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?

b. Without prejudice to your part a answer, assume the annual discount rate is 4%. What is the present value of the annual cost of Prime Bank’s services in perpetuity?

c. What is the present value of the daily processing fee in perpetuity?

d. What is the net present value of the proposed service? Should your company use the service?

e. What would be the net present value of the proposed service if the annual fee were to grow at a 2% rate -- the annual discount rate is still 4% from part b? Should your company use the service?

Answer 1

Answer (a):

Given:

Current cost of money is = .011% per day

Effective annual rate = (1 + .011%)^365-1 = 4.096% or 4.10%

Discount rate you should use to discount annual fees = 4.10%

Answer (b):

Present value of the annual cost of Prime Bank’s services in perpetuity = Perpetual annual fees / Annual Discount %

= 27500 / 4%

= $687,500

Present value of the annual cost of Prime Bank’s services in perpetuity = $687,500

Answer (c):

Present value of the daily processing fee in perpetuity = Perpetual daily processing fee / Daily discount rate

= 39.60 / 0.011%

= $360,000

Present value of the daily processing fee in perpetuity = $360,000

Answer (d):

Net present value of the proposed service = $1,138,500 - (687500 + 360000) = $91,000

Net present value of the proposed service = $91,000

Yes,

Your company should use the service. NPV is positive.

Answer (e):

Net present value of the proposed service if the annual fee were to grow at a 2% rate:

Given that annual processing fee is to be paid at the year:

NPV = 1138500 - 27500 / (4%-2%) - 360000

= - $596500

OR

($596,500)

Your company should not use the service as net present value is negative.