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CHAPTER 8
Stock Valuation
ANSWERS TO
END-OF-CHAPTER QUESTIONS
8-1. Preferred stock is often referred to as a hybrid security. This is because preferred stock has many characteristics of both common stock and bonds. It has characteristics of common stock, such as no fixed maturity date, nonpayment of dividends does not force bankruptcy, and the nondeductibility of dividends for tax purposes. But it is like bonds because the dividends are fixed in amount like interest payments. From the point of view of the preferred stockholder, this is not the most advantageous combination. On one hand, the dividends are limited as with bond interest, but the security of forced payment by the threat of bankruptcy is not there. Thus, from the point of view of the investor, the worst features of common stock and bonds are combined.
8-2. To a certain extent, preferred stock dividends can be thought of as a liability. The major difference between preferred dividends in arrears and normal liabilities is that nonpayment of them cannot force the firm into bankruptcy. However, since the goal of the firm is common shareholder wealth maximization, which involves getting money to the shareholders (dividends), preferred arrearages provide a barrier for achieving this goal.
8-3. A cumulative feature requires all past unpaid preferred stock dividends be paid before any common stock dividends are declared. A stockholder would like preferred stock to have a cumulative dividend feature because without it there would be no reason why preferred stock dividends would not be omitted or passed when common stock dividends were passed. Since preferred stock does not have the dividend enforcement power of interest from bonds, the cumulative feature is necessary to protect the rights of preferred stockholders.
Other frequent protective features serve to allow for voting rights in the event of nonpayment of dividends or to restrict the payment of common stock dividend if sinking-fund payments are not met or if the firm is in financial difficulty. In effect, the protective features included with preferred stock are similar to the restrictive provisions included with long-term debt.
8-4. Fixed rate preferred stock has dividends that do not vary from the fixed amount or from period to period.
Adjustable rate preferred stock is preferred stock that has quarterly dividends that fluctuate with interest rates under a formula that ties the dividend payment at either a premium or discount to the highest of the three-month Treasury bill rate, the 10-year Treasury bond constant maturity rate, or the 20-year Treasury bond constant maturity rate. The rates have maximum and minimum levels called the dividend rate band.
The purpose of allowing the interest rate to fluctuate is to minimize the fluctuation in the value of the preferred stock. It is also very appealing in times of high and fluctuating interest rates.
8-5. With PIK (payment-in-kind) preferred stock, investors receive no dividends initially; they merely get more preferred stock, which in turn pays dividends in even more preferred stock. Usually after 5 or 6 years, if all goes well for the issuing company, cash dividends should replace the preferred stock dividends, generally ranging from 12 percent to 18 percent, to entice investors to purchase PIK preferred.
8-6. Convertibility allows a preferred stockholder to convert or exchange preferred stock for shares of common stock at a predetermined exchange rate. This option gives preferred stockholders more freedom in investment decisions by allowing them to convert into common stock at their discretion. It gives the preferred stockholder a higher cash return then the common stock but allows for sharing in some of the future appreciation of the common stock.
Preferred stock may be callable by the issuer so that in the event interest rates decline and cheaper funding becomes available, the stock may be called and new securities may be issued at a lower cost. To agree to the call feature, the investor requires a slightly higher rate of return. Call of a convertible preferred stock enables a company to turn the preferred stock into common equity; i.e., calling it without having to spend the cash.
8-7. Both values are based on future cash flows to be received by stockholders. Preferred stock typically has a predetermined constant dividend. For common stock, the dividend is based on profitability of the firm and on management’s decision to pay dividends or to retain the profits for reinvestment purposes. Thus, the growth of future dividends is a prime distinguishing feature of common stock.
8-8. The expected rate of return is the rate of return that may be expected from purchasing a security at the prevailing market price. Thus, the expected rate of return is the rate that equates future cash flows with the actual selling price of the security in the market.
8-9. The required rate of return is the discount rate that equates the present value of future cash flows with the value of the security. As with the internal rate of return for a capital budgeting problem, we have to find the rate of return that sets the future cash flows equal to the cost of the security. This rate may have to be developed by trial and error.
