Example of Derivatives Valuation to Value Real Investments
Lincoln Copper Company has a mine that will produce a total of 75,000 pounds of copper: 25,000 pounds
of copper at the end of the first year and 50,000 pounds of copper at the end of the second year. Extraction
costs are always $0.10 per pound. The current forward prices are $0.65 per pound for a one-year contract
and $0.60 per pound for a two-year contract. The annually compounded risk-free rates are 5 percent for
one-year zero-coupon bonds and 6 percent for two-year zero-coupon bonds.
What is the present value of the cash flows from the mine, assuming that payments for the mined
copper are received at the end of each year?
SOLUTION USING Forward Contracts and zero-coupon bonds:
F1 = Year 1 forward price = $.65 per pound
F2 = Year 2 forward price = $.60 per pound
Inverstment
Beginning of year 0
Beginning of
year 1
Beginning of
year 2
Copper Mine
PV Unknown
25,000(p1 - $.10) 50,000(p2 - $.10)
------------------------------------------------------------------------------------------------------------------------------ --a. Forward contract to buy
$0
25,000(p1 - $.65)
$0
25,000 pounds of copper at
beginning of year 1
b. Forward contract to buy
50,000 pounds of copper at
beginning of year 2
$0
c. Buy zero-coupon bonds:
Maturity = 1 year
Face amount = $25,000(.65-.10)
-25,000(.65-.10)
1.06
d. Buy zero-coupon bonds:
Maturity = 1 year
Face amount = $50,000(.60-.10)
-50,000(.60-.10)
1.08
Total:
$.10)
-$35,345
$0
$25,000(.65-.10)
$0
50,000(p2 - $.60)
$0
50,000(.60-.10)
$25,000(p1 - $.10) $50,000(p2 -