Chapter 17, Problem 6P

a.

Summary Introduction

To determine: The net pre-tax benefits if annual sales are $15 million.

Answer to Problem 6P

The net pre-tax benefits if annual sales are $15 million is $8,630.14.

Explanation of Solution

Determine the annual pre-tax earnings

$\begin{array}{c}Annual\mathrm{Pr}etaxEarnings=\left[\begin{array}{l}AverageDailyCollection\times InterestRate\times \\ \mathrm{Re}ductioninCollectionTime\end{array}\right]\\ =\left[\left(\frac{\$15,000,000}{\$365}\right)\times 7\%\times 3\right]\\ =\$8,630.14\end{array}$

Therefore, the amount of funds released is $8,630.14.

Determine the additional collection costs

$\begin{array}{c}AdditionalCollectionCosts=\left[\begin{array}{l}VariableCosts\times TotalCollectionCenters\times \\ TotalWorkingDays\end{array}\right]\\ =\left[\left(\$10-\$0.50\right)\times 6\times 250\right]\\ =\$14,250\end{array}$

Therefore, the additional collection costs is $14,250.

Determine the net pre-tax benefits

$\begin{array}{c}Net\mathrm{Pr}etaxBenefits=\left[Annual\mathrm{Pr}etaxEarnings-AdditionalCollectionCosts\right]\\ =\left[\$8,630.14-\$14,250\right]\\ =-\$5,619.86\end{array}$

Therefore, the net pre-tax benefits is -$5,619.86.

b.

Summary Introduction

To determine: The net pre-tax benefits if annual sales are $75 million.

Answer to Problem 6P

The net pre-tax benefits if annual sales are $75 million is $28,900.68.

Explanation of Solution

Determine the net pre-tax benefits

$\begin{array}{c}Net\mathrm{Pr}etaxBenefits=\left[Annual\mathrm{Pr}etaxEarnings-AdditionalCollectionCosts\right]\\ =\left[\left(\left(\frac{\$75,000,000}{\$365}\right)\times 7\%\times 3\right)-\left(\left(\$10-\$0.50\right)\times 6\times 250\right)\right]\\ =\left[\$43,150.68-\$14,250\right]\\ =\$28,900.68\end{array}$

Therefore, the net pre-tax benefits is -$28,900.68.

c.

Summary Introduction

To determine: The net pre-tax benefits if annual sales are $15 million with 2 days of collection time.

Answer to Problem 6P

The net pre-tax benefits if annual sales are $15 million is $2,753.42.

Explanation of Solution

Determine the net pre-tax benefits

$\begin{array}{c}Net\mathrm{Pr}etaxBenefits=\left[Annual\mathrm{Pr}etaxEarnings-AdditionalCollectionCosts\right]\\ =\left[\left(\left(\frac{\$15,000,000}{\$365}\right)\times 7\%\times 2\right)-\left(\left(\$2.50-\$0.50\right)\times 6\times 250\right)\right]\\ =\left[\$5,753.42-\$3,000\right]\\ =\$2,753.42\end{array}$

Therefore, the net pre-tax benefits is $2,753.42.

d.

Summary Introduction

To determine: The net pre-tax benefits if annual sales are $75 million with 2 days of collection time.

Answer to Problem 6P

The net pre-tax benefits if annual sales are $75 million is $25,767.12.

Explanation of Solution

Determine the net pre-tax benefits

$\begin{array}{c}Net\mathrm{Pr}etaxBenefits=\left[Annual\mathrm{Pr}etaxEarnings-AdditionalCollectionCosts\right]\\ =\left[\left(\left(\frac{\$75,000,000}{\$365}\right)\times 7\%\times 2\right)-\left(\left(\$2.50-\$0.50\right)\times 6\times 250\right)\right]\\ =\left[\$28,767.12-\$3,000\right]\\ =\$25,767.12\end{array}$

Therefore, the net pre-tax benefits is $25,767.12.