1. If we ignore tax considerations and assume that Sally is free to sell options at any time after her joins Telstar, which compensation package is worth more? If tax consideration is ignored and assume that Ms. Jameson is free to sell options at any time after her joins Telstar. First scenario If Ms.
Jameson chooses stock options, she will hold until maturity date. Cash compensation at the end of the 5th year = $5,000(1+6. 02%)^5 = $6,697.
44 To equal $6,697. 44, the stock price must increase to at least $37. 23 at the end of the 5th year.The stock price has to be higher than $35 in order to be exercised and make a gain, otherwise she will leave it expire worthlessly. However, from Exhibit 2, Telstar stock price has increased higher than $35 only once and 10-year average stock price is $21.
17. Therefore, the chance that the value of option is greater than the cash compensation is very rare. The options will even worth nothing to Ms. Jameson if the stock price is below $35 at the maturity date. If Sally holds options until maturity, she should choose cash compensation. Second scenario Because, Ms.Jameson is free to sell options at any time after her joins Telstar, she may sell her option immediately after receiving (at the time that the value of option is greatest) We price the value of stock option by using Black and Schole’s Model and compare it with cash compensation of $5,000. [pic] [pic] and [pic] S0 = 18.
75 K = 35 T = 5 (refer in case) rf = 6. 02% (use 5 year T-bond yield, which match with time to maturity of the option) For volatility, we calculate both historical volatility and implied volatility. 1) Historical volatility : calculate from historical stock returns for 10 years. V = 0. 3687 or 36.
87% V comes from: The return of stocks = ln(stock priceT/stock priceT-1 Standard deviation of stock return = 0. 023 per day, Convert to per annum = [pic] (253 = number of trading days per annum) So, V = 0. 3687 or 36. 87% Put variables into the equation [pic]; [pic] [pic] ; [pic] [pic] Hence, by using historical volatility, we get the price of call option at $4. 07 per option. There are 3,000 call options, so the value of option equals to $4. 7*3000 = $12,209.
50. If Sally can sell the option as soon as she receives them, she will get $12,209. 50 which obviously worth more than cash $5,000. (2) Implied volatility: Calculated from call options currently traded in the market Implied Volatility |Strike Price |Call Expiration Date | | |June 20, 1992 |July 18, 1992 |Oct 17, 1992 |Jan 22, 1994 | |$12. 0 | | | |0.
37 | |$17. 50 |0. 27 |0. 36 |0.
35 |0. 36 | |$20. 00 |0. 27 |0. 31 |0. 35 |0.
39 | |$22. 50 | |0. 33 |0. 34 | | Max: 0. 39, Min: 0.
27, Average: 0. 4 Value per option |Strike Price |Call Expiration Date | | |June 20, 1992 |July 18, 1992 |Oct 17, 1992 |Jan 22, 1994 | |$12. 50 | | | |$4. 09 | |$17.
50 |$2. 43 |$3. 92 |$3. 76 |$3. 92 | |$20.
00 |$2. 3 |$3. 09 |$3. 76 |$4. 43 | |$22.
50 | |$3. 42 |$3. 59 | | Max: 4. 43, Min: 2. 43, Average: 3. 53 Value for 3,000 options |Strike Price |Call Expiration Date | | |June 20, 1992 |July 18, 1992 |Oct 17, 1992 |Jan 22, 1994 | |$12. 0 | | | |$12,275.
83 | |$17. 50 |$7,295. 21 |$11,774. 10 |$11,272. 35 |$11,774. 10 | |$20.
00 |$7,295. 21 |$9,270. 85 |$11,272. 35 |$13,278. 34 | |$22. 50 | |$10,269.
89 |$10,770. 85 | | Max: $13,278. 4, Min: $7,295. 21, Average: $10,595. 37 All of the values of stock option using implied volatility exceed the cash compensation of $5,000, as well as by using historical volatility.
In conclusion, if we ignore tax considerations and assume that Ms. Jameson is free to sell options at any time after her joins Telstar. The stock option is worth more than cash compensation package. 2. How should we factor in the complications ignored in the above question? How would they affect the value of the option to Ms. Jameson? What should Ms. Jameson do?Why? There are several complications we should factor because these affect the value of option to Ms. Jameson; thus, affect her decision on choice of compensation package.
1) Taxes If Ms. Jameson chooses stock options for her compensation, she will not need to pay taxes until she actually exercises them and sells the shares. At that point, gains on the shares will be taxed at either ordinary tax rate or at capital gain tax rate, depending on whether she has held the stock for less than or more than one year after exercising the options.
If taxes are considered, the value of option after tax will decrease. In the case that Ms. Jameson holds stocks for less than 1 year, she risks to her income tax rate that could be changed at the fifth year. While there will be no risk regarding tax rate, if she hold the stocks for more than 1 year. The latter case, however, increases risk regarding the share price in the future, in which it will have an effect on her capital gain or loss. For cash compensation package, tax consideration also decreases the value. Cash bonus is taxed at ordinary tax rate, so Ms.
Jameson receive $5000 x (1-0. 28) = $3,600 today, and $4,450. 82 at the next five years. However, there is a risk that Ms. Jameson’s marginal tax rate is changed. For the worst case, tax rate might reach as high as 31%, and this results in the value of $4,265. 37 at the end of the fifth year.
2) Dividend Although Mr. Mark told that Telstar’s stock does not pay dividend and is not expected to pay one in the foreseeable future. However, there is a chance that it would happen, and if dividend is paid, will lower the value of the options. ) Vesting period = 5 years 4) Non-transferable: The constraint that the option cannot be sold to anyone 5) Probability that Ms. Jameson might leave Telstar before the fifth year with the company These 3 complicated factors have a significant effect on the value of option to Ms.
