Question

Prime Bank is offering your company the use of their cash collection service. They estimate that by speeding up your access to cash you can receive benefits with a present value of $1,138,500. The current cost of money is .011% per day. Prime Bank will charge your firm an annual fee of $27,500 (paid at the end of each year) plus a $39.60 processing fee (paid daily). Required: Assume a 365-day year. a. What discount rate should you use to discount the $27,500 annual fee

Answer 1

Given Information:

Current cost of money = r = 0.011% per day

Period = n = 365 days

Required Information:

Discount rate = ?

Answer:

Discount rate = 4.096%

Explanation:

The required annual discount rate to discount the annual fee is given by

$Discount \: rate = (1 + r)^{n}-1$

Where r is the current cost of money and n is the period in days

Current cost of money = r = 0.011/100 = 0.00011

$Discount \: rate = (1 + 0.00011)^{365}-1\\Discount \: rate = 0.04096\\Discount \: rate = 4.096 \%$

Therefore, 4.096% is the required annual discount rate to discount the annual fee of $27,500.