Units, quotes and conversions: from XAG/USD to euros per kilogram

What you will learn

• How to read XAG/USD and convert it into euros per troy ounce, gram and kilogram
• How fine weight and fineness work for silver coins and bars
• How to split a German retail price into VAT, dealer premium and metal value
• How to compare buy-back (bid) prices and round-trip costs for coins and bars

Explanation

The basic method of converting a dollar price per troy ounce into euros per gram was taught in the Gold course, lesson "Quoting and Units". The same formulas work for silver. What changes is the size of the numbers: silver prices per gram are small, typical purchases are in kilograms, and the premiums and taxes on top are far larger than for gold. Small errors therefore become big money.

The quote and the units

XAG/USD is the price of one troy ounce of silver in US dollars ("XAG" is the international code for silver). A troy ounce is 31.1034768 grams, so one kilogram is about 32.1507 troy ounces. The spot price is the wholesale price for immediate delivery.

The conversion chain for a euro buyer is:

1. Euro per ounce = XAG/USD ÷ EUR/USD.
2. Euro per gram = euro per ounce ÷ 31.1034768.
3. Euro per kilogram = euro per gram × 1,000 (or euro per ounce × 32.1507).

Fineness and fine weight

Fineness is the share of pure silver, written in thousandths. Modern bullion bars and coins are usually 999 or 999.9 fine. Older coins and silverware are often 925 ("sterling silver") or 900. The fine weight is the weight of pure silver: total weight × fineness. Only the fine weight has metal value; always calculate with it.

Bid, ask and premium

A dealer shows an ask price (you buy) and a bid price (the dealer buys back). The premium is the amount above the metal value at spot. For silver in Germany, the shop price normally includes 19% VAT (value added tax, Umsatzsteuer) for bars and most new coins; lesson 4 explains the VAT rules. To see the dealer's own markup, remove the VAT first:

• Net price = price including VAT ÷ 1.19.
• Net premium = net price ÷ metal value at spot − 1. This shows the dealer's markup for minting, handling and profit.
• Gross premium = price including VAT ÷ metal value at spot − 1. This is what the price must rise before you break even on a sale at spot.

Small units (1-ounce coins, 100-gram bars) usually carry higher net premiums per ounce than 1-kilogram or 5-kilogram bars. Popular coins are often easier to sell and may have better buy-back prices than unusual bars, so the cheapest purchase is not always the cheapest round trip.

Worked example

Hypothetical example: XAG/USD = $30.00 per troy ounce and EUR/USD = 1.15. These are invented round numbers, not current prices.

Step 1 – spot in euros.

1. Per ounce: $30.00 ÷ 1.15 ≈ €26.09.
2. Per gram: €26.087 ÷ 31.1034768 ≈ €0.8387.
3. Per kilogram: €0.8387 × 1,000 ≈ €838.72.

Step 2 – a 1-ounce coin offered at €35.00 including VAT.

1. Net price: €35.00 ÷ 1.19 ≈ €29.41.
2. Net premium: €29.41 ÷ €26.09 − 1 ≈ 12.7%.
3. Gross premium: €35.00 ÷ €26.09 − 1 ≈ 34.2%.

Step 3 – a 1-kilogram bar offered at €1,100 including VAT.

1. Net price: €1,100 ÷ 1.19 ≈ €924.37.
2. Net premium: €924.37 ÷ €838.72 − 1 ≈ 10.2%.
3. Gross premium: €1,100 ÷ €838.72 − 1 ≈ 31.2%.

Step 4 – buy-back. The dealer bids €25.00 for the coin (about 95.8% of spot) and €800 for the bar (about 95.4% of spot). If spot stays unchanged, the round-trip loss is (€35.00 − €25.00) ÷ €35.00 ≈ 28.6% on the coin and (€1,100 − €800) ÷ €1,100 ≈ 27.3% on the bar.

Fine weight check: an old 20-gram coin of 925 fineness contains 20 × 0.925 = 18.5 g of silver, worth 18.5 × €0.8387 ≈ €15.52 at spot.

Shipping, payment fees and taxes on gains are excluded.

Common mistake

Practice activity

Hypothetical: XAG/USD = $25.00, EUR/USD = 1.25. (a) Calculate spot in euros per ounce, per gram and per kilogram. (b) A 1-ounce coin costs €28.00 including 19% VAT. Calculate its net and gross premium. (c) A 1-kilogram bar costs €850 including 19% VAT. Calculate its net and gross premium, and its price per troy ounce.

Key takeaways

• Euro per gram = XAG/USD ÷ EUR/USD ÷ 31.1034768; one kilogram is about 32.15 troy ounces.
• Always calculate with fine weight (weight × fineness).
• Split a German silver price into 19% VAT, net premium and metal value before judging a dealer.
• Compare round-trip costs (ask versus bid), not only the purchase price.

Next step

In the next lesson you will see how VAT, storage and buy-back spreads decide the break-even price when you buy physical silver in Germany.