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# Finance: Share valuation and probabilities.

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9.4 You own one share in a company called Invest Co. Inc. Examining the balance sheet, you have determined that the firm has \$100,000 cash, equipment worth \$900,000, and 100,000 shares outstanding.

Calculate the price/value of each share in the firm, and explain how your wealth is affected if:

A. The firm pays out dividends of \$1 per share.

B. The firm buys back 10,000 shares for \$10 cash each, and you choose to sell your share back to the company.

C. The firm buys back 10,000 shares for \$10 cash each, and you choose not to sell your share back to the company.

D. The firm declares a 2-for-1 stock split.

E. The firm declares a 10% stock dividend.

F. The firm buys new equipment for \$100,000, which will be used to earn a return equal to the firm's discount rate.

10.1 A. Calculate the mean and standard deviation of the following securities' returns:

Year
Computroids Inc. Blazers Inc.
1
10% 5%
2
5% 6%

3 3% 7%
4 12% 8%
5 10% 9%

B.
Assuming these observations are drawn from a normally distributed probability space, we know that about 68% of values drawn from a normal distribution are within one standard deviation away from the mean or expected return; about 95% of the values are within two standard deviations; and about 99.7% lie within three standard deviations.

Using your calculations from part A, calculate the 68%, 95%, and 99% confidence intervals for the two stocks. To calculate the 68%, you would calculate the top of the confidence interval range by adding one standard deviation to the expected return, and calculate the bottom of the confidence interval by subtracting one standard deviation from the expected return. For 95%, use two standard deviations, and for 99%, use three.

Your answer should show three ranges from the bottom of the confidence interval to the top of the confidence interval.

C.
For each security, would a return of 14% fall into the 68% confidence interval range? If not, what confidence interval range would it fall into, or would it be outside all three confidence intervals?

[This is the same as asking whether a return of 14% has less than a 68% probability of occurring by chance for that security. If it's not inside the 68% confidence interval, it's unlikely to occur, since it will only occur by chance 32% of the time. Of course, the 99% confidence interval is much more likely to include the observed return, simply by chance. Only 1% of the time will it fall outside the 99% CI. Pretty rare.

10.3 You are starting a new business, and you want to open an office in a local mall. You have been offered two alternative rental arrangements. You can pay the landlord 10% of your sales revenue, or you can pay a fixed fee of \$1,000 per month. Describe the circumstances in which each of these arrangements would be your preferred choice.

https://brainmass.com/statistics/confidence-interval/finance-share-valuation-and-probabilities-384022

#### Solution Summary

The problem set deals with estimating share value and also calculating the probability of share returns.

\$2.19

## Bond Valuation, Stock Valuation, Preferred Stock Required Return, Preferred Stock Valuation, Bond Valuation/ YTM/ Interest Rate Risk, Bond Returns, Stock/ Business Valuation, CAPMCapital Structure Decisions & Credit Ratings Dividend Adjustment Model Dividend Policy Bond Funding: Public/Private Placement Net Advantage to Leasing

A1. A \$ 1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond's coupon rate is 7.4%. What is the fair value of this bond?

A 10. (Dividend Discount model) Assume RHM is expected to pay a total cash dividend of \$5.60 next year and its dividends are expected to grow at a rate of 6% per year forever. Assuming annual dividend payments, what is the current market value of a share of RHM stock if the required return on RHM common stock is 10%?

A12. (Required return for preferred stock) James River \$3.38 preferred is selling for \$45.25. The preferred dividend is nongrowing. What is the required return on James River preferred stock?

A 14. (Stock valuation) Suppose Toyota has nonmaturing (perpetual) preferred stock outstanding that pays a \$1.00 quarterly dividend and has a required return of 12% APR. What is the stock worth?

B 16. (Interest rate risk) Philadelphia Electric has many bonds trading on the New York Stock Exchange. Suppose PhilEl's bonds have identical coupon rates of 9.125% but that one issue matures in 1 year, one in 7 years, and the third in 15 years. Assume that a coupon payment was made yesterday
a. If the yield to maturity for all three bonds is 8%, what is the fair price of each bond?
b. Suppose that the yield to maturity for all of these bonds changed instantaneously to 7%. What is the fair price of each bond now?
c. Suppose that the yield to maturity for all of these bonds changed instantaneously again, this time to 9%. Now what is the fair price of each bond?
d. Based on the fair prices at the various yields to maturity, is interest-rate risk the same, higher, or lower for longer-versus shorter-maturity bonds?

