Case 1 Sally Jameson PDF

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Risk management and derivatives pricing (in groups)...

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Case 1 – Sally Jameson

October 28, 2018

Brian Zhou – 36069136 Junho Cho – 37557139 Jagdeep Grewal – 12271152 Zoe Wang – 50074146 Jesslyn Chang - 42631408

Q1) If we ignore tax considerations and assume that Sally Jameson is free to sell her options at any time after she joins Telstar, which compensation package is worth more? Based on our Black-Scholes model, the total value of her options now (which are call options) ignoring tax is $7,704 or $2.57/option*3,000 options (each allowing for purchase of 1 Telstar stock). With the cash signing bonus being $5,000, the option bonus is worth more so Sally should take the options, sell them immediately, and invest the proceeds, assuming she is risk averse. If she invests the proceeds, it will be worth $7,704e^(0.0602*5) = $10,408 in 5 years. If she chooses to exercise at expiration instead, her payoff in 5 years will be 3,000*(S_T – 35). Compared to the FV of the cash bonus ($6,754 = 5,000e^(0.0602*5)), S_T would need to be $37.25 to breakeven, but Sally can do better by investing proceeds from selling options. Therefore, compared to the FV of selling her options today and investing proceeds for 5 years, S_T would need to be $38.47 five years from today to be indifferent. Moreover, we also looked at breakeven volatility (i.e. a minimal standard deviation needed for Sally to be indifferent) by using a cash equivalent fair market option value of $1.67 (5,000 cash bonus/3,000 options). By using Black-Scholes, we can infer the breakeven standard deviation of the stock return is 23.24%. This means when the volatility of Telstar stock returns is greater than 23.24%, the market value of the call option is worth more than the cash bonus. This corroborates our volatility assumption based on the historical stock price as shown in Exhibit 3. Inputs for Black-Scholes & other assumptions: • Stock price of $18.75 • Strike price of $35 • Maturity of 5 years • 5 year risk-free rate of 6.02% (continuously compounded to be 6.20% 5 year US Treasury yield) • Volatility of 27.84% derived from taking the square root of the annual log return of Telstar stock price as at January of each year (1982 to 1992) • No dividends • Sally is risk averse • Sally does not need the money today and can invest the proceeds • Sally is able to sell the options at the derived value of $2.57/option Q2) 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? If we include tax considerations now, Sally should still take the options instead of the cash bonus. With both the marginal income tax rate and capital gains tax rate at 28%, it does not change Sally’s decision since her profit in all scenarios will proportionally decrease by the same amount. As such, the value of the option relative to cash bonus does not change from Sally’s perspective. By once again using Excel’s Goal Seek function, we see that the breakeven S_T price is the same as Q1 ($37.25 compared to cash bonus and $38.47 compared to investing proceeds from selling options). Key assumptions: • The cash bonus is taxed at the marginal income tax rate of 28% • The sale of the options is taxed at the capital gains tax rate of 28%