8-10. The two types of return are dividend income and capital gains. The dividend income for common stockholders differs from preferred stockholders, in that no specified dividend amount is to be received. However, the common stockholders are permitted to participate in the growth of the company. As a result of this growth, their second source of return, price appreciation, is realized.
SOLUTIONS TO
END-OF-CHAPTER PROBLEMS
Solutions to Problem Set A
8-1A. Value (Vps) = [pic]
= $50.00
8-2A. Growth rate = return on equity x retention rate
= (16%) ( (60%) = 9.6%
8-3A. Value (Vps) = [pic]
= [pic]
= $116.67
8-4A. Expected Rate of Return
ps = [pic] = [pic] = or .0463, or 4.63%
8-5A. (a) Expected return = [pic] = [pic] = .085 = 8.5%
(b) Given your 8 percent required rate of return, the stock is worth $42.50 to you.
Value = [pic] = [pic] = $42.50
Since the expected rate of return (8.5%) is greater than your required rate of return (8%), or since the current market price ($40) is less than the value ($42.50), the stock is undervalued and you should buy.
8-6A. Value (Vcs) = [pic] + [pic]
$50 = [pic] + [pic]
Rearranging and solving for P1:
P1 = $50 (1.15) - $6
P1 = $51.50
The stock would have to increase $1.50 ($51.50 - $50) or 3 percent ($1.50/$50) to earn a 15% rate of return.
8-7A. (a) [pic] = [pic] + [pic]
cs = [pic] + .10
cs = .1889, or 18.9%
(b) Vcs = [pic] = $28.57
Yes, purchase the stock. The expected return is greater than your required rate of return. Also, the stock is selling for only $22.50, while it is worth $28.57 to you.
8-8A. Value (Vcs) = [pic]
Vcs =
Vcs = $24.50
8-9A. Growth rate = return on equity x retention rate
= (18%) ( (40%) = 7.2%
8-10A. Expected Rate of Return ([pic]) = [pic] + Growth Rate
[pic] = + 0.095
[pic] = 0.193, or 19.3%
8-11A. Value (Vcs) = [pic] + [pic]
Vcs = [pic] + [pic]
Vcs = $39.96
8-12A. If the expected rate of return is represented by [pic]:
Current Price = [pic] + [pic]
[pic] = [pic] - 1
[pic] = [pic] - 1
[pic] = 0.1823, or 18.23%
8-13A.
(a) [pic] = [pic] = [pic]
[pic] = 0.1091, or 10.91%
(b) Value (Vps) = [pic] = [pic] = $36
(c) The investor's required rate of return (10 percent) is less than the expected rate of return for the investment (10.91 percent). Also, the value of the stock to the investor ($36) exceeds the existing market price ($33), so buy the stock.
8-14A.(a) Expected Rate of Return = [pic] + [pic]
= [pic] + 0.08
= 0.1407, or 14.07%
(b) Investor's Value = [pic]
= [pic]
= $57.02
(c) Yes, the expected rate of return (14.07%) is greater than your required rate of return (10.5 percent). Also, your value of the stock ($57.02) is greater than the current market price ($23.50).
