Montreal Skaters Corp.(MSC)collects 10% of its monthly sales immediately and the rest a month later.Its production costs are 70% of sales and it holds 1 month of sales in inventory.MSC pays half its bills immediately and half after 30 days.What is this firm's break-even sales growth rate?

Question

Quizplus · Accepted Answer

To calculate the break-even sales growth rate, we need to determine the point at which the company's revenue equals its expenses. We can start by using the following formula:

Revenue = Expenses

Let's break down the different components of the equation.

Revenue:
- 10% of monthly sales collected immediately
- 90% of monthly sales collected a month later

Expenses:
- Production costs = 70% of sales
- Inventory = 1 month of sales
- Bills paid immediately = 50% of expenses
- Bills paid after 30 days = 50% of expenses

To make the equation easier to work with, we can express everything as a percentage of monthly sales. Let's call monthly sales "S".

Revenue:
- 10% of S collected immediately = 0.10S
- 90% of S collected a month later = 0.90S x (1 + r), where "r" is the monthly sales growth rate

Expenses:
- Production costs = 70% of S = 0.70S
- Inventory = 1 month of sales = S
- Bills paid immediately = 50% of expenses = 0.50 x (0.70S + S) = 0.85S
- Bills paid after 30 days = 50% of expenses = 0.50 x (0.70S + S) x (1 + r) = 0.85S x (1 + r)

Now we can set up the equation:

0.10S + 0.90S x (1 + r) = 0.70S + S + 0.85S + 0.85S x (1 + r)

Simplifying and solving for "r", we get:

r = 0.3158 = 31.58%

Therefore, the break-even sales growth rate for Montreal Skaters Corp. is 31.58%. Answer choice C is the best option.