A material supplier offers a 3% discount for payment within 15 days on a $25,000 order. The contractor's cost of borrowing money is 8% annually. Should the contractor take the discount?
Correct Answer
A) Yes, the annualized discount rate exceeds the borrowing cost
The 3% discount for 15 days early payment equals an annualized rate of approximately 73% (3% × 365/15 days). This far exceeds the 8% borrowing cost, making it financially beneficial to take the discount even if borrowing is required.
Why This Is the Correct Answer
Option B is correct because the annualized discount rate of approximately 73% significantly exceeds the contractor's 8% borrowing cost. When a supplier offers early payment terms, you must calculate the annualized rate to compare it fairly against borrowing costs. The formula is (discount % ÷ discount period) × 365 days, which gives (3% ÷ 15) × 365 = 73%. Since 73% > 8%, taking the discount is financially advantageous even if the contractor must borrow money to pay early.
Why the Other Options Are Wrong
Option C: Yes, but only if cash flow permits
Option A incorrectly states that the cost of borrowing (8%) is less than the discount, but fails to recognize that the 3% discount must be annualized for proper comparison. The 3% is earned in just 15 days, making its annualized rate much higher than the 8% annual borrowing cost.
Option D: No, the cost of borrowing is less than the discount
Option D is partially correct about taking the discount but adds an unnecessary condition about cash flow. The financial analysis shows the discount should be taken even if borrowing is required, since the annualized discount rate (73%) far exceeds the borrowing cost (8%).
Memory Technique
Remember 'DAZE': Discount ÷ Days × 365 = Equivalent rate. If this rate beats your borrowing cost, take the discount in a daze (without hesitation).
Reference Hint
Business and Finance chapter covering time value of money, cash discounts, and cost of capital analysis
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