8-15A (a) Dividend yield: Dividend ( stock price = [pic] = 0.0229, or 2.29%
(b) [pic] = [pic] + beta ( [pic] - [pic]
= 3.8% + 1.10 ( (13.3% - 3.8%) = 14.25%
(c) [pic] = [pic] + [pic]
14.25% = [pic]+ g
.1425 = .0229 + g
g = .1196, or 11.96%
8-16A
Johnson & Johnson
| |2000 |1999 |1998 |1997 |1996 |
|EPS |$3.39 |$2.94 |$2.23 |$2.47 |$2.12 |
|Dividend |$1.24 |$1.09 |$0.97 |$0.85 |$0.74 |
Stock Price (2/20/01): $96.03
Growth rate: $3.39 = $2.12 (1 + i)4
i = .1245, or 12.45%
[pic]cs = [pic]
[pic]cs = [pic]
[pic]cs = .1390, or 13.90%
Solution to Integrative Problem
1. Value (Vb) based upon your required rate of return:
Bond:
Vb = [pic]+ [pic]
= $140(6.194) + $1,000(.257)
= $867.16 + $257
= $1,124.16
Preferred Stock:
Vps = [pic]
However, since the dividend is a constant amount each year with no maturity date (infinity), the equation can be reduced to
Vps = [pic]
= [pic]
= $85.71
Common Stock:
Step 1: Estimate Growth Rate
Company's earnings have doubled ($4 to $8) in ten years. What annual compound growth rate would cause an investment to double in ten years? Looking in Appendix B (Compound sum of $1) an interest factor of 2.000 for ten years is closest to seven percent (1.967). Thus, at about seven percent, money would double in ten years. (The same conclusion could have been reached by using Appendix C but by using a .500 present value interest factor.)
Growth Rate (g) = 7%
Step 2: Solve for Value
Vcs = [pic]
[pic]
If the seven percent growth rate (g) is assumed constant, the equation may be reduced to
Vcs = [pic]
= [pic]
= [pic]
= [pic]
= $24.69
2. Your Value Selling Price
Bond $1,124.16 $1,200.00
Preferred Stock 85.71 90.00
Common Stock 24.69 25.00
Purchase none of the investments as their market values are selling above their value to you.
3. Bond:
Vb = [pic]+ [pic]
= $140(5.660) + $1,000(.208)
= $792.40 + $208.00
= $1,000.00
You would not buy the bond; it is not worth $1,200.00.
Preferred Stock:
Vps = [pic]
= $75.00
Do not buy. Your value is less than what you would have to pay for the stock.
Common Stock:
Vcs = [pic]
= $29.18
Buy. Your value is greater than what you would have to pay for the stock.
4. Assuming a growth rate of 12 percent:
[pic]
Buy the stock. Because of the expected increase in future dividends, the stock is now worth more to you ($42) than you would have to pay for it ($25) –assuming that the selling price did not increase also.
Solutions to Problem Set B
8-1B. Value (Vps) = [pic]
= $70.00
8-2B. Growth rate = return on equity x retention rate
= (24%) × (70%) = 16.8%
8-3B. Value (Vps) = [pic]
= [pic]
= $133.33
8-4B. Expected Rate of Return
ps = [pic] = [pic] = .0426, or 4.26%
8-5B. (a) Expected return = [pic] = [pic] = .0844 , or 8.44%
(b) Given your 8 percent required rate of return, the stock is worth $40.62 to you
Value = [pic] = [pic] = $40.625
Since the expected rate of return (8.44%) is greater than your required rate of return (8%) or since the current market price ($38.50) is less than the value ($40.62), the stock is undervalued and you should buy.
8-6B. Value (Vcs) = [pic] + [pic]
$52.75 = [pic] +[pic]
Rearranging and solving for P1:
P1 = $52.75 (1.16) - $6.50
P1 = $54.69
The stock would have to increase $1.94 ($54.69 - $52.75), or 3.68 percent, ($1.94/$52.75) to earn a 16% rate of return.
8-7B.
(a) [pic] = [pic] + [pic]
[pic] = [pic] + .105
[pic] = 0.2137, or 21.37%
(b) Vcs = [pic] = $38.46
The expected rate of return exceeds your required rate of return, which means that the value of the security to you is greater than the current market price. Thus, you should buy the stock.
8-8B. Value (Vcs) = [pic]
Vcs = [pic]
Vcs = $28.39
8-9B. Growth rate = return on equity x retention rate
= (24%) ( (60%) = 14.4%
8-10B. Expected Rate of Return ([pic]) = [pic] + Growth Rate
[pic] = [pic] + 0.085 = 0.181, or 18.1%
8-11B. Value (Vcs) = [pic] + [pic]
Vcs = [pic] + [pic]
Vcs = $37.37
8-12B. If the expected rate of return is represented by [pic]:
Current Price = [pic] + [pic]
[pic] = [pic] - 1
[pic] = [pic] - 1
[pic] = 0.1136, or 11.36%
8-13B. (a) [pic] = [pic] = [pic] = 11.43%
(b) Value (Vps ) =[pic] = [pic] = $40
(c) The investor's required rate of return (10 percent) is less than the expected rate of return for the investment (11.43 percent). Also, the value of the stock to the investor ($40) exceeds the existing market price ($35). The investor should buy the stock.
