Question: Use the Black–Scholes model and redraw

> How does the position of an equipment lessor differ from the position of a secured lender when a firm falls into bankruptcy? Assume that the secured loan would have the leased equipment as collateral. Which is better protected, the lease or the loan? Doe

> The Safety Razor Company has a large tax-loss carry forward and does not expect to pay taxes for another 10 years. The company is therefore proposing to lease $100,000 of new machinery. The lease terms consist of eight equal lease payments prepaid annual

> Nodhead College needs a new computer. It can either buy it for $250,000 or lease it from Compulease. The lease terms require Nodhead to make six annual payments (prepaid) of $62,000. Nodhead pays no tax. Compulease pays tax at 35%. Compulease can depreci

> A lease with a varying rental schedule is known as a structured lease. Try structuring the Greymare Bus Lines lease to increase value to the lessee while preserving the value to the lessor. Assume that Greymare does not pay tax. (Note: In practice the t

> In Section 25-5 we stated that if the interest rate were zero, there would be no advantage in postponing tax and therefore no advantage in leasing. Value the Greymare Bus Lines lease with an interest rate of zero. Assume that Greymare does not pay tax. C

> In Section 25-5 we listed four circumstances in which there are potential gains from leasing. Check them out by conducting a sensitivity analysis on the Greymare Bus Lines lease, assuming that Greymare does not pay tax. Try, in turn, a. a lessor tax rat

> n Section 25-4 we showed that the lease offered to Greymare Bus Lines had a positive NPV of $820 if Greymare paid no tax and a +$700 NPV to a lessor paying 35% tax. What is the minimum lease payment the lessor could accept under these assumptions? What i

> Piglet Pies has issued a zero-coupon 10-year bond that can be converted into 10 Piglet shares. Comparable straight bonds are yielding 8%. Piglet stock is priced at $50 a share. a. Suppose that you had to make a now-or-never decision on whether to convert

> The Surplus Value Company had $10 million (face value) of convertible bonds outstanding in 2015. Each bond has the following features. Face value....................................$1,000 Conversion price..........................$25 Current cal

> Johnny Jones’s high school derivatives homework asks for a binomial valuation of a 12-month call option on the common stock of the Overland Railroad. The stock is now selling for $45 per share and has an annual standard deviation of 24%

> Explain carefully why bond indentures may place limitations on the following actions: a. Sale of the company’s assets. b. Payment of dividends to shareholders. c. Issue of additional senior debt.

> a. If interest rates rise, will callable or noncallable bonds fall more in price? b. Sometimes you encounter bonds that can be repaid after a fixed interval at the option of either the issuer or the bondholder. If the exercise price of each option is the

> Suppose that a company simultaneously issues a zero-coupon bond and a coupon bond with identical maturities. Both are callable at any time at their face values. Other things equal, which is likely to offer the higher yield? Why?

> After a sharp change in interest rates, newly issued bonds generally sell at yields different from those of outstanding bonds of the same quality. One suggested explanation is that there is a difference in the value of the call provisions. Explain how th

> a. Residential mortgages may stipulate either a fixed rate or a variable rate. As a borrower, what considerations might cause you to prefer one rather than the other? b. Why might holders of mortgage pass-through certificates wish the mortgages to have a

> Elixir Corporation has just filed for bankruptcy. Elixir is a holding company whose assets consist of real estate worth $80 million and 100% of the equity of its two operating subsidiaries. It is financed partly by equity and partly by an issue of $400 m

> Proctor Power has fixed assets worth $200 million and net working capital worth $100 million. It is financed partly by equity and partly by three issues of debt. These consist of $250 million of First Mortgage Bonds secured only on the company’s fixed as

> Bond prices can fall either because of a change in the general level of interest rates or because of an increased risk of default. To what extent do floating-rate bonds and puttable bonds protect the investor against each of these risks?

