Your firm has an average receipt size of $170. A bank has approached you concern
ID: 2777137 • Letter: Y
Question
Your firm has an average receipt size of $170. A bank has approached you concerning a lockbox service that will decrease your total collection time by one day. You typically receive 5,500 checks per day. The daily interest rate is .017 percent. The bank charges a lockbox fee of $130 per day.
NPV = 170294.12
**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 answer to 2 decimal places, e.g., 32.16.)**
**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 answer to 2 decimal places, e.g., 32.16.)**
Explanation / Answer
Total receipt size per day= average receipt size*5,500 checks per day=170*5500= $935000
Interest that is lost by bank per day=Total receipt size per day* daily interest rate=935000 * .017%=$158.95
lockbox fee = $130 per day
Total cost per day=158.95+130 =$288.95 per day
Total Savings per day be S, thus cash flow per day=S-288.95 =A
NPV= Present value of cash Flows/day for 365 days.
T=365,r=.017%,A=S-288.95
NPV=A*(1-1/(1+r)T)*(1/r)
170294.12=A*(1-1/(1.00017)365)*(1/.00017)
(170294.12*.00017)/(1-1/(1.00017)365)=A
=>A=(170294.12*.00017)/(1-1/(1.00017)365)
=> A=1.742
=>S-288.95=1.742 =>S=288.95+1.742 =290.692
The Savings per day is $290.692 therefore the total net annual savings =365*Savings per day=365*290.692 = 106102.58
Thus total net annual savings for the year is $106102.58.
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