Summary of NPV’s with Discount

In-Situ Value at $8500/t is $12.05B;

In-Situ Value at $12,000/t is $17.02B;

In-Situ Value at $16,000/t is $22.69B; and

In-Situ Value at $20,000/t is $28.36B

(constants 1.418 MT’s)

NPV- Net Present Value

NPV is calculated with these constants in mind, 1.418 MT’s, Capex $300M, 50 KTPA, 25 year minelife, mine/process costs $2000.

Formula, NPV = R x { [1 – (1 + i) ^-n] /i} – Initial Investment

R – Net Cash Flow Rec’d each period (each year for 25 years)

i – Required Rate of Return

n – Number of Periods (years)

Initial Investment $300M

Net Cashflow/Period $325M ($8500/t - $2000 = $6500 x 50 KTPA)

Discount Rate/Period 100% (IRR) / 25 (years) = 4%

NPV = $325m x { [1 – (1 + 4%) ^-25] / 4%} - $300m

$325m x {[1 – 1.04 ^-25] / 0.04} - $300m

$325m x {1 – 0.375116802 / 0.04} - $300m

$325m x {0.624883198 / 0.04} - $300m

($325 x 15.62) - $300m

$5.76B - $300M = $5.46B is the NPV (not discounted)

NPV is $5.46B at $8500 / tonne Graphite;

NPV is $7.51B at $12000/ tonne Graphite;

NPV is $10.6B at $16000/ tonne Graphite; and

NPV is $13.76B at $20000/ tonne Graphite

Now NPV has to be Discounted. The Discount Rate takes into account, the where else you could receive a safe investment return on your mining investment and is discounting the Risk in todays Net Present Value and for the Cash Flows spread over many years. For years Mining Companies have been using the 8%, 10% and 12% Discount Rates for Risk comparison. I would argue these are much too high today, as the discount rate is supposed to reflect, 1. A Safe Investment like the 10 year Bond, plus 2. An additional 3% for Risk Premium. Today the Cdn 10yr Bond is 2% + 3% Risk Premium should equal a Discount Rate of 5%.

“At the 1998 Berkshire Hathaway meeting, Buffett was quoted to have said:

“We don’t discount the future cash flows at 9% or 10%; we use the U.S. treasury rate. We try to deal with things about which we are quite certain. You can’t compensate for risk by using a high discount rate.”

With the above comment, I believe that Warren Buffett is highlighting the principle that too high of a discount rate will calculate a net present value (NPV) that would be unrealistically low. Conversely, using a discount rate that is too low will produce a value that is unrealistically high. This reminds me of the “Three Bears” porridge. It is no good if it is too hot, and no good if it’s too cold, to be good it needs to be just right.

NPV with Discount Rates (I used a NPV Discount calculator for the first 20 years production, after year 20 the discount is around 1/3 of that years Net Earnings, which would increase NPV totals somewhat for the remaining 5 years)

NPV ($5.46B) at $8500/t ($6500 x 50 ktpa = $325M/yr)

NPV ($5.46B) discounted at 8% = $2.8B

NPV discounted at 10% = $2.4B

NPV discounted at 12% = $2.09B

NPV discounted at 5% = $3.627B

NPV ($7.51B) at $12,000/t ($10,000 x 50 ktpa = $500M/yr)

NPV ($7.51B) discounted at 8% = $4.5B

NPV discounted at 10% = $3.88B

NPV discounted at 12% = $3.38B

NPV discounted at 5% = $5.74B

NPV ($10.6B) at $16,000/t ($14,000 x 50 ktpa = $700m/yr)

NPV ($10.6B) discounted at 8% = $6.7B

NPV discounted at 10% = $5.8B

NPV discounted at 12% = $5.15B

NPV discounted at 5% = $8.5B

NPV ($13.76B) at $20,000/t ($18,000 x 50ktpa = $900M/yr)

NPV ($13.76B) discounted at 8% = $8.6B

NPV discounted at 10% = $7.5B

NPV discounted at 12% = $6.6B

NPV discounted at 5% = $10.88B

I think, we shareholders are going to make big money, cheers, Mark

Example 1: Even Cash Inflows:Calculate the net present value of a project which requires an initial investment of $243,000 and it is expected to generate a cash inflow of $50,000 each month for 12 months. Assume that the salvage value of the project is zero. The target rate of return is 12% per annum.

Solution

We have,
Initial Investment = $243,000
Net Cash Inflow per Period = $50,000
Number of Periods = 12
Discount Rate per Period = 12% ÷ 12 = 1%

Net Present Value
= $50,000 × (1 − (1 + 1%)^-12) ÷ 1% − $243,000
= $50,000 × (1 − 1.01^-12) ÷ 0.01 − $243,000
≈ $50,000 × (1 − 0.887449) ÷ 0.01 − $243,000
≈ $50,000 × 0.112551 ÷ 0.01 − $243,000
≈ $50,000 × 11.2551 − $243,000
≈ $562,754 − $243,000
≈ $319,754