Question

A company sells two products: a standard model and a deluxe model. The standard model sells for $50 and has a contribution margin ratio of 40%. The deluxe model sells for $100 and has a contribution margin ratio of 50%. Last year, the company sold 5000 standard units and 2500 deluxe units.

There is $200,000 of cost that is “fixed” in the sense that it does not vary with the number of units produced. However, $100,000 of this cost is Direct Fixed Costs that are allocated between products as 80% to the deluxe product, while 20% is allocated to the standard model. The remaining $100,000 is Allocated Fixed Costs that are allocated equally between the two products.

1. In the space below, complete the following segmented income statement to calculate profit by product-line and for the overall company.

Standard          Deluxe                  Total___   

Sales

VariableCost_____________________________________________________________

Contribution Margin   

Direct Fixed Costs________________________________________________________

Segment Margin

Allocated Fixed Costs_____________________________________________________   

Pre-Tax Profit

2. If the sales mix stays the same as last year, how many standard and deluxe units would have to be sold next year in order to earn $42,000 after taxes of 40%?

3. If the sales mix stays the same as last year, what sales from standard and deluxe models would have to be in order to earn $42,000 after taxes of 40%?

4. Assume that the company decided to eliminate the deluxe model with the hope of increasing their profit by $5,000. Once again, they were disappointed to find that their expected results did not materialize. In the space below, compute the effect on profit of eliminating the deluxe model and briefly explain the flaw in the company’s plan.

Answer 1

Particulars	Standard	Deluxe	Total
Sales	250000	250000	500000
Variable Costs*	150000	125000	275000
Contribution Margin(Sales-VC)	100000	125000	225000
Direct Fixed Costs(DFC)	20000	80000	100000
Segment Margin(Contribution-DFC)	80000	45000	125000
Allocated Fixed Costs(50%of 100000 each)	50000	50000	100000
Pre-tax Profit(Segment Margin - Allocated Fixed Cost)	30000	(5000)	25000

* Variable Cost = Sales*(1-Contribution Margin)

2. The company had a total pre-tax profit of $25000. Out of which, if the tax of 40% is deducted i.e. $10,000. The after-tax profit will be $15,000. The company sold a total of 7500 units(Standard:5000 + Deluxe:2500) for a profit of $15000. Therefore, after-tax profit per unit is $2 per unit. So for a profit of $42,000 it needs to sell 21000(42000/2) units. The current sales mix of standard and deluxe units is 5000:2500 i.e. 2:1. Therefore, the company needs to sell,

Standard units = 2*21000/3 = 14000

Deluxe units = 21000 - Standard = 7000 units

3. Sales value of Standard units = $50*14000 = $7,00,000

Sales value of Deluxe units = $100*7000 = $7,00,000

4.

Particulars	Total (when Deluxe is produced)	Total(When Deluxe is not produced)
Sales	500000	250000
Variable Cost	275000	150000
Contribution Margin	22500
	00	100000
Segment Margin	125000	0
Allocated Fixed Cost	100000	100000
Pre-tax Profit	25000	(100000)

The company missed out that the net profit from sale of deluxe units turned negative after accounting the allocated fixed cost and had a positive contribution and segment margin. When it stopped producing Deluxe units, all fixed costs were attributed to Standard units leading to a loss of $1,00,000. Had it continued running production of Deluxe units, the segment might have turned profitable in the long run with increase in efficiency but shutting down its production deprived it of the profit of $25000.