Sean Moore

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
rf = .05
${\sigma}$ =.35
T = 2

(1)
\begin{align} d_1=\frac{ln(\frac{S}{PV(K)})}{\sigma\sqrt{T}}+\frac{\sigma\sqrt{T}}{2} \end{align}
(2)
\begin{align} d_1=\frac{ln\frac{30.57}{40.81}}{0.35\sqrt{2}}+\frac{0.35\sqrt{2}}{2} \end{align}
(3)
\begin{align} d_1=\frac{-0.2889}{0.4949}+\frac{0.4949}{2} \end{align}

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

CEo = (1000)*($1002.02-$300) = 702020
CE1 = (1000)*($1012.9-$315) = 697900
CE2 = (1000)*($1031.9-$330.75) = 701150
CE3 = (500)*($1045.1-$347.29) = 348905

Vo = 702020 + 697900/(1.03)1 + 701150/(1.03)2 + 348905/(1.03)3
Vo = 702020 + 664666.67 + 660901.12 + 319296.62

Vo = $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