Question

D&R Corp. has annual revenues of $250,000, an average contribution margin ratio of 35%, and fixed expenses of $118,200.

a. Management is considering adding a new product to the company's product line. The new item will have $8.8 of variable costs per unit. Calculate the selling price that will be required if this product is not to affect the average contribution margin ratio. (Round your answer to 2 decimal places.)

b. If the new product adds an additional $31,000 to D&R's fixed expenses, how many units of the new product must be sold at the price calculated in part a to break-even on the new product? (Do not round intermediate calculations.)

c. If 24,800 units of the new product could be sold at a price of $14.6 per unit, and the company's other business did not change, calculate D&R's total operating income and average contribution margin ratio. (Round your intermediate calculations to 2 decimal places. Round "Average contribution margin ratio" to 2 decimal places.)

Answer 1

a)

Let P be the price

Contribution margin ratio=(P-VC)/=(P-8.8)/P

We are given

Contribution margin ratio=35%=0.35

(P-8.8)/P=0.35

P-8.8=0.35P

0.65P=8.80

P=8.80/0.65=$13.54

b)

Additional Fixed Cost=FC=$31000

We have derived in part (a) that

P=8.80/0.65 (We are not considering direct value of price as no rounding is allowed for intermediate calculations)

BEP=(FC/CM Ratio)/Price=(31000/.35)/(8.8/.65)=6542.21 or say 6543

c)

Initial Contribution margin=CM₁=250000*35%=$87500

Initial Operating income=OI_i=CM₁-Fixed expanses=87500-118200=-$30700

Contribution margin due to new product=CM₂=(P-VC)*Q=(14.6-8.8)*24800=$143840

Addition to operating income due to new product=OI_a=CM₂-Additional Fixed cost=143840-31000=$112840

Additional Revenue due to new product=P*Q=14.6*24800=362080

Total Revenue=R=250000+362080=$612080

Total Contribution Margin=CM₁+CM₂=87500+143840=$231340

New operating income=OIi+OIa=-30700+112840=$82140

New CM Ratio=(CM1+CM2)/.R=231340/612080=37.80%