Question

Death By Chocolate sells its $4,000,000 accounts receivable to a bank for much needed cash at a 4% discount. The average collection period is two months. What is the effective annual rate that the bank is charging Death by Chocolate for the required cash?

a. 13.03%

b. 63.22%

c. 27.76%

d. 20.05%

e. 3.09%

Answer #1

Cash received by Death By Chocolate from bank = value of receivables discounted * (1 - discount rate)

Cash received by Death By Chocolate from bank = $4,000,000 * (1 - 4%)

Cash received by Death By Chocolate from bank = $3,840,000

Discount charged by bank = value of receivables discounted - Cash received by Death By Chocolate

Discount charged by bank = $4,000,000 - $3,840,000

Discount charged by bank = $160,000

From the perspective of Death By Chocolate, this is like borrowing $3,840,000 today to repay $4,000,000 after 2 months, thus paying interest of $160,000 for 2 months.

Interest rate charged for 2 months = $160,000 / $3,840,000 = 4.1667%

Effective annual rate = ((1 + periodic rate)number of periods) - 1

The number of 2-month periods in 1 year = 12 / 2 = 6

Effective annual rate = ((1 + 4.1667%)6) - 1

Effective annual rate = 27.76%

The answer is (c)

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