# Decreasing Your Average Cost: Buying vs Gifts

**8/1/17**

This article will take a look at how to lower your average cost. Specifically, it will look at using the two strategies of buying more and receiving gifts. Buying or receiving gifts of what you ask? This information is very generalized, but I will specifically look at buying silver coins, rounds, or bars.

Let's assume you have purchased n ounces of silver over time at different prices and that your average cost now is say $25 per troy oz. As of writing this article, the spot price of silver is $16.81/troy oz. The questions are

- How many oz do I need to buy to lower my cost to, say, $20? (or some other number between $16.81 plus a premium and $25).
- How many oz do I need to have gifted to me to lower my cost to $20?

Note that avg cost = total cost / number of oz. If you buy n more ounces, you've added to the total cost as well as the total oz. Replacing the $20 with just X, therefore, you want to solve

avg cost = (total costs+n*(spot + premium))/(total oz + n) = X

for n.

I added the premium term in there to specifically see how the premium of silver comes into play, since it can vary a bit. That is, it can act differently than the spot price itself, so I didn't want to lump the premium in with the spot price term.

Solving for n, we get n = (total costs-X*total oz)/(X-premium-spot).

The situation with receiving gifts is different and easier. We solve

avg cost = total cost / (total oz + n) = X

for n, to get n = (total cost/X) - total oz.

Notice that with gifts, someone else buys them for you so this does not add any costs from your viewpoint.

I'm going to compare these n's, so I will call the first one n_buy and the latter n_gift. Certainly n_buy > n_gift. What can we say about the ratio n_buy/n_gift?

If we simply calculate n_buy/n_gift = [(total costs-X*total oz)/(X-premium-spot)] / [total cost/X) - total oz] and simplify, we get n_buy/n_gift = X/(X-premium-spot).

Let's call this ratio K. This is saying you need to buy K times as many ounces of silver as have gifted to get your current average cost down to the new average cost of X.

Let's look at some real numbers using avg cost = $25, spot = $16.81, premium = $2, total oz = 100, total cost = $2,500, and you want a new average cost (X) of $20. Then, n_buy = 420.17 oz, and n_gift = 25 oz, and n_buy/n_gift = K = 16.8. In other words, with these parameters, you'd need to buy almost 17 times as much silver than have gifted to you to move your average cost from $25 to $20. Buying 420.17 oz of silver at these prices would be between $7,000 and $8,000. One can substitute in your own parameters and see how n_buy, n_gift, and the K ratio change, and how they change with varying premiums.

I hope I have demonstrated the importance of getting gifts if you are interested in lowering your average costs! Like I mentioned before, I looked at silver, but this logic and analysis can be extended to just about anything. Thanks for reading.

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