GST on Gold Selling

As questionable it may be, gold selling is a way to make money. Like any other Australian business, a Australian gold seller may get taxed on their proceeds, and if they have not been declaring such income on their BAS (business activity statement), they may well be running up a tax debt...

Josh, as well as his friends Guy and Sandy, have dipped their toes into the grey market, and are now wondering if they will have to pay GST (Goods and Services Tax). Unfortunately, they find the A New Tax System (Goods and Services Tax) Act 1999 (GST Act) too daunting to find out themselves. Will you be able to help them?

This problem has been taken out of Understanding Taxation Law 2011 (see bibliography for full citation), and the GST Act as of 1 November 2010 has been referred to.

How to attract the tax collector
In the GST Act:

• s 7-1 says that "GST is payable on taxable supplies and taxable importations".
• s 9-5 says that a taxable supply is made if a supply is made for consideration in the course or furtherance of an enterprise carried on, if it is connected with Australia and the supplier is registered or required to be registered.

WoW Mathematics: Your guild bank donation

Aim: To calculate the value of a deposit of gold to a guild bank (gbank) that discounts sales at a given rate.

Summary:

• A donation of G gold to a gbank with a decimal discount rate of r will be worth G/r gold. This means that G is multiplied by 1/r, the reciprocal of the discount rate. Keep in mind that Full price = Discounted price + Discount.
• As long as the discount rate is less than 100%, the donation is worth more than the amount donated (even in pure money terms)!
• A gbank donation's impact will grow according to the sum of a geometric series and approach a limiting value.

The given:

• The discount rate is fixed.
• There is no cost in performing transactions and the full proceeds of a gbank sale are deposited back in.
• All gold is used in buying other resources for resale. No gold is dispensed as a repair allowance (though it can be factored into the discount rate).

The detail:
Consider a gbank deposit of G gold. It is used in buying (for example) enchanting materials worth G gold. They are sold to a guild member at a discount rate of r, so the undiscounted proportion of the price is:

1 - r

The proceeds from that sale are:

G × (1 - r) = G(1 - r) gold

The proceeds are then used for buying potions worth G(1 - r) gold. There potions are sold at a discounted price of:

G(1 - r) × (1 - r) = G(1 - r)² gold

Continuing this process for n terms, we get the following progression of values:

G, G(1 - r), G(1 - r)², G(1 - r)³, ... , G(1 - r)^{n - 1}

The geometric series 1 + 1/2 + 1/4 + ... , with its value represented by area.

This is in fact a geometric progression with common ratio (1 - r) and first term B. Note that, while the amount deposited diminishes, it keeps making an impact with each gbank sale. The total impact for n sales is the following sum of the corresponding geometric series:

S(n) = G(1 - (1 - r)ⁿ) ÷ (1 - (1 - r)) = G(1 - (1 - r)ⁿ)/r gold

As n » ∞ , (1 - r)ⁿ » 0 , and (1 - (1 - r)ⁿ) » 1 . So, the total impact approaches the following limiting value as resales are conducted repeatedly with that amount:

S(∞) = G/r gold

Here is an example. Say 100 gold is donated to a gbank with a discount rate of 25% or 1/4. That donation will be worth:

100 ÷ 1/4 = 100 × 4 = 400 gold