7.01 Financial decisions

When dealing with financial situations, there are a few terms that are often used.

The cost price of an item is how much money you need to spend to get it. Multiple cost prices can be referred to collectively as expenses.

The sale price of an item is how much money you earn by, well, selling it. Money earned can be more generally referred to as money received or revenue.

The profit made on an item is the difference between the sale price and the cost price. A profit is only made if the sale price is greater than the cost price.

The loss incurred from an item is the difference between the cost price and the sale price. A loss is only made if the cost price is greater than the sale price.

Profit and loss can be calculated using the formulas: \begin{aligned} \text{Profit}&= \text{Sale price}-\text{Cost price} \\ \text{Loss}&=\text{Cost price}-\text{Sale price} \end{aligned}

Examples

Discounts and mark ups are percentage decreases and increases of item prices respectively. When an item has its price discounted, the cost price of that item is decreased by some percentage. When an item has its price marked up, the cost price of that item is increased by some percentage. We can calculate the effect of discounts and mark ups in the same way that we would calculate  percentage changes  to a value.

Since discounts and mark ups are multiplicative changes to the cost price, multiple discounts and/or mark ups can be applied to a cost price in any order without changing the final result.

Examples

When presented with two different prices for the same product, it is helpful to know which is greater and which is smaller. However, comparing the price of a 300 mL can of drink to a 2 L bottle of the same drink is not very useful since their costs are relative to their different quantities. In order to properly determine which is the best buy, we want to calculate their prices with respect to some common amount.

Suppose that the 300 mL can costs \$0.45 and the 2 L bottle costs \$2.90.

To properly compare these prices, we can find the costs of the can and bottle as rates of dollars per litre.

The can costs \$0.45 per 0.3 L, which can be expressed as \dfrac{0.45}{0.3} dollars per litre, which we can simplify to be \$1.50 per litre.

The bottle costs \$2.90 per 2 L, which can be expressed as \dfrac{2.90}{2} dollars per litre, which we can simplify to be \$1.45 per litre.

From our calculations, we can see that the bottle is the better buy, since it has a lower cost price per litre.

We can perform similar calculations for any situation where the same product is being sold in different quantities for different prices.

Examples