Sally. Due to the fact that the vesting period is 5 years and she cannot sell the option to anyone, accepting the option means her intention to stay at Telstar at least for 5 years. This is because if she leaves Telstar before her fifth year with the company, she will get nothing.In other words, her options will be worthless to her. Therefore, if there is high probability that Ms. Jameson might not stay at Telstar that long, she should choose cash compensation package instead.
However, we also found that the cash compensation is sill more attractive than the stock options even though she plans to stay at Telstar at least 5 years. This is because the choice to take the option would have much more risk as Ms. Jameson’s potential profits would be created solely by the Telstar stock price being greater than $35 by the end of the next five years.
To equal the $4,265. 7, the value of the cash compensation in the worst case, the stock would have to reach a price of at least $37. 06. Moreover, from the Exhibit 2, we see that Telstar’s stock price only rose to $35, once in 1990 during the last 10 years. It means that the chance of the rise of stock price to above $35, which is the option’s strike price, is very rare and Ms. Jameson will not exercise her option and therefore get nothing from the stock option compensation package.
Consequently, Ms. Jameson should choose the cash package rather than the stock options. 3. Does granting stock options cost company anything?If so, who pays? How might firms create more effective or more efficient incentive? The company’s objective is to maximize shareholders’ wealth.
However, the agency problem often occurs. Stock option compensation is one of incentives created to align managers’ interests with shareholders and enhance managers to behave in ways that will boost the company’s stock price. However, there are costs of granting stocks options as employee compensation.
(1) Granting stock options costs the company the value for which options are sold. In fact, the company does not pay for such value directly.Instead, by granting employee stock options, the company pays less cash compensation. In other words, employees pay for options value by receiving less cash compensation by an amount equivalent to options value. From the accounting view, stock options values are non-cash operating expenses to the company. (2) When stock options are granted, and especially when those options are in the money, the number of new shares used in calculating fully diluted earnings per share is increased to reflect the potential net number of new shares that would be issued if all options were exercised.This reduces or dilutes the earnings per share number.
If the dilution effect is significant, stock repurchases might be needed in order to reduce the dilution. Theses cost of dilution and cost of repurchase are paid by the shareholders of the company. There are several ways to create more effective stock options. (1) The exercise price should be appropriate to employees and company. To employees, the exercise price should be in a possible range. In this case, the strike price is inappropriately high and this would not be effective to motivate mployees as it is not likely that the stock price will be able to reach that high and they may choose cash compensation instead. On the other hand, the strike price has to increase equal to the company’s cost of capital since it is the minimum rate of return the company has to pay to capital providers.
If the company’s stocks do not perform above cost of capital, the option is, then, not in the money. (2) The stock options should be granted as compensation only for employees in executive or decision-making positions that have the ability to impact the profitability and growth of the company.Employees in operation position, like Ms. Jameson, are not likely to improve the company’s performance and thereby compensating them with stock options is not likely to be effective incentive. (3) If the managers are able to achieve goals, such as stock price reaching the strike price, they should get some rewards. For instance, they might be allowed to exercise their options immediately. (They do not have to wait until the maturity) Note that the company needs to set the holding period in order to protect managers to make a short-term profit from stock manipulation.
4) To protect situation that share price movement are not attributed to managerial performance because “all ships rise in a rising tide”, the company should reward their managers on relative performance, i. e. relative to industry peers or market index. In addition to employee stock option, there are some alternatives of compensation which might be more efficient to the company.
1) A non-qualified stock option is one type of stock option, in which the company gains a tax deduction after employees exercise their options. Therefore, this incentive is more efficient to the company for compensating employees. ) A bonus formula might be another remuneration scheme to compensate employees. Only if employees are able to perform above the pre-determined goal, they would receive bonus from the company, in addition to their salaries.
It is necessary for the company to set transparent and appropriate performance measures. As accounting measures, such as net income, can be easily manipulated by managers and the opportunity cost is not in consideration, one alternative way of measurement is the residual income or Economic Value Added (EVA).This forces managers to focus on investing on the projects which generate higher return than its cost of capital in order to maximize EVA and then are able to receive bonus from the company. 4. Assume Ms Jameson works at Telstar and accepts the option, is there anything she can do to untie some of her wealth from Telstar? If Ms. Jameson accepts the stock option package, it means her wealth is tied with Telstar’s stock price in the next 5 years, which is uncertain.
Thereby, she might negotiate with the company regarding some of constraints of her stock options.For example, she should be allowed to sell some of her options. However, if the negotiation fails, she will have no choice but to find ways to untie some of her wealth from Telstar by herself. (1) The first way is to enter a future contract to sell a stock at $35 and has the same maturity with that of stock option. When the market is bullish, the minimum total pay off will be limited at $0. However, if the market is bear, the maximum gain is equal to $35-St. Such strategy allows Ms. Jameson to make a profit when the market falls.
|Stock price |Total pay off | St ; 35 | 35 – 35 = 0 | |St ; 35 |35 – St | Short future pay off (2) The other alternative is using option strategies, which we suggest bull spread, bear spread, and straddle strategy. If Ms. Jameson expects the market will be in moderately bullish environments, she should employ the bull call spread to untie her wealth. In order to use bull spread, she has to long a call at strike price is $35, which is her stock option compensation, and short a call at a higher strike price.
Both options are the same expiration. For example, |Given | | | | | – The higher strike price is option A eg. $40 which call premium is $3 | | – The lower strike price is $35 | | | |Stock price |Total pay off |Initial |Net profit/loss | |St ? 40 |40 – 35 = 5 |3 |8 | |35