Chapter 17, Problem 3P

a.

Summary Introduction

To determine: The amount of funds released.

Answer to Problem 3P

The amount of funds released is $2,465,753.42.

Explanation of Solution

Determine the reduction in collection time

$\begin{array}{c}\mathrm{Re}ductioninCollectionTime=\left[\begin{array}{l}\mathrm{Re}ductioninMailingTime+\\ \mathrm{Re}ductionin\mathrm{Pr}oces\sin gTime\end{array}\right]\\ =\left[\left(3-1.5\right)+\left(6-2.5\right)\right]\\ =5days\end{array}$

Therefore, the reduction in collection time is 5 days.

Determine the average daily collection

$\begin{array}{c}AverageDailyCollection=\left[\frac{AnnualCreditSales}{365}\right]\\ =\left[\frac{\$180,000,000}{365}\right]\\ =\$493,150.68\end{array}$

Therefore, the average daily collection is $493,150.68.

Determine the amount of funds released

$\begin{array}{c}AmountofFunds\mathrm{Re}leased=\left[\begin{array}{l}AverageDailyCollection\times \mathrm{Re}ductionin\\ CollectionTime\end{array}\right]\\ =\left[\$493,150.68\times 5\right]\\ =\$2,465,753.42\end{array}$

Therefore, the amount of funds released is $2,465,753.42.

b.

Summary Introduction

To determine: The annual earnings on the released funds.

Answer to Problem 3P

The annual earnings on the released funds is $2,465,753.42.

Explanation of Solution

Determine the annual earnings on the released funds

$\begin{array}{c}AnnualEarnings=\left[AmountofFunds\mathrm{Re}leased\times InterestRate\right]\\ =\left[\$2,465,753.42\times 10\%\right]\\ =\$246,575.34\end{array}$

Therefore, the annual earnings on the released funds is $246,575.34.

c.

Summary Introduction

To determine: The annual fee.

Answer to Problem 3P

The annual fee is $315,000.

Explanation of Solution

Determine the annual fee

$\begin{array}{c}AnnualFee=\left[FixedCost+VariableCost\right]\\ =\left[\$75,000+\left(\$0.05\times 4,800,000\right)\right]\\ =\$315,000\end{array}$

Therefore, the annual fee is $315,000.

d.

Summary Introduction

To determine: The annual net benefits.

Answer to Problem 3P

The annual net benefits are -$18,424.66.

Explanation of Solution

Determine the annual net benefits

$\begin{array}{c}AnnualNetBenefits=\left[AnnualEarnings+DecreaseinPayment-AnnualFee\right]\\ =\left[\$246,575.34+\$50,000-\$315,000\right]\\ =-\$18,424.66\end{array}$

Therefore, the annual net benefits are -$18,424.66.

e.

Summary Introduction

To determine: The annual net benefits.

Answer to Problem 3P

The annual net benefits are $121,917.95.

Explanation of Solution

Determine the amount of funds released

$\begin{array}{c}AmountofFunds\mathrm{Re}leased=\left[\begin{array}{l}AverageDailyCollection\times \mathrm{Re}ductionin\\ CollectionTime-BankCompensatingBalance\end{array}\right]\\ =\left[\$493,150.68\times 4.5-\$1,500,000\right]\\ =\$719,179.50\end{array}$

Therefore, the amount of funds released is $2,465,753.42.

Determine the annual net benefits

$\begin{array}{c}AnnualNetBenefits=\left[\begin{array}{l}AmountofFunds\mathrm{Re}leased\times InterestRate-\\ ReductioninPayment\end{array}\right]\\ =\left[\left(\$719,179.50\times 10\%\right)+\$50,000\right]\\ =\$121,917.95\end{array}$

Therefore, the annual net benefits are $121,917.95.

f.

Summary Introduction

To discuss: The lockbox system the firm should select.

Answer to Problem 3P

The lockbox system the firm should select is SLC bank’s lockbox system.

Explanation of Solution

Since SLC’s bank provides a higher net benefits for the firm, the lockbox system that the firm should select is SLC bank’s lockbox system.