Question: Put Pricing Model Use the Black–Scholes

> Watters Umbrella Corp. issued 15-year bonds 2 years ago at a coupon rate of 5.9 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM?

> In each of the following cases, find the unknown variable. Ignore taxes. Accounting Break-Even Unit Variable Unit Price Cost Fixed Costs Depreciation 86,300 $ 42 $30 $ 820,000 143,806 81 2,750,000 $1,150,000 7,835 97 235,000 105,000

> Down Under Boomerang, Inc., is considering a new three- year expansion project that requires an initial fixed asset investment of $1.65 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which it will b

> Eckely, Inc., recently issued bonds with a conversion ratio of 14.5. If the stock price at the time of the bond issue was $53.16, what was the conversion premium?

> Gasworks, Inc., has been approached to sell up to 5 million gallons of gasoline in three months at a price of $2.65 per gallon. Gasoline is currently selling on the wholesale market at $2.34 per gallon and has a standard deviation of 62 percent. If the r

> Use the option quote information shown here to answer the questions that follow. The stock is currently selling for $114. a. Suppose you buy 10 contracts of the February 110 call option. How much will you pay, ignoring commissions? b. In part (a), supp

> What is the price of a 15-year, zero coupon bond paying $1,000 at maturity, assuming semiannual compounding, if the YTM is: a. 6 percent? b. 8 percent? c. 10 percent?

> What is a call option? A put option? Under what circumstances might you want to buy each? Which one has greater potential profit? Why?

> You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a common practice with expensive, high-tech equipment). The scanner costs $5,800,000, and it would be depreciated straight-line to zero over four ye

> Stone Shoe Co. has concluded that additional equity financing will be needed to expand operations and that the needed funds will be best obtained through a rights offering. It has correctly determined that as a result of the rights offering, the share pr

> For the company in Problem 2, show how the equity accounts will change if: a. The company declares a four-for-one stock split. How many shares are outstanding now? What is the new par value per share? b. The company declares a one-for-five reverse stock

> For the company in the previous problem, what is the dividend yield? What is the expected capital gains yield?

> Define each of the following investment rules and discuss any potential shortcomings of each. In your definition, state the criterion for accepting or rejecting independent projects under each rule. a. Payback period. b. Internal rate of return. c. Profi

> What is the difference between an American option and a European option?

> What are some of the potential problems with looking at IRRs when evaluating a leasing decision?

> It is sometimes suggested that firms should follow a “residual” dividend policy. With such a policy, the main idea is that a firm should focus on meeting its investment needs and maintaining its desired debt−equity ratio. Having done so, a firm pays out

> Due to large losses incurred in the past several years, a firm has $2 billion in tax loss carryforwards. This means that the next $2 billion of the firm’s income will be free from corporate income taxes. Security analysts estimate that it will take many

> How does the existence of financial distress costs and agency costs affect Modigliani and Miller’s theory in a world where corporations pay taxes?

> In a world with no taxes, no transaction costs, and no costs of financial distress, is the following statement true, false, or uncertain? Moderate borrowing will not increase the required return on a firm’s equity. Explain.

> What are the key differences between leasing and borrowing? Are they perfect substitutes?

> Preferred stock doesn’t offer a corporate tax shield on the dividends paid. Why do we still observe some firms issuing preferred stock?

> Which of the following statements are true about the efficient market hypothesis? a. It implies perfect forecasting ability. b. It implies that prices reflect all available information. c. It implies an irrational market. d. It implies that prices do not

> David McClemore, the CFO of Ultra Bread, has decided to use an APT model to estimate the required return on the company’s stock. The risk factors he plans to use are the risk premium on the stock market, the inflation rate, and the price of wheat. Becaus

> Your company currently produces and sells steel shaft golf clubs. The board of directors wants you to consider the introduction of a new line of titanium bubble woods with graphite shafts. Which of the following costs are not relevant? a. Land you alread

> Suppose a project has conventional cash flows and a positive NPV. What do you know about its payback? Its discounted payback? Its profitability index? It’s IRR? Explain.

