number of shares outstanding equals 6,239 million. This means its total market cap equals $223,044 million, computed as $35.75 stock price per share x 6,239 million shares. From these measures we compute WACC:




a. AT&T’s consolidated statements of stockholders’ equity reports that $1.35 in dividends per common share were declared in 2006.

b. We use the Gordon growth DDM as follows:

Solving for growth, this implies that the market expects the growth in dividends to be 5.92%

c. The implied growth rate of 5.92% seems reasonable for AT&T. It might be on the low end compared to the valuation parameters of other comparable companies.




a. Most analysts interpret a company’s decision to increase its dividends as good news. This is because it reveals management confidence that the company’s future operation can generate enough income to finance those increased dividend payments. As we can see from the dividend discount model, an increase in future expected dividends, ceteris paribus, increases a stock’s value.

Further, the decision to buy back stocks is interpreted by some analysts as an indication that management believes its stock to be undervalued. This usually results in a stock price increase.

b. When AT&T made the announcements referenced, its stock price jumped by 4.1%. This jump is less than the 12.7% increase in its dividends. Such a result can occur for several reasons:

As evident from the solution for D 12-45, part of the increase in dividends is anticipated by market participants. As a result, some of the increase is already incorporated into the stock price before the announcement is made.

Additional market-wide factors determine a stock’s price. For instance, the discount factor might change. Specifically, the stock market, overall, declined on that same day (for example, the S&P 500 index fell by 2.5% on that day).

Market participants might not expect the 12.7% increase in dividends to be permanent.



12_fsav2e_sm_final_05.20

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