Question

The Silver Spokes Bicycle Shop has decided to offer credit to its customers during the spring selling season. Sales are expected to be 700 bicycles. Silver Spokes will receive revenues with a present value of $1000 for each bicycle and will incur costs with a present value of $650 for each bicycle.

a. What is the break-even probability of collection? What is the break-even probability of default? Draw the credit decision tree.

b. If the Silver Spokes Bicycle Shop offers terms of 2/10, net 60. What effective annual interest rate does the shop earn when a customer does not take the discount? Each bicycle sells for $1000.

c. If a customer can borrow money against their line of credit at an interest rate of 12% per annum compounded monthly, what should the customer do?

Answer 1

a	Sr. No	Particulars	Nos/Amt
	1	Bicycles	700
	2	Revenues per cycle	$1,000
	3	Costs per cycle	$650
	4=2-3	Profit per cycle	$350
	5=1*2	Revenue Assuming 100% collection	$700,000
	6=3*1	Total Costs irrespective of collection	$455,000
	7=5-6	Margin	$245,000
	8=1-(7/2)	Break even units	455
	9=8/1	Break even Probability of collection (p)	0.65
	10=1(no)-9	Break even Probability of default (1-p)	0.35
	If expected collection > 65% exercise the option else not
b		Considering companies cost of capital is not given we assume company will save on 2% for 50 (60 days - 10 days) days of credit, which would annualise to 2%*365/50 = 14.6%
c		Considering the effective interest rate benefit for exercising the discount option is 14.6% p.a , if the effective cost of borrowing is lesser than the benefit customer should taked the terms of discount
		In the current case customer can borrow at 12% p.a monthly compounded, ie 12.68% p.a (1% per month*12 periods). Customer should accept the discount proposal