Question

Lancaster Lumber buys $8 million of materials (net of discounts) on terms of 3/5, net 30; and it currently pays on the 5^th day and takes discounts. Lancaster plans to expand, which will require additional financing. Assume 365 days in year for your calculations.

1. If Lancaster decides to forgo discounts, how much additional credit could it obtain? Write out your answer completely. For example, 5 million should be entered as 5,000,000. Round your answer to the nearest cent.
   $
2. 
   
3. What would be the nominal cost of that credit? Do not round intermediate calculations. Round your answer to two decimal places.
   %
4. 
   
5. What would be the effective cost of that credit? Do not round intermediate calculations. Round your answer to two decimal places.
   %
6. 
   
7. If the company could get the funds from a bank at a rate of 12%, interest paid monthly, based on a 365-day year, what would be the effective cost of the bank loan? Do not round intermediate calculations. Round your answer to two decimal places.
   %
8. Should Lancaster use bank debt or additional trade credit?

Answer 1

a). Additional Credit = Purchases * [(Total Period - Discount Period) / 365]

= $8,000,000 * [(30 - 5) / 365] = $8,000,000 * 0.0685 = $547,945.21

b). Nominal Cost of Trade Credit = [Discount% / (1 - Discount%)] * [365 / (Total Period - Discount Period)]

= [0.03 / (1 - 0.03)] * [365 / (30 - 5)]

= 0.0309 * 14.6 = 0.4515, or 45.15%

c). Effective Cost of Trade Credit = [1 + {Discount% / (1 - Discount%)}]^{[365 / (Total Period - Discount Period)]} - 1

= [1 + {0.03 / (1 - 0.03)}]^{[365 / (30 - 5)]} - 1

= [1 + 0.0309]^14.6 - 1 = 1.5600 - 1 = 0.5600, or 56.00%

d). EAR = [1 + (APR/m)]^m - 1; m = no. of compounding periods in a year

= [1 + (0.012/12)]¹² - 1 = 1.1268 - 1 = 0.1268, or 12.68%

e). Because the effective cost of the bank loan is less than half the effective cost of the trade credit, the bank loan should be used.