Question

Creative Genius (CG) sells science kits for children for $35 and has been doing very well for the last three years. The Vice President of Sales has asked the Credit Manager to review the company’s policies with regards to extending credit. You are given the following information: Currently, CG uses terms of net 30, and the Collections manager indicates that the uncollectible estimate is 4%. The interest rate per month is 1% and the present value of the costs of production are $21. Required:

1. Creative Genius wants to know if it should be extending credit to one-time orders?

2. What is the break-even probability of collections?

3. If Mad Scientist, a new customer, wants to place recurring monthly orders, and their credit check determines that they are not a default risk, should credit be extended?

4. What is the break-even probability of collections for Mad Scientist?

please show all work and formulas!

the break-even probability of collections for Mad Scientist?

Answer 1

Selling Price = $35

Uncollectible estimate = 4%

Sales collection = $35*(1-4%) = $33.6

Net 30 means, this amount is recovered at T = 30 = 1month

Interest rate = 1% per month

Present value of sales collection = $33.6/(1+1%)^1 = $33.27

Present value of costs = $21

1. Present value of profit = $33.27 - $21 = $12.27, since the project is profitable (ie present value > 0), it can increase its credit period

2 Let Break even probability of collection = p

Selling Price = $35

Sales collection = $35*p

Net 30 means, this amount is recovered at T = 30 = 1month

Interest rate = 1% per month

Present value of sales collection = $35p/(1+1%)^1 = $34.65p

Present value of costs = $21

Break even probability means

Present value of sales collection = present value of cost

$34.65p = $21

p = 0.606 = 60.6%

Means company can absorb uncollectable sales of upto (100 - 60.6) = 39.4%

3. Exisiting present value of profit = $12.27 (part1)

Mad scientist

Selling Price = $35

Uncollectible estimate = 0%

Sales collection = $35*(1-0%) = $35

Collection period for Mad scientist = T months (assume)

Interest rate = 1% per month

Present value of sales collection = $35/(1+1%)^t

Present value of costs = $21

Profit = 35/(1+1%)^t - 21

12.27 = 35/(1+1%)^t - 21

33.27 = 35/(1+1%)^t

1.01^t = 1.05199

t = ln(1.05199)/ln(1.01) = 5.1

Hence, credit period of Net 5.1 months can be extended to Mad Scientist

4. Mad scientist

Selling Price = $35

Break even probability = p

Sales collection = $35*p

Collection period for Mad scientist = 5.1 months

Interest rate = 1% per month

Present value of sales collection = $35p/(1+1%)^5.1 = $33.27p

Present value of costs = $21

Break even point

Profit = $33.27p - $21 = 0

p = 0.6312 = 63.12% (break even probability for Mad scientist)