Question

cash flows are end-of-period unless otherwise specified.

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.

1. What discount rate should you use to discount the $27,500 annual fee?

2. 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?

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

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

5. 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 :

given discount rate 0.011% daily

Year has 365 days

Annual Fees =$27,500

Annual Fees is paid at the end of the year

Discount rate used to discounts $27,500 annual Fees :

dicounr rate =0.011%*365=4.015%

So discount rate of 4.015% should you use to discount the $27,500 annual fee

The present value of the annual cost of Prime Bank’s services in perpetuity at 4% annual discount rate is :

=$27,500/4%

=$687,500

So the present value of the annual cost of Prime Bank’s services in perpetuity at 4% annual discount rate is $687,500

The present value of the daily processing fee in perpetuity:

processing fees paid daily=$39.60

daily disount rate =0.011%

Present value =$39.60/0.011%=$360,000

So the present value of the daily processing fee in perpetuity is $360,000

The net present value of the proposed service :

=Cash Inflows(Present benefits received)-Cash Out Flows(Present value of annual fees+Present value of Processing fees)

=$1,138,500-$687,500-$360,000

=$1,138,500-$1,047,500

=$91,000

So the net present value of the proposed service is $91,000(positive).Company should use the service

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

The present value of the annual cost =$27,500/(4%-2%)=$27,500/2%=$1,375,000

net present value of the proposed service:

=Cash Inflows(Present benefits received)-Cash Out Flows(Present value of annual fees+Present value of Processing fees)

=$1,138,500-$1,375,000-$360,000

=$1,138,500-$1,735,000

= -$596,500

So the net present value of the proposed service is -$596,500(negative).Company should not use the service