Sean's Extra Credit

*Chapter 8*

Using the Black-Scholes Model, determine a European call option on a stock with a strike price of $45 and expiration time of 2 years and has a price of $17. The stock has a volatility of 0.35 and a current price of $30.57.

S = 30.57

PV(K) = 40.81

r_{f} = .05

${\sigma}$ =.35

T = 2

4. Solve for $d_{1}$ and N($d_{1}$) using Table A.5 in the Appendix p.864

$d_{1}$ = -0.33

N($d_{1}$) = N(-0.33) = 0.3707 Shares

5. Solve for $d_{1}$ - $sigma * sqrt(T)$ and N($d_{1}$ - $sigma * sqrt(T)$) using Table A.5 in the Appendix p.864

$d_{1}$ - $sigma * sqrt(T)$= -0.3362 - 0.4949

N($d_{1}$ - $sigma * sqrt(T)$) = 0.2033 Shares

6. Solve for $c_{0}$

$c_{0}$ = S*N($d_{1}$) - PV(K)*N($d_{1}$ - $sigma * sqrt(T)$)

$c_{0}$ = 30.57*(0.3707) - 40.81*(0.2033)

$c_{0}$ = 19.62

*Chapter 12*

A gold mine will extract the following supply based on the following conditions

In three years the total extraction will be 3500 ounces

There is no option to shut down the mine prematurely

The current price of gold is $1002.02

The one year forward price of gold is $1012.90 per ounce

The two year forward price of gold is $1031.90 per ounce

The three year forward price of gold is $1045.10 per ounce

The cost of extraction ore purification, and selling is $300 per ounce and increases at 5% per year

The risk free return is 3% per year.

What is the value of the gold mine?

Extraction and Ounces

Sale Date

Today 1000

One year from now 1000

Two years from now 1000

Three years from now 500

CE_{o} = (1000)*($1002.02-$300) = 702020

CE_{1} = (1000)*($1012.9-$315) = 697900

CE_{2} = (1000)*($1031.9-$330.75) = 701150

CE_{3} = (500)*($1045.1-$347.29) = 348905

V_{o} = 702020 + 697900/(1.03)^{1} + 701150/(1.03)^{2} + 348905/(1.03)^{3}

V_{o} = 702020 + 664666.67 + 660901.12 + 319296.62

V_{o} = $2,346,884.41

*Chapter 22*

You are the CFO of a midsized US based company and your US company is expecting to sell it’s goods to the British market. You expect to see £ 3 million in sales (worse case scenario) and £ 4.5 million (best case scenario) over the next 15 months. You have a 50/50 chance of either occurring. Given the following information, you are assigned the task of recommending the best method of hedging (what is the highest $ amount you can lock in today).

Current US$/£ spot rate = US$1.42/£

Current forward rate for currency exchanged

15 months from today = US$1.38/£

15 months US$ LIBOR = 6%

15 months £ LIBOR = 11%

1. Calculate $ value to hedge and convert to $

£ 4.5 million * .5 + £ 3 million * .5 = £3.75 Million

£3.75 Million * US$1.42/£ = $5.325 Million

2. Borrow $

$5.325 Million / (1 + rf)^t = $5.325 Million / (1.07555) = $4.95096

3. Convert the borrowed $ to £

$4.95096 Million / US$1.42/£ = £3.48 Million

4. Invest the £

£3.48 Million * (1.11)^t = £3.48 Million * (1.11)^1.25 = $3.96491 Million

Or

1. Forward contract

£3.75 Million * US$1.38/£ = $5.17

Use the forward contract method to hedge