Please help explain

A manufacturer of motorcycle batteries has a plant capacity of 100,000 per year. Overhead costs are $500,000 per year. Variable costs are $10 per unit. Sales have been running at 50,000 per year at a wholesale price of $25 each. Recently, a large department store offered to purchase an additional 50,000 batteries a year at $20 each. (a) Should they take the offer? Explain why or why not. (b) Suppose the department store offered to buy the entire output for $15. Should they take the offer? Explain why or why not

Sure, I'd be happy to help explain! Let's break it down.

(a) Should they take the offer of selling an additional 50,000 batteries a year at $20 each? Well, let's calculate the numbers. The fixed overhead costs are $500,000 per year, which means for 100,000 batteries, the fixed cost per unit is $5 ($500,000 / 100,000). The variable cost per unit is $10, as given. So, the total cost per unit is $15 ($5 + $10).

Now, if they sell the batteries to the department store at $20 each, they will make a profit of $5 per unit ($20 - $15). For 50,000 batteries a year, the total profit would be $250,000 ($5 x 50,000).

Considering the profit margin, it seems like a good deal. The manufacturer should take the offer because they can make a profit by selling the batteries to the department store.

(b) Now, let's consider the offer of selling the entire output of 100,000 batteries for $15 each. In this scenario, the manufacturer would not make a profit as the total cost per unit is $15 ($5 + $10), which is the same as the selling price.

So, if the department store offered to buy the entire output for $15 each, the manufacturer should not take the offer. Selling at cost would mean they won't make any profit, and considering the overhead costs, they would actually end up operating at a loss.

In summary, (a) Yes, they should take the offer of selling an additional 50,000 batteries a year at $20 each because it would result in a profit. (b) No, they should not take the offer of selling the entire output for $15 each because it would result in no profit and operating at a loss.

To determine if the manufacturer should take the department store's offer, we need to calculate the costs and revenues associated with the offer.

(a) Offer to purchase an additional 50,000 batteries at $20 each:

1. Variable Costs: Variable costs per unit are given as $10. Therefore, the total variable costs for the additional 50,000 batteries can be calculated as:
Variable Costs = Variable Cost per Unit * Number of Units
= $10 * 50,000
= $500,000

2. Revenue: The revenue generated from the department store's offer can be calculated as follows:
Revenue = Selling Price per Unit * Number of Units
= $20 * 50,000
= $1,000,000

3. Profit: The profit is calculated by subtracting the variable costs from the revenue:
Profit = Revenue - Variable Costs
= $1,000,000 - $500,000
= $500,000

Since the additional revenue from the department store's offer is higher than the additional variable costs, accepting the offer would result in a profit of $500,000. Thus, the manufacturer should take the offer.

(b) Offer to purchase the entire output for $15:

1. Variable Costs: Variable costs per unit remain the same at $10. Therefore, the total variable costs for the 100,000 batteries can be calculated as:
Variable Costs = Variable Cost per Unit * Number of Units
= $10 * 100,000
= $1,000,000

2. Revenue: The revenue generated from selling the entire output at $15 each can be calculated as:
Revenue = Selling Price per Unit * Number of Units
= $15 * 100,000
= $1,500,000

3. Profit: The profit is calculated by subtracting the variable costs from the revenue:
Profit = Revenue - Variable Costs
= $1,500,000 - $1,000,000
= $500,000

Accepting the offer to sell the entire output for $15 would result in the same profit of $500,000 as in the previous scenario. Therefore, the manufacturer should still take the offer.

In both cases, accepting the department store's offer would result in increased profit for the manufacturer, as the revenue generated from the offer exceeds the additional variable costs incurred.

To answer these questions, we need to calculate the total costs and revenue associated with each scenario. Let's break it down step by step:

(a) Should the manufacturer take the offer from the department store to purchase an additional 50,000 batteries a year at $20 each?

First, let's calculate the total costs:
Fixed overhead costs = $500,000
Variable costs per unit = $10
Number of units to be produced (additional 50,000 batteries) = 50,000

So, the total production costs can be calculated as:
Total production costs = Fixed overhead costs + (Variable costs per unit * Number of units)
Total production costs = $500,000 + ($10 * 50,000)
Total production costs = $500,000 + $500,000
Total production costs = $1,000,000

Next, let's calculate the total revenue:
Number of units sold at wholesale price = 50,000
Wholesale price per unit = $25

So, the total revenue from wholesale sales can be calculated as:
Total revenue from wholesale sales = Number of units sold * Wholesale price per unit
Total revenue from wholesale sales = 50,000 * $25
Total revenue from wholesale sales = $1,250,000

Now, let's calculate the total revenue from the department store offer:
Number of units offered by the department store = 50,000
Offered price per unit = $20

So, the total revenue from the department store offer can be calculated as:
Total revenue from department store offer = Number of units offered * Offered price per unit
Total revenue from department store offer = 50,000 * $20
Total revenue from department store offer = $1,000,000

Finally, let's compare the total revenue from the wholesale sales ($1,250,000) and the total revenue from the department store offer ($1,000,000). Since the total revenue from wholesale sales is higher, it would be more profitable for the manufacturer to stick with the current sales arrangement and not take the department store offer.

(b) Should the manufacturer take the offer from the department store to buy the entire output for $15?

Using the same calculations as above, let's calculate the total revenue from the department store offer if the price per unit is $15:

Offered price per unit = $15

Total revenue from the department store offer = Number of units offered * Offered price per unit
Total revenue from the department store offer = 100,000 * $15
Total revenue from the department store offer = $1,500,000

Now, let's compare the total revenue from the wholesale sales ($1,250,000) and the total revenue from the department store offer ($1,500,000). Since the total revenue from the department store offer is higher, it would be more profitable for the manufacturer to accept the offer and sell the entire output to the department store.

In conclusion, (a) the manufacturer should not take the offer to purchase an additional 50,000 batteries a year at $20 each as the revenue from wholesale sales is higher, and (b) the manufacturer should take the offer to buy the entire output for $15 as the revenue from the department store offer is higher.

a) no because the company earns less

b) yes, because they company would earn more