Your firm has an average receipt size of $130. A bank has approached you concern
ID: 2647119 • Letter: Y
Question
Your firm has an average receipt size of $130. A bank has approached you concerning a lockbox service that will decrease your total collection time by two days. You typically receive 6,000 checks per day. The daily interest rate is 0.018 percent. The bank charges a lockbox fee of $185 per day.
What would the net annual savings be if the service were adopted? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Your firm has an average receipt size of $130. A bank has approached you concerning a lockbox service that will decrease your total collection time by two days. You typically receive 6,000 checks per day. The daily interest rate is 0.018 percent. The bank charges a lockbox fee of $185 per day.
Explanation / Answer
Part a)
To calculate the NPV, we first need to calculate the present value of savings and cost. The value of savings can be calculated with the use of average receipt, number of checks per day and time saved (in number of days). The formula that can be derived for calculating savings is:
Savings = Number of Checks Per Day*Average Value of Receipt*Number of Days Saved
Present value of cost will inolve the use of lockbox fee per day and daily interest rate. The formula for calculcating present value of cost would be:
Present Value of Cost = Lockbox Fee Per Day/Daily Interest Rate
NPV = Savings - Present Value of Cost
_________________
Using the information provided in the question, we get,
Savings = 6000*130*2 = $1,560,000
Present Value of Cost = $185/.018% = $1,027,777.78
_______
NPV = $1,560,000 - $1,027,777.78 = $532,222.22
__________________
Part b)
Net annual savings would be calculated with the use of annual savings and annual cost. The formula for calculating annual savings and annual cost can be derived as follows:
Annual Savings = Savings*(1+Daily Interest Rate)^n - Savings where n is period
Annual Cost = Lockbox Fee*FVIFA(n,Interest Rate) where n is period and FVIFA is the future value interest factor for an annuity
Net Annual Savings = Annual Savings - Annual Cost
___________
Using the values calculated in part a) and information provided in the question, we get,
Annual Savings = 1,560,000*(1+.018%)^365 - 1,560,000 = $105,923.97
Annual Cost = 185*FVIFA(365,.018%) = $69,786.09 (FVIFA value can be calculated with the use of a Financial Calculator)
_______
Net Annual Savings = $105,923.97 - $69,786.09 = $36,137.88
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.