Chapter 26, Problem 24PS

Futures and options A gold-mining firm is concerned about short-term volatility in its revenues. Gold currently sells for $1,300 an ounce, but the price is extremely volatile and could fall as low as $1,220 or rise as high as $1,380 in the next month. The company will bring 1,000 ounces to the market next month.

1. a. What will be total revenues if the firm remains unhedged for gold prices of $ 1,220, $1,300, and $1,380 an ounce?
2. b. The futures price of gold for delivery one month ahead is $1,310. What will be the firm’s total revenues at each gold price if the firm enters into a one-month futures contract to deliver 1,000 ounces of gold?
3. c. What will total revenues be if the firm buys a one-month put option to sell gold for $1,300 an ounce? The put option costs $110 per ounce.

Summary Introduction

To determine: Total revenue when firm remains unhedged at $1,220, $1,300 and $1,380 an ounce.

Explanation of Solution

Given information:

Gold current price of gold is $1,300

The prices are volatile to $1,220 or $1,380 in the next month.

Company will bring 1,000 to market next month.

Calculation of total revenue:

When unhedged at the price of $1,220,

$\begin{array}{c}\text{Unhedged}\text{revenue}=\text{Price}\text{per}\text{ounce}\times \text{ounces}\\ =\$1,220\times 1,000\\ =\$1,220,000\end{array}$

Therefore, unhedged revenue is $1,220,000

When unhedged at the price of $1,300,

$\begin{array}{c}\text{Unhedged}\text{revenue}=\text{Price}\text{per}\text{ounce}\times \text{ounces}\\ =\$1,300\times 1,000\\ =\$1,300,000\end{array}$

Therefore, unhedged revenue is $1,300,000

When unhedged at the price of $1,380,

$\begin{array}{c}\text{Unhedged}\text{revenue}=\text{Price}\text{per}\text{ounce}\times \text{ounces}\\ =\$1,380\times 1,000\\ =\$1,380,000\end{array}$

Therefore, unhedged revenue is $1,380,000

Summary Introduction

To determine: Futures unhedged revenue.

Explanation of Solution

Calculation of futures hedged revenue:

When futures hedged at the price of $1,220

$\begin{array}{c}\text{Futures hedged}\text{revenue}=\text{Futures}\text{price}\text{per}\text{ounce}\times \text{ounces}\\ =\$1,310\times 1,000\\ =\$1,310,000\end{array}$

Therefore, futures hedged revenue is $1,310,000

When futures hedged at the price of $1,300,

$\begin{array}{c}\text{Futures hedged}\text{revenue}=\text{Futures}\text{price}\text{per}\text{ounce}\times \text{ounces}\\ =\$1,310\times 1,000\\ =\$1,310,000\end{array}$

Therefore, futures hedged revenue is $1,310,000

When futures hedged at the price of $1,380,

$\begin{array}{c}\text{Futures hedged}\text{revenue}=\text{Futures}\text{price}\text{per}\text{ounce}\times \text{ounces}\\ =\$1,310\times 1,000\\ =\$1,310,000\end{array}$

Therefore, futures hedged revenue is $1,310,000

Summary Introduction

To determine: Put options-hedged revenue.

Explanation of Solution

Calculation of put options-hedged revenue:

When the gold price at $1,220

$\begin{array}{c}\text{Put-options hedged}\text{revenue}=\text{Max}\left[\left(\text{Market}\text{price,exercise}\text{price}\right)-\text{premium}\right]\times \text{ounces}\\ =\left(\$1,300-\$110\right)\times 1,000\\ =\$1,190,000\end{array}$

Therefore, put options hedged revenue is $1,190,000

When the gold price at $1,300

$\begin{array}{c}\text{Put-options hedged}\text{revenue}=\text{Max}\left[\left(\text{Market}\text{price,exercise}\text{price}\right)-\text{premium}\right]\times \text{ounces}\\ =\left(\$1,300-\$110\right)\times 1,000\\ =\$1,190,000\end{array}$

Therefore, put options hedged revenue is $1,190,000

When the gold price at $1,380

$\begin{array}{c}\text{Put-options hedged}\text{revenue}=\text{Max}\left[\left(\text{Market}\text{price,exercise}\text{price}\right)-\text{premium}\right]\times \text{ounces}\\ =\left(\$1,380-\$110\right)\times 1,000\\ =\$1,270,000\end{array}$

Therefore, put options hedged revenue is $1,270,000