Question

Colter Steel has \(4,200,000 in assets.

Temporary current assets	\)1,000,000
Permanent current assets	\(2,000,000
Fixed assets	\)1,200,000
Total assets	\(4,200,000

Short-term rates are 8 percent. Long-term rates are 13 percent. Earnings before interest and taxes are \)996,000. The tax rate is 40 percent. If long-term financing is perfectly matched (synchronized) with long-term asset needs, and the same is true of short-term financing, what will earnings after taxes be? For a graphical example of perfectly matched plans, see Figure 6-5.

Short answer

The earnings after taxes will be $300,000.

Step-by-step solution

Information given in the question 

The following information is provided:

Long-term interest rates = 13%

Short-term interest rates =8%

Earnings before interest and taxes = $996,000

Tax rate = 40%

Calculation of long-term financing 

The long-term financing is $3,200,000.

$$\begin{gathered} \mathbf{Long}\mathbf{}\mathbf{term}\mathbf{}\mathbf{financing}\mathbf{}\mathbf{=}\mathbf{}\mathbf{Permanent}\mathbf{}\mathbf{}\mathbf{current}\mathbf{}\mathbf{asset}\mathbf{}\mathbf{}\mathbf{+}\mathbf{}\mathbf{Fixed}\mathbf{}\mathbf{asset} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{+}\mathbf{}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000} \end{gathered}$$

Calculation of short-term financing 

The short-term financing is $1,000,000. This is the amount of current temporary assets of the organization.

Calculation of interest expense 

The interest expense is $496,000.

$$\begin{gathered} \mathbf{Interest}\mathbf{}\mathbf{expense}\mathbf{}\mathbf{=}\mathbf{}\mathbf{Long}\mathbf{-}\mathbf{term}\mathbf{}\mathbf{interest}\mathbf{}\mathbf{expenses}\mathbf{}\mathbf{+} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{Short}\mathbf{-}\mathbf{term}\mathbf{}\mathbf{interest}\mathbf{}\mathbf{}\mathbf{expenses} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{13}\mathbf{\%}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{\%}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{416}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{+}\mathbf{\$}\mathbf{80}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{416}\mathbf{,}\mathbf{000} \end{gathered}$$

Calculation of earnings after taxes 

The earning after taxes is $300,000.

$$\begin{gathered} \mathbf{Earnings}\mathbf{}\mathbf{after}\mathbf{}\mathbf{taxes}\mathbf{}\mathbf{=}\mathbf{}\mathbf{Earnings}\mathbf{}\mathbf{before}\mathbf{}\mathbf{interest}\mathbf{}\mathbf{and}\mathbf{}\mathbf{taxes}\mathbf{} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{}\mathbf{Interest}\mathbf{}\mathbf{expenses} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{\$}\mathbf{996}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{-}\mathbf{}\mathbf{\$}\mathbf{496}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{-}\mathbf{}\mathbf{\$}\mathbf{200}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{\$}\mathbf{300}\mathbf{,}\mathbf{000}\mathbf{} \end{gathered}$$