Question

Consider the case of the Cast Iron Company. On each nondelinquent sale, Cast Iron receives revenues with a present value of $1,300 and incurs costs with a present value of $1,000. Cast Iron’s costs have increased from $1,000 to $1,150. Assuming that there is no possibility of repeat orders and that the probability of successful collection from the customer is p = 0.96, answer the following. a-1. What is the expected profit of granting credit? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.) a-2. Should Cast Iron grant or refuse credit? Grant Refuse b. What is the break-even probability of collection? (Enter your answer as a percent rounded to 1 decimal place.)

Answer 1

a)

Calculate profit of granting credit

profit= $1,300-$1,000

= $300

Calculate profit of granting credit if cost increases from $1,000 to $1,150

profit= $1,300-$1,150

= $150

a-2)

Calculate the probability of successful collection if the costs have increased to $1,150 with the probability of 96%

Loss (if unsuccessful)= $0-$1,150

= -$1,150

Expected profit= $150*0.96+(-$1,150)*0.04 =$144 - $46

= $98

The expected profit shows a value greater than zero. Hence, the Cast Iron should grant the credit.

b)

Calculate the break-even probability of collection:

Profit (if success)*(p)-Loss (if unsuccessful)*(1-p)

$150p-1150*(1-p)

150p-$1,150+1,150p=0

1,300p=$1,150

p= $1,150/$1,300

= 88.5%

Hence, 88.5% is the probability to break-even the collection.

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