Question

# Death By Chocolate sells its \$4,000,000 accounts receivable to a bank for much needed cash at...

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%

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%