> Suppose that the J.C. Penney bond was issued at face value and that investors continue to demand a yield of 8.25%. Sketch what you think would happen to the bond price as the first interest payment date approaches and then passes. What about the price of

> Maple Aircraft has issued a 4¾% convertible subordinated debenture due 2020. The conversion price is $47.00 and the debenture is callable at 102.75% of face value. The market price of the convertible is 91% of face value, and the price of the common is $

> For which of the following options might it be rational to exercise before maturity? Explain briefly why or why not. a. American put on a non-dividend-paying stock. b. American call—the dividend payment is $5 per annum, the exercise price is $100, a

> True or false? Briefly explain in each case. a. It is better to hold unsecured bonds than secured bonds in the event of default. b. Many new and exotic debt securities are triggered by government policies or regulations. c. Call provisions give a valuabl

> a. As a senior bondholder, would you like the company to issue more junior debt to finance its investment program, would you prefer it not to do so, or would you not care? b. You hold debt secured on the company’s existing property. Would you like the co

> Occasionally it is said that issuing convertible bonds is better than issuing stock when the firm’s shares are undervalued. Suppose that the financial manager of the Butternut Furniture Company does have inside information indicating that the Butternut s

> This question illustrates that when there is scope for the firm to vary its risk, lenders may be more prepared to lend if they are offered a piece of the action through the issue of a convertible bond. Ms. Blavatsky is proposing to form a new start-up fi

> Dorlcote Milling has outstanding a $1 million 3% mortgage bond maturing in 10 years. The coupon on any new debt issued by the company is 10%. The finance director, Mr. Tulliver, cannot decide whether there is a tax benefit to repurchasing the existing bo

> Zenco, Inc. is financed by 3 million shares of common stock and by $5 million face value of 8% convertible debt maturing in 2026. Each bond has a face value of $1,000 and a conversion ratio of 200. What is the value of each convertible bond at maturity i

> In 1996, Marriott International made an issue of unusual bonds called liquid yield option notes, or LYONS. The bond matured in 2011, had a zero coupon, and was issued at $532.15. It could have been converted into 8.76 shares. Beginning in 1999 the bonds

> Iota Microsystems’ 10% convertible is about to mature. The conversion ratio is 27. a. What is the conversion price? b. The stock price is $47. What is the conversion value? c. Should you convert?

> Alpha Corp. is prohibited from issuing more senior debt unless net tangible assets exceed 200% of senior debt. Currently the company has outstanding $100 million of senior debt and has net tangible assets of $250 million. How much more senior debt can Al

> A puttable bond is a bond that may be repaid before maturity at the investor’s option. Sketch a diagram similar to Figure 24.3 showing the relationship between the value of a straight bond and that of a puttable bond.

> “A call option is always riskier than the stock it is written on.” True or false? How does the risk of an option change when the stock price changes?

> True or false? a. Convertible bonds are usually senior claims on the firm. b. The higher the conversion ratio, the more valuable the convertible. c. The higher the conversion price, the more valuable the convertible. d. Convertible bonds do not share ful

> Explain the three principal ways in which the terms of private placement bonds commonly differ from those of public issues.

> Look at Table 24.1:
a. Suppose the debenture was issued on September 1, 1992, at 99.489%. How much would you have to pay to buy one bond delivered on September 15? Don’t forget to include accrued interest. b. When is the first interest payment on the

> Use Table 24.1 (but not the text) to answer the following questions: a. Who are the principal underwriters for the J.C. Penney bond issue? b. Who is the trustee for the issue? c. How many dollars does the company receive for each debenture after deductio

> For each of the following sinking funds, state whether the fund increases or decreases the value of the bond at the time of issue (or whether it is impossible to say): a. An optional sinking fund operating by drawings at par. b. A mandatory sinking fund

> Select the most appropriate term from within the parentheses: a. (High-grade utility bonds/Low-grade industrial bonds) generally have only light sinking fund requirements. b. Collateral trust bonds are often issued by (utilities/industrial holding compan

