Herbet --
An unhedged position for the mining company makes it impossible to
predict future cash flows, which basically turns the business into a
gamble. After all, even with a guarantee of customers for the next
year at $275 (which ABC Mining doesn't have), what's to say that next
year's gold price won't be $240?
Of course the managers could gamble -- but since it's likely banks or
stockholders are providing the capital, they'll require either
guaranteed customer contracts or a hedge for gold production.
Futures prices will change based on interest rate, volatility of the
market and the price of gold, according to the Black-Scholes option
pricing model -- but a simple assumption would be that the 6% for a
one-year option will hold. For more detail on Black-Scholes modeling
of options and futures, here is a concise summary:
QuickMBA Finance
"Black-Scholes Option Pricing Formula" (undated)
http://www.quickmba.com/finance/black-scholes/
With gold at $275, this reduces ABC Mining's cash flows by $16.5 per
ounce or $33,000 per year. (There are no taxes assumed in this
problem. The impact of taxes -- and depreciation credits -- would
impact the cash flows.) The project never achieves a positive NPV, as
the discounted cash flows (assuming revenues at the end of the year)
are as follows.
One other note: the futures contract will be purchased a full year
before revenues, so its discount timing is a year ahead of the
revenues:
Discounted Cash Flow @ Gold = $275
---------------------------------------------
1. $90,000 - $33,000 = $67,000
2. $81,000 - $29,700 = $51,300
3. $72,900 - $26,730 = $46,170
4. $65,610 - $24,057 = $41,553
TOTAL = $206,023
The next question becomes -- is there a positive NPV even at $310, if
we are forced to hedge every year? Again, we'll assume 6%, bringing
the cost of the hedge up to $37,200 per year.
The project costs under this assumption shift to $25,000 in year one
because we'll have to exercise the option this year; and $450,000 in
year two (the $500,000 is discounted for timing) -- for a total of
$475,000 in today's dollars We'll start discounting the cash flows
against that investment at the END of year 2 and the options at the
end of year 1:
Discounted Cash Flow @ Gold = $310
---------------------------------------------
2. $137,700 - $33,480 = $100,500
3. $123,930 - $30,132 = $93,798
4. $111,537 - $27,118 = $84,419
5. $100,383 - $24,407 = $75,976
6. $90,345 - $21,966 = $68,379
7. $81,310 - $19,769 = $61,541
TOTAL = $484,613
Thus, NPV comes after the sixth year of investment -- still a fairly long period.
The answer becomes obvious: purchase the option and wait for the price
of gold to rise. While at current prices, it appears to be a
profitable investment, the absence of a firm fixed contract price for
gold makes the prediction of future cash flows a gamble.
Google search strategy:
"Black-Scholes" + options
Best regards,
Omnivorous-GA |
Clarification of Answer by
omnivorous-ga
on
27 Nov 2003 17:25 PST
Herbert --
Your discounted cash flow is $206,000 and you've put in $500,000
upfront -- making a NET cash flow of NEGATIVE $294,000. That's not an
investment that you make. The critical point here is that at a $275
price for gold, you have to hedge the position as insurance for the
original investors.
With the choice to invest now not making any economic sense, the
alternate option of potential gold price hikes and land that may make
money is the logical choice.
Your calculation is incorrect here inasmuch as the effect of interest
rates are exponential (10% per year is 10% year is in fact 21% over
two years; 33% over three years; etc):
> NPV = (((258.50-225) * 2000) / 0.10 ) - $500,000
That particular formula is NOT increasing the discounting of cash flow past year 1.
That's how you arrive at the revenue numbers that I've cited in 1-4,
but compounding your discounting. To be clear, with a 10%
cost-of-money, here are the factors that you want to divide by:
1: 1.1
2: 1.1 * 1.1 = 1.21
3. 1.1 * 1.1 * 1.1 = 1.33
4. 1.1 * 1.1 * 1.1 * 1.1 = 1.46
5. 1.1 * 1.1 * 1.1 * 1.1 * 1.1 = 1.61
Finally, if you're spending $16.50 for the option today, it's in
essence an upfront or capital cost. Of course an option a year from
now is discounted by 10% (money a year from now is worth 10% less,
whether in revenue or in expense or in capital); money two years from
now is worth 21% less; three years from now it's 33% less.
And finally, be aware of timings in these investment problems. You'll
be buying an option or investing today, so there's no discount on it.
An option purchased for year two has only one year's discounting
(you'd buy it next November) -- but revenues come later, so they have
to be discounted over two years.
Let me know if this is clear enough or if you'd like me to start anew
with the calculation of discount rates.
Best regards,
Omnivorous-GA
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