Question

Cast Iron Company, on each nondelinquent sale, receives revenues with a present value of $1,280 and incurs costs with a value of $1,040. Cast Iron has been asked to extend credit to a new customer. You can find little information on the firm but you believe that the probability of payment is no better than .78 and that there will be a repeat order in one year if payment occurs.

If the discount rate is 17%, calculate the minimum probability of payment on the repeat order at which credit can be extended. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Also, 81.25 is NOT correct

Answer 1

Let's say you extend the credit to Cast Iron company for the first time.

The expected payoff ( during the extension of credit for the first time), considering the probability of payment as 0.78 ,is given by:

p*PV(Revenue-cost) - (1-p)*PV(costs incurred)

Here, p= probability of payment =0.78

PV=present value

Hence, expected payoff for the first year is 0.78*(1280-1040) - ( 1-0.78)*(1040) = -41.6$

Hence, for the first payment the payoff expected is negative.

However, if the probability of the second payment is good enough, the credit can be extended.

But this time, the present value of the payment should be at least greater than $41.6, in order to offset the loss from the first credit. Hence:

p*PV(Revenue-cost) - (1-p)*PV(costs incurred) = 41.6

Here, p= required probability of re-payment

p*(1280-1040) - (1-p)*(1040)=41.6

240p-1040+1040p=41.6

1280p=1081.6

This gives p=0.845

Hence, the minimum probability of payment on the repeat order at which credit can be extended is 0.845 or 84.50%