Question

A factory currently manufactures and sells 800 boats per year. Each boat costs $5,000 to produce. $4,000 of the per-boat costs are for materials and other variable costs, while the per-boat fixed costs (incurred on yearly rent, administrative, and other fixed costs) are $1,000. If boat orders increase to 1000 boats per year, how do per-unit costs change?

Answer 1

Answer :

Variable costs are unchanged at $4000 per boat and  fixed costs falls to $800 per boat.

Explanation -

Given :

Cost of per boat = $5000 in which $4000 are variable cost and $1000 are fixed.

Finding Variable cost -

1 boat = $4000

800 boats =4000 x 800 = $3,200,000

1000 boats = 1000 x 4000 = $4,000,000

1 boat = 4,000,000/1000 = $4000  

So, Variable cost of per boat is $4000

Finding Fixed cost -

1 boat = $1000

800 boats = 800 x 1000 = $800,000

1000 boats = $800,000 ( Fixed cost remain same)

1 boat = $800,000/1000 = $800

So, Fixed cost per boat = $800

The fixed costs $800,000 are spread to 1000 boats. So, this result in fixed cost per boat is $800.

Hence :

Variable costs are unchanged at $4000 per boat and  fixed costs fall to $800 per boat.

Answer 2

Variable costs remain unchanged at $4000 per boat wereas the fixed costs goes below $800 per boat.

We will see here how this happens.

The given cost of a boat is $5000 out of which $4000 are variable cost and $1000 are fixed.

To find the variable cost of a boat, we need the price of one, which is $4000.

Therefore,  800 boats will cost 4000 x 800 = $3,200,000.

Hence, 1000 boats will cost 1000 x 4000 = $4,000,000.

The variable cost of a boat is 4,000,000/1000 = $4000.  

So, the variable cost per boat stays at $4000.

For finding the fixed cost. we need the price of a boat, that is $1000.

Therefore, for 800 boats, the price is $800,000.

For 1000 boats, the price will be $800,000 as the fixed cost remains the same.

Therefore, for 1 boat, $800,000/1000 = $800.

Hence, the fixed cost per boat is $800

The fixed cost of $800,000 are spread over all 1000 boats.

This results in a fixed cost boat price of $800.

Hence, variable costs remain unchanged at $4000 a boat whereas the fixed cost falls to $800 for a boat.