> It was one of Morse’s most puzzling cases. That morning Rupert Thorndike, the autocratic CEO of Thorndike Oil, was found dead in a pool of blood on his bedroom floor. He had been shot through the head, but the door and windows were bol

> Look back at the first Backwoods Chemical example at the start of Section 23-1. Suppose that the firm’s book balance sheet is
The debt has a one-year maturity and a promised interest payment of 9%. Thus, the promised payment to Backwoods’s creditors is

> Digital Organics has 10 million outstanding shares trading at $25 per share. It also has a large amount of debt outstanding, all coming due in one year. The debt pays interest at 8%. It has a par (face) value of $350 million, but is trading at a market v

> How much would it cost you to insure the bonds of Backwoods Chemical against default? (See Section 23-1.) Section 23-1: (In 2009, Caesars Entertainment issued $3.7 billion of second lien notes maturing in 2018.1 By late 2014 these notes were trading at o

> Use the Black–Scholes formula to value the following options: a. A call option written on a stock selling for $60 per share with a $60 exercise price. The stock’s standard deviation is 6% per month. The option matures in three months. The risk free inte

> What problems are you likely to encounter when using a market-based approach for estimating the probability that a company will default?

> Discuss the problems with developing a numerical credit scoring system for evaluating personal loans. You can only test your system using data for applicants who have in the past been granted credit. Is this a potential problem?

> Company X has borrowed $150 maturing this year and $50 maturing in 10 years. Company Y has borrowed $200 maturing in five years. In both cases asset value is $140. Sketch a scenario in which X does not default but Y does.

> Company A has issued a single zero-coupon bond maturing in 10 years. Company B has issued a coupon bond maturing in 10 years. Explain why it is more complicated to value B’s debt than A’s.

> The following table shows some financial data for two companies:
Use the formula shown in Section 23-4 to calculate which has the higher probability of default.

> You own a 5% bond maturing in two years and priced at 87%. Suppose that there is a 10% chance that at maturity the bond will default and you will receive only 40% of the promised payment. What is the bond’s promised yield to maturity? What is its expecte

> What variables are required to use a market-based approach to calculate the probability that a company will default on its debt?

> The difference between the value of a government bond and a simple corporate bond is equal to the value of an option. What is this option and what is its exercise price?

> Other things equal, would you expect the difference between the price of a Treasury bond and a corporate bond to increase or decrease with a. The company’s business risk? b. The degree of leverage?

> Over the coming year Ragwort’s stock price will halve to $50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%. a. What is the delta of a one-year call option on Ragwort stock with an exercise price of $100? b. U

> Why is it more difficult to estimate the value at risk for a portfolio of loans rather than for a single loan? Why did this pose a problem for rating agencies that needed to assess the risk of packages of mortgage loans before the financial crisis?

> You have an A-rated bond. Is a rise in rating more likely than a fall? Would your answer be the same if the bond were B-rated?

> Suppose you expect to need a new plant that will be ready to produce turbo-encabulators in 36 months. If design A is chosen, construction must begin immediately. Design B is more expensive, but you can wait 12 months before breaking ground. Figure 22.9 s

> In binomial trees, risk-neutral probabilities are set to generate an expected rate of return equal to the risk-free interest rate in each branch of the tree. What do you think of the following statement: “The value of an option to acquire an asset increa

> Respond to the following comments. a. “You don’t need option pricing theories to value flexibility. Just use a decision tree. Discount the cash flows in the tree at the company cost of capital.” b. “These option pricing methods are just plain nutty. The

> In Section 10-4 we considered two production technologies for a new Wankel-engined outboard motor. Technology A was the most efficient but had no salvage value if the new outboards failed to sell. Technology B was less efficient but offered a salvage val

> You have an option to purchase all of the assets of the Overland Railroad for $2.5 billion. The option expires in nine months. You estimate Overland’s current (month 0) present value (PV) as $2.7 billion. Overland generates after-tax fr

