Question

Neon Light Company of Kansas City ships lamps and lighting appliances throughout the country. Ms. Neon has determined that through the establishment of local collection centers around the country, she can speed up the collection of payments by three days. Furthermore, the cash management department of her bank has indicated to her that she can defer her payments on her accounts by one-half day without affecting suppliers. The bank has a remote disbursement center in Florida.

a. If Neon Light Company has \(2.25 million per day in collections and \)1.05 million per day in disbursements, how many dollars will the cash management system free up?

b. If Neon Light Company can earn 6 percent per annum on freed-up funds, how much will the income be?

c. If the total cost of the new system is $400,000, should it be implemented?

Short answer

The cash management has freed up $7,275,000.

Step-by-step solution

Information provided in question

Per day collections = $2.25 million

Per day disbursements = $1.05 million

Increase in collection time = 3 days

Reduction in disbursement time = 0.5 days

Money freed up by the cash management system.

The cash management system has freed up $7,275,000.

$\begin{array}{rcl}\mathit{C}\mathit{h}\mathit{a}\mathit{n}\mathit{g}\mathit{e}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{c}\mathit{o}\mathit{l}\mathit{l}\mathit{e}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}& \mathbf{=}& \mathit{P}\mathit{e}\mathit{r}\mathbf{}\mathit{d}\mathit{a}\mathit{y}\mathbf{}\mathit{c}\mathit{o}\mathit{l}\mathit{l}\mathit{e}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{\times }\mathit{R}\mathit{e}\mathit{d}\mathit{u}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{c}\mathit{o}\mathit{l}\mathit{l}\mathit{e}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{t}\mathit{i}\mathit{m}\mathit{e}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{250}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{3}\mathbf{}\mathit{d}\mathit{a}\mathit{y}\mathit{s}\\ & \mathbf{=}& \mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{750}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathit{C}\mathit{h}\mathit{a}\mathit{n}\mathit{g}\mathit{e}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{d}\mathit{i}\mathit{s}\mathit{b}\mathit{u}\mathit{r}\mathit{s}\mathit{e}\mathit{m}\mathit{e}\mathit{n}\mathit{t}& \mathbf{=}& \mathit{P}\mathit{e}\mathit{r}\mathbf{}\mathit{d}\mathit{a}\mathit{y}\mathbf{}\mathit{d}\mathit{i}\mathit{s}\mathit{b}\mathit{u}\mathit{r}\mathit{s}\mathit{e}\mathit{m}\mathit{e}\mathit{n}\mathit{t}\mathbf{\times }\mathit{I}\mathit{n}\mathit{c}\mathit{r}\mathit{e}\mathit{a}\mathit{s}\mathit{e}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{d}\mathit{i}\mathit{s}\mathit{b}\mathit{u}\mathit{r}\mathit{s}\mathit{e}\mathit{m}\mathit{e}\mathit{n}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{050}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{5}\mathbf{}\mathit{d}\mathit{a}\mathit{y}\mathit{s}\\ & \mathbf{=}& \mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{250}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{rcl}\mathit{F}\mathit{r}\mathit{e}\mathit{e}\mathit{d}\mathbf{}\mathit{u}\mathit{p}\mathbf{}\mathit{c}\mathit{a}\mathit{s}\mathit{h}& \mathbf{=}& \mathit{i}\mathit{n}\mathit{c}\mathit{r}\mathit{e}\mathit{a}\mathit{s}\mathit{e}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{c}\mathit{o}\mathit{l}\mathit{l}\mathit{e}\mathit{c}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{+}\mathit{D}\mathit{e}\mathit{l}\mathit{a}\mathit{y}\mathit{e}\mathit{d}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{d}\mathit{i}\mathit{s}\mathit{b}\mathit{u}\mathit{r}\mathit{s}\mathit{e}\mathit{m}\mathit{e}\mathit{n}\mathit{t}\\ & \mathbf{=}& \mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{750}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{525}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{7}\mathbf{,}\mathbf{275}\mathbf{,}\mathbf{000}\end{array}$