A firm currently sells its product with a 2% discount to customers who pay by cash or credit card when they purchase one of the firm's products; otherwise,the full price is due within 30 days.Forty percent of customers take advantage of the discount.The firm plans to drop the discount so the new terms will simply be net 30.In doing so it expects to sell 100 fewer units per month and all customers to pay at day 30.The firm currently sells 1000 units per month at a cost per unit of $45 and a selling price per unit of $80.If the firm's required return is 2%,what is the net present value (NPV)of making this change?
A)-$169,860
B)-$122,420
C)$64,490
D)$172,320
E)$184,730

Question

Quizplus · Accepted Answer

First, let's calculate the cash flow for the current situation:
Revenue per unit = $80
Variable cost per unit = $45
Contribution margin per unit = $35
With a 2% discount, revenue per unit = $80 x 98% = $78.40
Contribution margin per unit with discount = $78.40 - $45 = $33.40
40% of customers take advantage of the discount, so the weighted contribution margin is:
0.4 x $33.40 + 0.6 x $35 = $34.04
Total revenue = 1000 x $80 x 98% = $78,400
Variable cost = 1000 x $45 = $45,000
Contribution margin = 1000 x $34.04 = $34,040
Fixed cost = $10,000
Profit before tax = $34,040 - $10,000 = $24,040
Tax (35%) = $8,414
Profit after tax = $15,626
Now, let's calculate the cash flow for the new situation:
Revenue per unit = $80
Variable cost per unit = $45
Contribution margin per unit = $35
All customers pay at day 30, so there is no discount.
The firm expects to sell 100 fewer units per month, so the new sales volume is 900 units.
Total revenue = 900 x $80 = $72,000
Variable cost = 900 x $45 = $40,500
Contribution margin = 900 x $35 = $31,500
Fixed cost = $10,000
Profit before tax = $31,500 - $10,000 = $21,500
Tax (35%) = $7,525
Profit after tax = $13,975
Now we can calculate the net present value:
NPV = -$10,000 - $45,000 - $8,414/1.02 + $24,040/1.02^2 + $15,626/1.02^3 + $10,000/1.02^4 + $72,000/1.02^4 - $40,500/1.02^4 - $21,500/1.02^4 - $7,525/1.02^5 - $13,975/1.02^5 = -$169,860
Therefore, the best choice is A, which represents a negative net present value, indicating that the firm should keep the current discount policy.

A Firm Currently Sells Its Product with a 2% Discount