> A variation on Problem 12: Suppose the land is occupied by a warehouse generating rents of $150,000 after real estate taxes and all other out-of-pocket costs. The present value of the land plus warehouse is again $1.7 million. Other facts are as in Probl

> You own a one-year call option to buy one acre of Los Angeles real estate. The exercise price is $2 million, and the current, appraised market value of the land is $1.7 million. The land is currently used as a parking lot, generating just enough money to

> Look back at the Malted Herring option in Section 22-2. How did the company’s analysts estimate the present value of the project? It turns out that they assumed that the probability of low demand was about 45%. They then estimated the e

> Imagine that Google’s stock price will either rise by 33.3% or fall by 25% over the next six months (see Section 21-1). Recalculate the value of the call option (exercise price = $530) using (a) the replicating portfolio method and (b) the risk-neutral

> Look again at Table 22.2. How does the value in 1982 of the option to invest in the Mark II change if a. The investment required for the Mark II is $800 million (vs. $900 million)? b. The present value of the Mark II in 1982 is $500 million (vs. $467 mi

> Describe each of the following situations in the language of options: a. Drilling rights to undeveloped heavy crude oil in Northern Alberta. Development and production of the oil is a negative-NPV endeavor. (Assume a break-even oil price is C$90 per bar

> True or false? a. Real-options analysis sometimes tells firms to make negative-NPV investments to secure future growth opportunities. b. Using the Black–Scholes formula to value options to invest is dangerous when the investment project would generate

> In Chapter 4, we expressed the value of a share of stock as P0 = EPS1 /r + PVGO where EPS1 is earnings per share from existing assets, r is the expected rate of return required by investors, and PVGO is the present value of growth opportunities. PVGO

> Redo the example in Figure 22.8, assuming that the real option is a put option allowing the company to abandon the R&D program if commercial prospects are sufficiently poor at year 2. Use put–call parity. The NPV of the drug at date

> Josh Kidding, who has only read part of Chapter 10, decides to value a real option by (1) setting out a decision tree, with cash flows and probabilities forecasted for each future outcome; (2) deciding what to do at each decision point in the tree; and

> Alert financial managers can create real options. Give three or four possible examples.

> Why is quantitative valuation of real options often difficult in practice? List the reasons briefly.

> Gas turbines are among the least efficient ways to produce electricity, much less thermally efficient than coal or nuclear plants. Why do gas-turbine generating stations exist? What’s the option?

> You own a parcel of vacant land. You can develop it now, or wait. a. What is the advantage of waiting? b. Why might you decide to develop the property immediately?

> Take another look at our two-step binomial trees for Google, for example, in Figure 21.2. Use the replicating-portfolio or risk-neutral method to value six-month call and put options with an exercise price of $450. Assume the Google stock pri

> Some corporations have issued perpetual warrants. Warrants are call options issued by a firm, allowing the warrant holder to buy the firm’s stock. a. What does the Black–Scholes formula predict for the value of an infinite-lived call option on a non-div

> In Section 21-1 we used a simple one-step model to value two Google options each with an exercise price of $530. We showed that the call option could be replicated by borrowing $233.22 and investing $294.44 in .556 shares of Google stock. The put option

> Flip back to Tables 6.2 and 6.6, where we assumed an economic life of seven years for IM&€™s guano plant. What’s wrong with that assumption? How would you undertake a more complete analysis? Tables 6.2: Table 6.6: Per

> Your company has just awarded you a generous stock option scheme. You suspect that the board will either decide to increase the dividend or announce a stock repurchase program. Which do you secretly hope they will decide? Explain.

