# Durban Deep Price Predictor Model

When analyzing a mining stock such as DROOY for valuation, there are many variables to consider. Some values, such as production numbers and balance sheet items (assets, liabilities, etc.) can be estimated with some degree of confidence (no snickering please). Others, such as risk of operations and future PM prices are far more difficult to predict. I like to simplify a stock's valuation into three components, listed here in declining predictability: 1. Current earnings/share based on current production, total production costs and realized price of gold (profit), 2. Future expectations of the same variables (profit potential) and 3, miscellaneous unpredictable risk variables such as natural disasters and investor mania/depression.

One method of determining future stock prices, which tend to factor out unknown variables, is to perform a *relative* price analysis. This method assumes that non-core data such as future expectations, taxes, political risk and investor trends are already factored into the current price such that short term movements can be attributed solely to basic known variables such as gold sales, cost of production and POG. This then simplifies to the basic economic principle of Total Profit = Units Sold x Profit/Unit, where Profit/Unit = (Sales Price - Production Cost)/Unit. Units are, of course, in oz. of gold. Furthermore, Earnings/Share can be calculated by dividing Total Profit by the Number of Shares outstanding.

Statistically, a stock's price rarely fluctuates more than a few percentage points from day to day, regardless of its actual fair value. In PM stocks, large moves in the POG sometimes move stocks 10% - 20% or more per day, but these days have been few and far between in recent PM market activity. However, these moves indicate a strong positive correlation between the POG and share prices. Thus, in the short-to-medium term, assuming a mine is profitable, future valuations can be estimated solely on expected movements in the POG. Other variables such as amount of production, cost of production and number of shares outstanding tend to remain constant for short periods of time. One other factor that must be considered is the Dollar exchange rate in the country where the mine is located. This variable is a little more volatile, but is well known.

For a marginal producer such as DROOY, the distribution of the three above mentioned price components is heavily weighted towards future expectations and miscellaneous speculative factors. Indeed, for much of the past few years, DROOY's price has languished at or below $1/share because of low gold prices resulting in negative profit. However, now that the POG is comfortably above $300/oz. and Durban Deep has lowered production costs (due mostly to the favorable Rand/Dollar exchange rate), we should expect to see actual earnings begin to dominate the relative price action of this stock and those of other high cost producers.

**The basic formula I came up with for South African producers is:**

P(f) = P(i) * [(PoG(f)-ProdCost)/(PoG(i)-ProdCost)] * [USDZAR(f)/USDZAR(i)]

where:

P = stock price

PoG = POG (in U.S. $)

ProdCost = total production costs (in U.S. $)

USDZAR = SA Rand / U.S. Dollar

(Use USDCAD and USDAUD for Canada and Australia respectively. Of course you could eliminate the third term by pricing everything in local currency).

The subscripts (i) and (f) are initial conditions and final conditions, respectively. In simple terms, the future price should be the current price times the leveraged earnings profit gain or loss, adjusted for the Rand/Dollar exchange rate. With me so far?

I decided to use $270 for DROOY's current total production cost to account for other costs that affect the bottom line, but aren't reflected in their reported cash cost numbers. Recent historical data show that this number works remarkably well when plugged into the equations. For example:

With (i) = April 15, (f) = May 15

P(f) = 3.7 * [(308-270)/(300-270)] * [10.2 / 11.2] = 4.27

With (i) = May 15, (f) = June 4

P(f) = 4.27 * [(324-270)/(308-270) * [9.7 / 10.2] = 5.77 (5.6 actual)

However, if (i) = June 4, (f) = June 12

P(f) = 5.6 * [(319-270)/(324-270) * [10.2 / 9.7] = 5.34

By this method, either DROOY is way undervalued at 4.18, or it is pricing in a POG of $310. If the recent run up in price were due to speculation or mania, it would have been exposed as being overpriced in the second equation. Clearly this was not the case.