> A substantial percentage of the companies listed on the NYSE and the NASDAQ don’t pay dividends, but investors are nonetheless willing to buy shares in them. How is this possible given your answer to the previous question?

> You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a common practice with expensive, high-tech equipment). The scanner costs $5,800,000, and it would be depreciated straight-line to zero over four ye

> A convertible bond with a par value of $1,000 has a conversion price of $72.45. What is the conversion ratio of the bond?

> Explain what is meant by business and financial risk. Suppose Firm A has greater business risk than Firm B. Is it true that Firm A also has a higher cost of equity capital? Explain.

> What is the essential difference between sensitivity analysis and scenario analysis?

> What are the two options that many businesses have?

> In the aggregate, debt offerings are much more common than equity offerings and typically much larger as well. Why?

> Taxes are an important consideration in the leasing decision. Which is more likely to lease: A profitable corporation in a high tax bracket or a less profitable one in a low tax bracket? Why?

> A corollary to the Rule of 72 is the Rule of 69.3. The Rule of 69.3 is exactly correct except for rounding when interest rates are compounded continuously. Prove the Rule of 69.3 for continuously compounded interest.

> A useful rule of thumb for the time it takes an investment to double with discrete compounding is the “Rule of 72.” To use the Rule of 72, you simply divide 72 by the interest rate to determine the number of periods it takes for a value today to double.

> What is the equation for the present value of a growing perpetuity with a payment of C one period from today if the payments grow by C each period?

> A check-cashing store is in the business of making personal loans to walk-up customers. The store makes only one-week loans at 6.5 percent interest per week. a. What APR must the store report to its customers? What is the EAR that the customers are actua

> As discussed in the text, an annuity due is identical to an ordinary annuity except that the periodic payments occur at the beginning of each period and not at the end of the period. Show that the relationship between the value of an ordinary annuity and

> What is the value of an investment that pays $50,000 every other year forever, if the first payment occurs one year from today and the discount rate is 13 percent compounded daily? What is the value today if the first payment occurs four years from today

> What are the main differences between corporate debt and equity? Why do some firms try to issue equity in the guise of debt?

> Your financial planner offers you two different investment plans. Plan X is a $20,000 annual perpetuity. Plan Y is a 10-year, $34,000 annual annuity. Both plans will make their first payment one year from today. At what discount rate would you be indiffe

> J. Smythe, Inc., manufactures fine furniture. The company is deciding whether to introduce a new mahogany dining room table set. The set will sell for $6,100, including a set of eight chairs. The company feels that sales will be 1,900, 2,250, 2,700, 2,45

> You purchase one call and sell one put with the same strike price and expiration date. What is the delta of your portfolio? Why?

> Assume Stocks A and B have the following characteristics: The covariance between the returns on the two stocks is .001. a. Suppose an investor holds a portfolio consisting of only Stock A and Stock B. Find the portfolio weights, X A and X B, such that

> What is the impact of a stock repurchase on a company’s debt ratio? Does this suggest another use for excess cash?

> After extensive medical and marketing research, Pill, Inc., believes it can penetrate the pain reliever market. It is considering two alternative products. The first is a medication for headache pain. The second is a pill for headache and arthritis pain.

> A stock is currently priced at $50. The stock will never pay a dividend. The risk-free rate is 12 percent per year, compounded continuously, and the standard deviation of the stock’s return is 60 percent. A European call option on the stock has a strike

> There are two stocks in the market, Stock A and Stock B. The price of Stock A today is $75. The price of Stock A next year will be $64 if the economy is in a recession, $87 if the economy is normal, and $97 if the economy is expanding. The probabilities

> O’Bannon Electronics has an investment opportunity to produce a new HDTV. The required investment on January 1 of this year is $145 million. The firm will depreciate the investment to zero using the straight-line method over four years.

> How do you determine the appropriate cost of debt for a company? Does it make a difference if the company’s debt is privately placed as opposed to being publicly traded? How would you estimate the cost of debt for a firm whose only debt issues are privat

> Suppose you observe the following situation: a. Calculate the expected return on each stock. b. Assuming the capital asset pricing model holds and Stock A’s beta is greater than Stock B’s beta by .25, what is the exp

> The Biological Insect Control Corporation (BICC) has hired you as a consultant to evaluate the NPV of its proposed toad ranch. The company plans to breed toads and sell them as ecologically desirable insect control mechanisms. They anticipate that the bu

> In the chapter we noted that the delta for a put option is N(d1) − 1. Is this the same thing as −N(−d1)? (Hint: Yes, but why?)