> Show how the option delta changes as the stock price rises relative to the exercise price. Explain intuitively why this is the case. (What happens to the option delta if the exercise price of an option is zero? What happens if the exercise price becomes

> Use the put-call parity formula (see Section 20-2) and the one-period binomial model to show that the option delta for a put option is equal to the option delta for a call option minus 1. Section 20-2: Look now at Figure 20.4 (a), which shows

> A start-up company is moving into its first offices and needs desks, chairs, filing cabinets, and other furniture. It can buy the furniture for $25,000 or rent it for $1,500 per month. The founders are of course confident in their new venture, but nevert

> Use the Black–Scholes program from the Beyond the Page feature to value the Owens Corning warrants described in Section 21-4. The standard deviation of Owens Corning stock was 41% a year and the interest rate when the warrants were issued was 5%. Owens C

> Is it better to exercise a call option on the with-dividend date or on the ex-dividend date? How about a put option? Explain.

> Other things equal, which of these American options are you most likely to want to exercise early? a. A put option on a stock with a large dividend or a call on the same stock. b. A put option on a stock that is selling below exercise price or a call o

> a. Can the delta of a call option be greater than 1.0? Explain. b. Can it be less than zero? c. How does the delta of a call change if the stock price rises? d. How does it change if the risk of the stock increases?

> a. In Section 21-3 we calculated the risk (beta) of a six-month call option on Google stock with an exercise price of $530. Now repeat the exercise for a similar option with an exercise price of $450. Does the risk rise or fall as the exercise price is r

> Suppose you construct an option hedge by buying a levered position in delta shares of stock and selling one call option. As the share price changes, the option delta changes, and you will need to adjust your hedge. You can minimize the cost of adjustment

> The current price of United Carbon (UC) stock is $200. The standard deviation is 22.3% a year, and the interest rate is 21% a year. A one-year call option on UC has an exercise price of $180. a. Use the Black–Scholes model to value the

> The current price of the stock of Mont Tremblant Air is C$100. During each six-month period it will either rise by 11.1% or fall by 10% (equivalent to an annual standard deviation of 14.9%). The interest rate is 5% per six-month period. a. Calculate the

> Suppose that you have an option that allows you to sell Buffelhead stock (see Problem 12) in month 6 for $165 or to buy it in month 12 for $165. What is the value of this unusual option? Problem 12: Buffelhead’s stock price is $220 and could halve or dou

> Recalculate the value of the Buffelhead call option (see Problem 12), assuming that the option is American and that at the end of the first six months the company pays a dividend of $25. (Thus the price at the end of the year is either double or half the

> Suppose that you own an American put option on Bufflehead stock (see Problem 12) with an exercise price of $220. a. Would you ever want to exercise the put early? b. Calculate the value of the put. c. Now compare the value with that of an equivalent Eu

> Buffelhead’s stock price is $220 and could halve or double in each six month period (equivalent to a standard deviation of 98%). A one-year call option on Buffelhead has an exercise price of $165. The interest rate is 21% a year. a. What is the value of

> Look again at the bus lease described in Table 25.2.
a. What is the value of the lease if Greymare’s marginal tax rate is Tc = .20? b. What would the lease value be if, for tax purposes, the initial investment had to be written off in equal amounts ov

> Suppose that National Waferonics has before it a proposal for a four-year financial lease. The firm constructs a table like Table 25.2. The bottom line of its table shows the lease cash flows:
These flows reflect the cost of the machine, depreciation

> Look at Table 25.1.
How would the initial break-even operating lease rate change if rapid technological change in limo manufacturing reduces the costs of new limos by 5% per year?

> The price of Moria Mining stock is $100. During each of the next two six-month periods the price may either rise by 25% or fall by 20% (equivalent to a standard deviation of 31.5% a year). At month 6 the company will pay a dividend of $20. The interest r

> In Problem 8 we assumed identical lease rates for old and new desks. a. How does the initial break-even lease rate change if the expected inflation rate is 5% per year? Assume that the real cost of capital does not change. (Hint: Look at the discussion o

> Refer again to Problem 8. Suppose a blue-chip company requests a six year financial lease for a $3,000 desk. The company has just issued five-year notes at an interest rate of 6% per year. What is the break-even rate in this case? Assume administrative c