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What is the (risk-neutral) expected life for the employee stock option in Example? What is the value of the option obtained by using this expected life in Black-Scholes- Merton?
Example :
Suppose a company grants stock options that last 8 years and vest after 3 years. The stock price and strike price are both $40. The stock price volatility is 30%, the risk-free rate is 5%, and the company pays no dividends. Figure 15.1 shows how a four-step tree could be used to value the option. (This is for illustration; in practice more time steps would be used.) In this case, so that, with the notation of Chapter 12, The probability on the ''up branches'' is 0.5158 and the probability on the ''down branches'' is 0.4842.
There are three nodes where early exercise could be desirable: D, G, and H. (The option has not vested at node B and is not in the money at the other nodes prior to maturity.) We assume that the probabilities that the holder will choose to exercise at nodes D, G, and H (conditional on no earlier exercise) have been estimated as 40%, 80%, and 30%, respectively. We suppose that the probability of an employee leaving the company during each time step is 5%. (This corresponds to an employee turnover rate of approximately 2.5% per year.) For the purposes of the calculation, it is assumed that employees always leave at the end of a time period. If an employee leaves the company before an option has vested or when the option is out of the money, the option is forfeited. In other cases the option must be exercised immediately.
Louise Manufacturing uses 2,300 switch assemblies per week and then reorders another 2,300. The relevant carrying cost per switch assembly is $9.00, and the fixed order cost is $1,150. What are the current carrying costs?
CSN reported net income of $100 million last year. CSN expects net income to grow at 7% next year, at 5% in the following year, and then at a constant rate of 3.5% per year forever. CSN expects that its current ROE will remain constant forever. Find ..
Kyle Corporation is comparing two different capital structures, an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, Kyle would have 715,000 shares of stock outstanding. Under Plan II, there would be 465,000 shares of stock outstan..
A company makes apple butter to supply local vendors. The manufacturing company can make 330 pounds of apple butter per day and demand from vendors in 190 pounds per day. Each time the manufacturing company makes apple butter, it costs $176 to set up..
First City Bank pays 7% simple interest on its savings account balances, whereas Second City Bank pays 7% compounded annually. If you made a $6,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end..
Many regulators would like to see bank capital requirements raised. Consider a proposal to increase the minimum Tier 1 and total capital ratios to 9 percent and 12 percent, respectively. What impact would this have on bank risk? Would small banks and..
Nevertheless, Ms. H did make an error in her favor. When she received formal notification that she owed an additional $4,350 tax, she was dismayed that the IRS also billed her for $920 interest on the deficiency. She doesn't understand why she must p..
We learned that one of the key variables in determining the value of any cash flow is the interest rate (sometimes referred to as discount rate). However, interest rates may be quoted in more than one way. What do the terms EAR and APR mean?
Calculate the beta for the following portfolio, What is the portfolio beta for this company?
You expect to receive $41,000 at graduation in two years. You plan on investing it at 9.25 percent until you have $176,000. Required: How long will you wait from now? (Enter rounded answer as directed, but do not use rounded numbers in intermediate c..
Your employer offers a 401k that you can invest in as an employee of the firm. If you put in 3% of your pre-tax income (listed in question 1.a.), your employer will match 3%. a. Assuming you put in the full 3% during your first year of employment, ho..
The Manassas Company has 55 obsolete keyboards that are carried in inventory at a cost of $9,600. If these keyboards are upgraded at a cost of $6,900, they could be sold for $18,200. Alternatively, the keyboards could be sold “as is” for $8,100. What..
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