Q3) Does granting stock options cost companies anything? If so, who pays? What incentives do executive stock option plans create for their recipients? Can firms create more effective incentives? If so, explain how. Although granting stock options is a non-cash expense, there are definite costs associated with employee stock options. Given the stock options are in-the-money, for example a spot price of higher than $35 for the Sally Jameson case, these options create a dilutive effect on the company’s equity value. When the options are exercised, it will dilute shareholders’ equity as it increases the number of shares outstanding. All other things equal (revenue, earnings), an increase in the number of shares outstanding decreases the company’s earnings per share [EPS = (Net Income – Preferred Dividends)/Shares Outstanding]. Hence, the costs of employee stock options are split between all shareholders who hold an equity stake in the company. In many cases, companies implement a stock buyback program to account for this dilutive effect. If a company buys back its shares to mitigate for the dilutive effect, it is as if the company is paying cash wages to its employees. Executive stock options encourage employees to maximize shareholder value by aligning their incentives with those of the shareholders. As employees hold ownership of the company, a certain part of their wealth, not just income, is now dependent on the company’s performances. This reduces the principal-agent problem, which is a common misalignment of incentives between employees and their employers/shareholders that reduces shareholder value and profitability. Firms can create more effective incentive structures – pay-for-performance or incentive piecework aim to maximize each employee’s productivity by structuring their compensation strictly based on their levels of production and performance. These types of incentive structures are more common in manufacturing or sales and are less applicable to jobs that require team-consolidated results. Q4) What if Ms. Jameson decided that the option was a better deal, but that she didn’t want all of her financial wealth (as well as her human capital) tied to the fortunes of Telstar? Assuming she works at Telstar and accepts the option grant, is there anything she can do to “untie” some of her wealth from Telstar? If Ms. Jameson accepted the option offer, she can untie her wealth from Telstar by constructing a riskless hedged portfolio. She can do this by acquiring the call options and short the underlying stock in a way that replicates a bond. Essentially, subtracting ΔS from c. Δ can be found by taking the partial derivative of c and dividing it by the partial derivative of S. Alternatively, you can set Δ = N(d1), where d1 is. Solving for Δ with S=18.75, X=35, r=0.0602, sd=0.2784, T=5.

Solving for d1, we get: ((ln(18.75/35)+(0.0602+0.2784^2/2)*5)/(0.2784*2.23606))= –0.20784 Once you solve for d1, use excel's NORMSDIST function to solve for N(d1) and we get 0.417675. So, for every call option Ms. Jameson receives, she should short .417675 stocks of the underlying stock to replicate the riskless bond. So for 3000 call options, Ms. Jameson should short ~1253 shares. This will effectively untie Ms. Jameson’s wealth from the fortune of Telstar.

Appendix Salary Cash Bonus today (no tax) Cash Bonus today (with tax) FV Cash Bonus in 5 years (no tax) FV Cash Bonus in 5 years (with tax)

50,000 5,000 3,600 6,754 4,863

Black Scholes Current Stock Price (S) Strike Price (X) Maturity (years, T) Risk-free rate ( r ) Volatility (sigma) Dividend Yield (delta)

18.75 35.00 5.00 6.02% 27.84% -

Call Option Price Total Option Value Today (no tax)

$ $

2.57 7,704

Total Option Value Today (with tax) FV Option Proceeds (no tax) FV Option Proceeds (with tax)

$ $ $

5,547 10,408 7,494

Marginal Income Tax Rate Capital Gains Tax Rate

28% 28%

Number of Stocks Purchasable (1 option = 1 stock)

3,000

d1 d2

- 0.20813 - 0.83071

N1 N2

0.41756 0.20307

Cash Bonus Breakeven (no tax) S_T Payoff at T (no tax)

$ 37.25 $ 6,754

Option Bonus Investment Breakeven (no tax) S_T Payoff at T (no tax)

$ 38.47 $ 10,408

Cash Bonus Breakeven (with tax) S_T Payoff at T (with tax)

$ $

Option Bonus Investment Breakeven (with tax) S_T Payoff at T (with tax)

$ 38.47 $ 7,494

37.25 4,863

Volatility Year Stock Price 1982 13.00 1983 17.00 1984 19.00 1985 20.00 1986 25.00 1987 28.00 1988 20.00 1989 27.00 1990 25.00 1991 14.00 1992 15.00

Log Return 0.26826 0.11123 0.05129 0.22314 0.11333 -0.33647 0.30010 -0.07696 -0.57982 0.06899 0.07752 Variance 0.27843 St Dev

Risk-Free Rate Annualized Continuous 1 month 3.73% 3.66% 2 month 3.75% 3.68% 3 month 3.72% 3.65% 6 month 3.85% 3.78% 1 year 4.07% 3.99% 2 year 5.37% 5.23% 5 year 6.20% 6.02%...