> There are three securities in the market. The following chart shows their possible payoffs: a. What are the expected return and standard deviation of each security? b. What are the covariances and correlations between the pairs of securities? c. What a

> Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $400 and has an existing customer base of 700. Paul plans to raise the annual fee by 6 percent every year and expects the club membership to grow at a consta

> What is the main difference between the WACC and APV methods?

> Burklin, Inc., has earnings of $21 million and is projected to grow at a constant rate of 5 percent forever because of the benefits gained from the learning curve. Currently, all earnings are paid out as dividends. The company plans to launch a new proje

> Hardwick Enterprises is evaluating alternative uses for a three-story manufacturing and warehousing building that it has purchased for $1,250,000. The company can continue to rent the building to the present occupants for $60,000 per year. The present oc

> The put–call parity condition is altered when dividends are paid. The dividend-adjusted put–call parity formula is: where d is again the continuously compounded dividend yield. a. What effect do you think the dividen

> Suppose you observe the following situation: Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market? What is the risk-free rate? Security Beta Expected Return Pete Corp. 1.35 12.28% Repete Co. .80

> How does a bond issuer decide on the appropriate coupon rate to set on its bonds? Explain the difference between the coupon rate and the required return on a bond.

> You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $900 per month in a stock account in real dollars and $300 per month in a bond account in real dollars. The effective annual return of the stock accou

> The Stambaugh Corporation currently has earnings per share of $8.20. The company has no growth and pays out all earnings as dividends. It has a new project that will require an investment of $1.95 per share in one year. The project is only a two-year pro

> Suppose we are thinking about replacing an old computer with a new one. The old one cost us $450,000; the new one will cost $580,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $130,

> In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black–Scholes option pricing model with dividends is: All of the variables are the same as the Black–Scholes

> Consider the following information about Stocks I and II: The market risk premium is 7.5 percent, and the risk-free rate is 4 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is â€&#156

> When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost

> Why do we use an aftertax figure for cost of debt but not for cost of equity?

> This one’s a little harder. Suppose the current share price for the firm in the previous problem is $62.40 and all the dividend information remains the same. What required return must investors be demanding on Storico stock? (Hint: Set up the valuation f

> Your company has been approached to bid on a contract to sell 15,000 voice recognition (VR) computer keyboards a year for four years. Due to technological improvements, beyond that time they will be outdated and no sales will be possible. The equipment n

> Strudler Real Estate, Inc., a construction firm financed by both debt and equity, is undertaking a new project. If the project is successful, the value of the firm in one year will be $213 million, but if the project is a failure, the firm will be worth

> Assume a firm is considering a new typical project that requires an initial investment with sales, variable costs and fixed costs over its life. Will the project usually reach the accounting, cash, or financial break-even point first? Which will it reach

> Suppose the risk-free rate is 4.7 percent and the market portfolio has an expected return of 11.2 percent. The market portfolio has a variance of .0382. Portfolio Z has a correlation coefficient with the market of .28 and a variance of .3285. According t

> The following Treasury bond quote appeared in The Wall Street Journal on May 11, 2004: Why would anyone buy this Treasury bond with a negative yield to maturity? How is this possible?

> Storico Co. just paid a dividend of $3.40 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend

> The technique for calculating a bid price can be extended to many other types of problems. Answer the following questions using the same technique as setting a bid price; that is, set the project NPV to zero and solve for the variable in question. a. In

> Brozik Corp. has a zero coupon bond that matures in five years with a face value of $40,000. The current value of the company’s assets is $38,000, and the standard deviation of its return on assets is 50 percent per year. The risk-free rate is 6 percent

> A portfolio that combines the risk-free asset and the market portfolio has an expected return of 8 percent and a standard deviation of 17 percent. The risk-free rate is 4.3 percent, and the expected return on the market portfolio is 11 percent. Assume th

> The Frush Corporation has two different bonds currently outstanding. Bond M has a face value of $30,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $800 every six months over the subsequent eight years, and fina

> Consider the following statement: For the APT to be useful, the number of systematic risk factors must be small. Do you agree or disagree with this statement? Why?