8-14B. (a) Expected Rate of Return = [pic] +
= [pic] + 0.08
= 0.1232, or 12.32%
(b) Investor's Value = [pic]
= [pic]
= $36.00
(c) Yes, the expected rate of return is greater than your required rate of return (12.32 percent versus 11 percent). Also, your value of the stock ($36.00) is higher than the current market price ($25.00).
8.15B (a) Dividend yield: Dividend ( stock price = [pic] = 2.22%
(b) [pic] = [pic] + beta ( [pic] - [pic]
= 3.8% + 0.90 ( (13.3% - 3.8%) = 12.35%
(c) [pic] = [pic] + [pic]
12.35% = [pic] + g
.1235 = .0222 + g
g = .1013, or 10.13%
8-16B
First Union Corporation
| |1999 |1998 |1997 |1996 |1995 |
|EPS |$3.33 |$2.95 |$2.99 |$2.58 |$2.38 |
|Dividend |$1.88 |$1.58 |$0.90 |$1.10 |$0.98 |
Stock Price (12/31/99): $32.9375
Growth rate: $3.33 = $2.38 (1 + i)4
i = .0876, or 8.76%
[pic]cs = [pic]
[pic]cs = [pic]
[pic]cs = .1497, or 14.97%
Solutions to Appendix 8A
8A-1. Using the NVDG model,
Vcs = [pic] + [pic]
where kcs = the investor's required rate of return
EPS1 = the firm's earning per share in year 1
g = the growth rate, which is the firm's earnings retention rate times its return on equity.
PV1 = [pic]- r x EPS1
r = the firm's earnings retention rate
ROE = the firm's return on equity investment
For our problem,
PV1 = [pic]- (0.65) x ($5)
= $4.0625 - $3.25
= $0.8125
and Pcs = [pic]
= $31.25 + $27.08
= $58.33
Using the more traditional dividend-growth model, we get:
Vc = [pic]
Since D1 = EPS1(1 - the retention rate), and
g = the retention rate x return on equity
Pcs = [pic] = [pic] = $58.33
8A-2. Given the EPS1 is expected to be $7 and the investor's required rate of return is 18 percent, the value of the stock, assuming no growth opportunities would be:
Pcs = [pic] = $38.89
where kcs = the investor's required rate of return
EPS1 = the firm's earning per share in year 1
To compute the present value of the growth opportunities, PVDG, for each scenario, we use the following equation:
NVDG = [pic]
where PV1 = [pic]- r x EPS1
g = the growth rate, which is the firm's earnings retention rate times its return on equity.
r = the firm's earnings retention rate
ROE = the firm's return on equity investment
Given the different possible retention rates and ROEs, we may solve for the respective PV1s. The results are as follows:
Possible Different Retention Rates
ROEs 0% 30% 60%
16% 0.00 -0.23 -0.47
18% 0.00 0.00 0.00
24% 0.00 0.70 1.40
We next calculate the NVDG for each scenario by dividing the above PV1 values by kcs - g, which gives the following results:
Possible Different Retention Rates
ROEs 0% 30% 60%
16% 0.00 -1.74 -5.60
18% 0.00 0.00 0.00
24% 0.00 6.48 38.89
Adding the $38.89 price, assuming no growth, to the above NVDGs, we get:
Possible Different Retention Rates
ROEs 0% 30% 60%
16% 38.89 37.15 33.29
18% 38.89 38.89 38.89
24% 38.89 45.37 77.78
Thus, our results show that value is created only when management reinvests at above the investor's required rate of return. That is, growth may actually decrease the firm's value if the profitability of the new investments are not adequate enough to satisfy the investor's required returns.
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