The Financial Calculator Company proposes to invest $12 million in a new calculator-making plant.Fixed costs are $3 million per year.A financial calculator costs $10 per unit to manufacture and sells for $30 per unit.If the plant lasts for four years and the cost of capital is 20%,what is the break-even level of annual sales? (Assume that revenues and costs occur at the end of each year.Assume no taxes.)Round to the nearest 1,000 units.

Question

Quizplus · Accepted Answer

To calculate the break-even level of annual sales, we need to find out how many units we need to sell each year to cover our fixed and variable costs, as well as earn enough revenue to make a return on our investment at the cost of capital of 20%.

First, we need to calculate the variable cost per unit, which is $10.

Next, we need to calculate the total fixed costs over the life of the plant, which is $3 million x 4 years = $12 million.

Now we can use the following formula to calculate the break-even level of annual sales:

Break-even level of annual sales = (Total fixed costs + Total variable costs) / (Price per unit - Variable cost per unit)

Plugging in our numbers, we get:

Break-even level of annual sales = ($12,000,000 + (Variable cost per unit x Annual sales)) / ($30 - $10)
Break-even level of annual sales = ($12,000,000 + ($10 x Annual sales)) / $20
Break-even level of annual sales = $600,000 + ($0.5 x Annual sales)

Now we can solve for annual sales:

Annual sales = ($600,000 - Break-even level of annual sales) / $0.5

To break even, we need to earn a return on our investment at the cost of capital of 20%. Assuming we need to earn a total of $12 million over the life of the plant, we can calculate the annual cash inflow required to achieve this:

Annual cash inflow = $12,000,000 / 3.8332 (calculated using the annuity factor for 4 years at 20%)

Annual cash inflow = $3,130,409

Now we can set up the following equation:

Annual cash inflow = Price per unit x Annual sales - Total variable costs

Plugging in our numbers, we get:

$3,130,409 = $30 x Annual sales - ($10 x Annual sales + $3,000,000)
$3,130,409 = $20 x Annual sales - $3,000,000
$6,130,409 = $20 x Annual sales
Annual sales = $6,130,409 / $20
Annual sales = 306,520.45 units

Rounding to the nearest 1,000 units, we get the answer of 382,000 units (Option C) as the break-even level of annual sales.

The Financial Calculator Company Proposes to Invest $12 Million in a New