B 18. (Default risk) You buy a very risky bond that promises a 9.5% coupon and return of \$1,000 principal in 10 years. You pay only \$500 for the bond.
a) You receive the coupon payments for three years and the bond defaults. After liquidating the firm, the bondholders receive a distribution of \$150 per bond at the end of 3.5 years. What is the realized return on your investment?
b) The firm does far better than expected and bondholders receive all of the promised interest and principal payments. What is the realized return on your investment?

B 20. (Constant growth model) Medtrans is a profitable firm that is not paying a dividend on its common stock. James Weber, an analyst for A.G. Edwards, believes that Medtrans will begin paying a \$1.00 per share dividend in two years and that the dividend will increase 6% annually thereafter. Bret Kimes, one of James' colleagues at the same firm, is less optimistic. Bret thinks that Medtrans will begin paying a dividend in four years, that the dividend will be \$1.00, and that it will grow at 4% annually. James and Bret agree that the required return for Medtrans is 13%.
a. What value would James estimate for this firm?
b. What value would Bret assign to the Medtrans stock?

C1. (Beta and required return) The riskless return is currently 6%, and Chicago Gear has estimated the contingent returns given here.
a. Calculate the expected returns on the stock market and on Chicago Gear stock.
b. What is Chicago Gear's beta?
c. What is Chicago Gear's required return according to the CAPM?

Realized Return
State of the market Probability that state occurs Stock market Chicago Gear
Stagnant 0.20 -10.00% -15.00%
Slow growth 0.35 10.00% 15.00%
Average growth 0.30 15.00% 25.00%
Rapid growth 0.15 25.00% 35.00%

B1. (Choosing financial targets) Bixton Company's new chief financial officer is evaluating Bixton's capital structure. She is concerned that the firm might be underleveraged, even though the firm has larger-than-average research and development and foreign tax credits when compared to other firms in its industry. Her staff prepared the industry comparison shown here.
a. Bixton's objective is to achieve a credit standing that falls, in the words of the chief financial officer, "comfortably within the 'A' range." What target range would you recommend for each of the three credit measures?
b. Before settling on these target ranges, what other factors should Bixton's chief financial officer consider?
c. Before deciding whether the target ranges are really appropriate for Bixton in its current financial situation, what key issues specific to Bixton must the chief financial officer resolve?
Rating Category Fixed Charge Coverage Funds From Operations/Total Debt Long-Term Debt/Capitalization
Aa 4.00-5.25x 60-80% 17-23%
A 3.00-4.30 45-65 22-32
Baa 1.95-3.40 35-55 30-41

A10. (Dividend adjustment model) Regional Software has made a bundle selling spreadsheet software and has begun paying cash dividends. the firm's chief financial officer would like the firm to distribute 25% of its annual earnings (POR = 0.25) and adjust the dividend rate to changes in earnings per share at the rate ADJ = 0.75. Regional paid \$1.00 per share in dividends last year. It will earn at least \$8.00 per share this year and each year in the foreseeable future. Use the dividend adjustment model, Equation (18.1), to calculate projected dividends per share for this year and the next four.

B2. (Dividend policy) A firm has 20 million common shares outstanding. It currently pays out \$1.50 per share year in cash dividends on its common stock. Historically, its payout ratio has ranged from 30% to 35%. Over the next five years it expects the earnings and discretionary cash flow shown below in millions.
A.over the five year period, what is the maxium overall payout ratio the firm could acieve without triggering a securities issue?
B. Recommend a reasonable dividend policy for paying out discretionary cash flow in years 1 through 5.

1 2 3 4 5 Thereafter
Earnings 100 125 150 120 140 150+ per year
Discrecreary cash flow 50 70 60 20 15 50+per year

A2. (Comparing borrowing costs) Stephens Security has two financing alternatives: (1) A publicly placed \$50 million bond issue. Issuance costs are \$1 million, the bond has a 9% coupon paid semiannually and the bond has a 20-year life. (2) A \$50 million private placement with a large pension fund. Issuance costs are \$500,000, the bond has a 9.25% annual coupon, and the bond has a 20-year life. Which alternative has the lower cost (annual percentage yield)?