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Corporation is considering the credit application of a customer. The customer
is expected to buy $5000 worth of material from James every month in future,
and pay for it within a month. There is a 20% probability that the customer may
default on his monthly payment. If that happens, then James will not be able to
recover anything from the customer. The cost of capital to James is 12%. The
cost of goods to James is 80% of its sales. Find the following:

(A) The value of this customer to James.
(B) Decide if he should get credit.
A. Sales $5,000 COGS=0.8*5000=$4000 Gross profit=5000-4000=$1000 Cost of capital (monthly)=12%/12=1% Prob of default=20% Prob of no default=80% Gross profit 1000 Rate 12%/12=1% Prob of no default 80% 0 1 2 3 4 5 6 7 8 9 10 11 12 800 800 800 800 800 800 800 800 800 800 800 800 PV of payments 792.0792 784.2368 776.4721 768.7843 761.1726 753.6362 746.1744 738.7866 731.4719 724.2296 717.059 709.9594 Sum of PV of payments 9004.06 Calculate the gross profit=Sales-COGS 5000-0.8*5000=1000 Probability of no default is (100%-20%)*gross…

profit which is 800 throughout from month 1 to month 12 Find the PV of payments using the formula PV=FV/(1+rate)^n; for the second month the formula gives 800/(1.01)^2=$784.24 Sum up the present values to get the value as $9004.06 The value of customer to james is $9004.06 B. Yes he should be given credit as theactual value is less than the sum of PV.


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