Question

A company is considering a lockbox system that will reduce the collection time by 2 days on average. The company can earn an APR of 3.82% compounded daily on any cash balance. The average number of daily payments submitted to the lockbox is 1,969 with an average cheque size of $71. If the processing fee per cheque is $0.01, what is the NPV of adopting this lockbox? (Assume 365 days in one year.)

Question 2 options:

$91,461

$93,747

$96,034

$98,320

$100,607

Answer 1

Computation of Daily Collection Amount

No.of Cheques received = 1969

Cheque Amount = $ 71

Daily Collection = No.of Cheques received * Cheque Amount

= 1969 * $ 71

= $ 139799

Computation of Present value of the lockbox service

Present value of lockbox service = Average Daily Collection * No. of days float reduced

= $ 139799*2

= $ 279598

We can save $ 279598due to implementation of lock box system

Computation of Present value of Cost

No.of Cheques proceesed in a day = 1969

Processing fees per Cheque = $ 0.01

Hence Processing fees in a day = 1969* $ 0.01

= $ 19.69

Given Interest rate = 3.82% Compounded daily

Interest rate per day = 3.82% /365

= 0.010466%

Hence Present value of Cost in perpetuity = Daily Cost / Effective Daily interest rate

= $ 19.69/ 0.010466%

= $ 188133

Hence Present value of Cost of Lockbox system is $ 188133.

Computation of NPV

NPV of lockbox system = Present value of savings - Present value of lockbox system

= $ 279598-$ 188133

= $ 91465

NPV = $ 91465 Approximaately is close to $ 91461 due to rounding off decimals.Hence option 1) $ 91461 is the Correct answer.