Sally Jameson - Valuing Stock Options in a Compensation Pack

Sally Jameson: Valuing Stock Options in a Compensation Package

By Group 10

1.

If we ignore tax consideration and assume that Sally Jameson is free

to

sell

her

options

at

any

time

after

she

joins

Telstar,

which

compensation package is worth more?

First scenario, if Sally chooses stock options and hold until maturity date.

Ignoring

the

taxation

and

other

constraints,

the

future

value

of

cash

compensation

at

the

end

of

the

5

th

year

will

be

5000

*

(1

+

0.0602)

^

5

=

6697.44. We can easily form the equation 3000 * (P

–

35) = 6697.44, where P

is the future stock price of Telstar, so the stock price must increase to at least

37.23 at the end of 5

th

year to get the same amount of the cash compensation

and

if

the

stock

price

where

to

stay

below

35,

Sally

’

option

would

be

worth

nothing. The stock, which pays no dividend and is not expected to pay one in

the

foreseeable

future,

is

trading

at

18.75.

It

seems

significant

difference

between the exercise price and the spot price. As shown in Exhibit 2, Telstar

stock

price

has

increased

higher

than

$$35

only

once

and

10-year

average

stock

price

is

around

20.

Therefore,

the

chance

that

the

value

of

option

is

greater than the cash compensation is very rare.

Second scenario, assume Sally is free to sell options at any time after her

joining Telstar, she may sell her option immediately after receiving. Then we try

to price the value of stock option by using Black - Scholes Model.

We know that the stock is currently trading at $$18.75 and the exercise price is

$$35. We take the 5 year T-bill rate 6.02% as the risk free rate. From the Exhibit

2, we can calculate the volatility of Telstar stock return is around 27.65%. Plug

them into the formula, the call option price will be 2.53. At this amount, Sally

’

s

options would be presently worth 2.53 * 3000 = 7590. She is better off taking

the option.

2.

How

should

we

factor

in

the

complications

ignored

in

question

1?

How would they affect the value of the option to Ms. Jameson? What

should she do? Why?

In

considering

taxes,

transaction

costs

and

difficulty

of

option

liquidity,

we

conclude

that

cash

package

is

worth

more

than

stock

option

package

and

therefore, it is suggested that Sally choose cash package.

The tax impact calculation:

Senario 1

：

Cash signing bonus

Bonus

a

Tax rate

b

Amount after tax

c = a *(1-b)

Interest (equ. Risk free rate)

d

Future value

e=c*(1+d)^4+a*d*(1+d)^4

Note: tax will be deducted at the end of year 1.

5,000

28%

3,600

6.02%

4,928.64

Senario 2

：

Stock option

Since tax rate cannot be put in Black-Scholes model directly to calculate the option present value, we

used following approach to estimate the potential future share price, if ms. Jameson would like to earn

the same. Assume that she will hold the stock more than 1 year and applicable tax rate is 28%, capital

gain tax rate.

Future value

Price of share 5 year later

Current stock price

Growth rate

4,928.64 = (FV-35)*3000*(1-28%)

37.28

18.75

98.8%

= 37.28/18.75-1

Note: If Ms. Jameson would like to have a gain equivalent to what she earns from cash bonus (4,928),

the stock price after five year shall at least exceed USD 37.28/share.

Taking account of the calculation above and following uncertainties that exist if

Sally

selects

stock

option,

we

consider

it

is better for

her

to

choose

signing

bonus.

?

The likelihood that stock price exceeds USD 37.28 is low. From the exhibit

2, we note that ceiling of Telstar Common Stock seems to be nearly USD

35.

?

?

Uncertain factors from the time value and other risk points in the future.

If

Ms.

Jameson

leaves

Telstar

during

the

vesting

period

(<5

year),

she

cannot obtain the option. It gives rise the opportunity cost to Sally that she