Another explanation for DROOY's apparently low current price. could be the non-linear discontinuation at the magic $5 mark, at which point the stock becomes margin able, and hits the big mutual funds' radar screens. This 1-month chart shows the discontinuity at $5 rather clearly, gapping up above $5 on May 22, and gapping down through $5 and plummeting like a rock on June 10:

http://quotes.ino.com/chart/?s=NASDAQ_DROOY&v=d1&w=1&t=f&a=5

Now let's look at some hypothetical cases:

**Case #1 - assuming USDZAR remains constant:**

@350: P(f) = 4.18 * [(350 - 270)/(319 - 270)] = 6.82

@400: P(f) = 4.18 * [(400 - 270)/(319 - 270)] = 11.10

@450: P(f) = 4.18 * [(450 - 270)/(319 - 270)] = 15.4

@500: P(f) = 4.18 * [(500 - 270)/(319 - 270)] = 19.6

**Case #2 - using P(i) = 5.34 instead of 4.18:**

@350: P(f) = 6.82 * (5.34/4.18) = 8.71

@400: P(f) = 14.18

@450: P(f) = 19.67

@500: P(f) = 25.04

However, a more realistic scenario would be for the Rand/Dollar ratio to decrease in (some unknown) proportion to the increase in POG, since the POG is generally inversely proportional to the U.S. dollar. Let's assume the dollar decreases at half the rate that POG rises (with respect to the Rand). Then we must add the third term to each equation. Note that the Rand term cancels out:

@350: USDZAR(f)/USDZAR(i) = ((319/350-1)/2)+1 = 0.956

@400: USDZAR(f)/USDZAR(i) = ((319/400-1)/2)+1 = 0.899

@450: USDZAR(f)/USDZAR(i) = ((319/450-1)/2)+1 = 0.854

@500: USDZAR(f)/USDZAR(i) = ((319/500-1)/2)+1 = 0.819

Thus, the U.S. dollar and adjusted share prices become:

@350: $ = 106.6, P(f) = 6.52 - 8.74

@400: $ = 99.97, P(f) = 9.98 - 13.37

@450: $ = 94.96, P(f) = 13.15 - 17.62

@500: $ = 91.07, P(f) = 16.05 - 21.79

Also, with gold at $500/oz., it is likely that Durban will re-open mines previously put on care-and-maintenance. They may also issue more shares to finance the re-opening of these mines or to expand existing projects. An increase in production and/or dilution of total shares would directly affect the result. You would need to multiply the result by a fourth and fifth term, Prod(f)/Prod(i) and Shares(i)/Shares(f), to account for these changes. To complicate matters more, the total average production costs are likely to increase with a dramatic rise in the POG, because although it would become profitable to re-open mothballed mines, the production cost associated with these mines will be higher.

Thus, these equations are much more useful for predicting short-to-medium term relative price movements, over perhaps several weeks to a few months. There are just too many variables to consider when pricing a stock long term. For more information on absolute pricing, see durbandude's work:

www.gold-eagle.com/editorials_02/durbandude032802.html

As an interesting side note, compare these numbers with Adam Hamilton's report "Roodepoort Rocket" from Aug. 2000:

www.zealllc.com/commentary/rocket.htm

At a P/E ratio of 13.5 his numbers were (Approximately):

@350 P = $4

@400 P = $8

@450 P = $12

@500 P = $16

However, I believe he assumed a total production cost of $300, so if you shift the x-axis on his graph $30 to the right (to compensate for my estimated production costs of around $270) you get:

@350 P = $6

@400 P = $10

@450 P = $14

@500 P = $18

Which match up pretty well with my numbers.

In conclusion, you may find these equations useful for short-to-medium term predictions, based on recent price behavior. But, like hurricane predicting, the further out in time you go, the less reliable the results will be. Also, this indicator ignores fluctuations in daily price, so care must be taken in determining initial reference points.