Q1 Your insurance firm processes claims through its newer, larger high-tech facility and its older,
smaller low-tech facility. Each month, the high-tech facility handles 10,000 claims, incurs
$100,000 in fixed costs and $100,000 in variable costs. Each month, the low-tech facility
handles 2,000 claims, incurs $16,000 in fixed costs and $24,000 in variable costs. If you
anticipate a decrease in the number of claims, where will you lay off workers?
What costs would be avoided under the two options? The fixed costs at each facility must be
incurred. Only the variable costs can be avoided. In the high-tech facility, the average variable
cost per claim - an approximation of the marginal costs
$100,000/10,000 = $10 per claim.
In the low-tech facility, the average variable cost per claim is $24,000/2,000 = $12 per claim.
Therefore, by reducing the work apportioned to the low-tech facility will help you avoid more
costs.
The Variable Cost per claim is equal to the Variable Cost divided by the number of claims.High
Tech: $100,000/10,000 claims = $10/claimLow Tech: $24,000/2000 claims = $12/claimThe
Fixed Cost per claim is equal to the Fixed Cost divided by the number of claims.High Tech:
$100,000/10,000 claims = $10/claimLow Tech: $16,000/2000 claims = $8/claimThe Total Cost
per claim is equal to the sum of the fixed and variable cost divided by the of claims.High Tech:
$200,000/10,000 claims = $20/claimLow Tech: $40,000/2000 claims = $20/claimThe total cost
per claim is equal between both locations with the current amount of claims beingreceived. If the
expected amount of claims received is expected to go down, then it would make the mostsense
to layoff employees from the low tech facility. This is because the variable cost can be avoided
whilefixed costs can not, and the low-tech facility has higher variable costs than the high-tech
facility.
Solution 2 –
Answer:
2 copiers produce 100,000 additional pages per day => 1 copier produce 50,000additional
pages per day.5 workers produce 50,000 additional pages per day => 1 worker produce
10,000additional pages per day. In order to increase profit, the company should increase
spending on whichever options that have the higher marginal effect. Therefore, the company
should choose to buy an additional copier because although it cost twice as much as the worker
does, it produces five times as much
100,000 pages/2 copiers = 50,000 pages/copier50,000 pages/5 workers = 10,000
pages/workerIf a copier costs twice as much as a worker, then 50% of a copier's production is
equal in cost to the productionof one worker.50,000 pages * 0.50 = 25,000 pagesThe company
should buy another copier instead of hiring another employee because the copier is
moreproductive for its cost.
Q3 George's T-Shirt Shop produces 5,000 custom printed T-shirts per month. George's fixed costs are
$15,000 per month. The marginal cost per T-shirt is a constant $4. What is his break-even price? What
would be George's break-even price if he were to sell 50% more shirts?
The breakeven price is the average unit cost which equals
$15,000/5,000 + $4 = $7.
If George sold 50% more he would sell 7,500 units and the breakeven price would be $15,000/7,500 + $4
=$6.
FC + VC - PQ = 0, where FC - fixed costs, VC - variable costs, PQ - Volume of sales
15000 + 5000*4 - 5000*x = 0, x is break-even price
x = $7.
If sell will be increased on 50%, then
15000 + (5000+50%)*4 - (5000+50%)*x = 0
x = $6
Q4
Break-even price is the price that you must charge to at least break
even (make zero profit). It is equal to average avoidable cost per unit.
Break-even analysis:
2,000,000/100,000 = $20 per truck + $3 per truck = $23 per truck is the
break-even price per truck
Relevant costs - all costs that vary with the consequence of a decision.
Relevant costs = 2,000,000 (not $2.6 because the $2.5M paid for the
injection mold machine and the $100,000 in molds are sunk costs
irrelevant to the discussion as they have already incurred)
Quantity = 100,000
To make shutdown decisions, we work with break-even prices rather
than quantities. If you shut down, you lose your revenue, but you get
back your avoidable cost. If revenue is less than avoidable cost, or
equivalently, if price is less than average avoidable cost, then shut
down.
If the company can sell the truck for $23, they should stay open. If they
are unable to charge $23 per truck they should shut down.