> Most corporations pay quarterly dividends on their common stock rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers, or maintains the current dividend once a year and then pays this dividend out in eq

> Another utilization of cash flow analysis is setting the bid price on a project. To calculate the bid price, we set the project NPV equal to zero and find the required price. Thus the bid price represents a financial break- even level for the project. Gu

> In our capital budgeting examples, we assumed that a firm would recover all of the working capital it invested in a project. Is this a reasonable assumption? When might it not be valid?

> McLemore Industries has a zero coupon bond issue that matures in two years with a face value of $75,000. The current value of the company’s assets is $46,000, and the standard deviation of the return on assets is 60 percent per year. a. Assume the risk-f

> Beginning with the cost of capital equation—that is: show that the cost of equity capital for a levered firm can be written as follows: RAce =B + SR, B R. + B+SR, WACC R, = R, + GR, – R,) R.)

> The market portfolio has an expected return of 11 percent and a standard deviation of 19 percent. The risk-free rate is 4.3 percent. a. What is the expected return on a well-diversified portfolio with a standard deviation of 9 percent? b. What is the sta

> The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). a. Suppose that today you buy a bond with

> The Cornchopper Company is considering the purchase of a new harvester. Cornchopper has hired you to determine the break-even purchase price in terms of present value of the harvester. This break-even purchase price is the price at which the project’s NP

> Consider four different stocks, all of which have a required return of 14 percent and a most recent dividend of $3.50 per share. Stocks W, X, and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 7 percent, 0 per

> A proposed cost-saving device has an installed cost of $710,000. The device will be used in a five-year project but is classified as three-year MACRS property for tax purposes. The required initial net working capital investment is $65,000, the marginal

> An investor is said to take a position in a “collar” if she buys the asset, buys an out-of-the-money put option on the asset, and sells an out-of-the-money call option on the asset. The two options should have the same time to expiration. Suppose Marie w

> Classify the following events as mostly systematic or mostly unsystematic. Is the distinction clear in every case? a. Short-term interest rates increase unexpectedly. b. The interest rate a company pays on its short-term debt borrowing is increased by it

> Suppose a firm’s business operations mirror movements in the economy as a whole very closely—that is, the firm’s asset beta is 1.0. Use the result of the previous problem to find the equity beta for this firm for debt–equity ratios of 0, 1, 5, and 20. Wh

> Under what two assumptions can we use the dividend growth model presented in the chapter to determine the value of a share of stock? Comment on the reasonableness of these assumptions.

> Milano Pizza Club owns three identical restaurants popular for their specialty pizzas. Each restaurant has a debt–equity ratio of 40 percent and makes interest payments of $41,000 at the end of each year. The cost of the firm’s levered equity is 19 perce

> You have been provided the following data about the securities of three firms, the market portfolio, and the risk-free asset: a. Fill in the missing values in the table. b. Is the stock of Firm A correctly priced according to the capital asset pricing

> Bond P is a premium bond with a coupon of 8.5 percent. Bond D has a coupon of 5.5 percent and is selling at a discount. Both bonds make annual payments, have a YTM of 7 percent, and have 10 years to maturity. What is the current yield for Bond P? For Bon

> M.V.P. Games, Inc., has hired you to perform a feasibility study of a new video game that requires an initial investment of $8 million. M.V.P. expects a total annual operating cash flow of $1.5 million for the next 10 years. The relevant discount rate is

> Fincher Manufacturing has projected sales of $135 million next year. Costs are expected to be $76 million and net investment is expected to be $15 million. Each of these values is expected to grow at 14 percent the following year, with the growth rate de

> Some people argue that the efficient market hypothesis cannot explain the 1987 market crash or the high price-to-earnings ratios of Internet stocks during the late 1990s. What alternative hypothesis is currently used for these two phenomena?