Locust Software sells computer training packages to its business customers at a

Question

Locust Software sells computer training packages to its business customers at a price of $104. The cost of production (in present value terms) is $96. Locust sells its packages on terms of net 30 and estimates that about 9% of all orders will be uncollectible. An order comes in for 20 units. The interest rate is 1.3% per month.

a-1. Should the firm extend credit if this is a one-time order?

Yes

No

a-2. Calculate the profit or loss if the sale will not be made unless credit is extended. (Do not round intermediate calculations. Round your answer to 2 decimal places Enter the value answer as a positive number.)

b. What is the break-even probability of collection? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

c-1. Now suppose that if the customer pays this month's bill, they will place an identical order in each month indefinitely and can be safely assumed to pose no risk of default.Calculate the present value of the sale. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c-2. Should credit be extended?

Yes

No

d. What is the break-even probability of collection in the repeat-sales case? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.)

Explanation / Answer

PV(COST) = 96

PV(REV) = 104/1.01 = 102.97

a.The expected profit from a sale is: .93(102.97– 96) – .07(96) = 6.48-6.72=-0.24

The firm should not extend credit.

b.At the break-even probability, expected profit equals zero:

(102.97 – 96) – (1 – p)(96) = 0

Which implies that p = 1.

So if the firm is to break even, 100% of its customers must pay their bills.

c.A paying customer now represents perpetuity of profits of 102.97 – 96 = 6.97 per month.

The present value is 6.97/.01 = 697

So the present value of a sale, given a 7% default rate, is

.93(697) – .07(96) = 648.21-6.72=641.49

It clearly pays to extend credit.

d.p(697) – (1 – p)96 = 0

697p – 96 = 0

p = .137 =13.77%.

So the probability of payment needs to be greater than only 13.77% to justify extending credit.

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