Question

In Problem 12, assume the term structure of interest rates becomes inverted, with short-term rates going to 11 percent and long-term rates 5 percentage points lower than short-term rates. If all other factors in the problem remain unchanged, what will earnings after taxes be?

Short answer

The earnings after taxes will be $416,400

Step-by-step solution

Information given in the question 

The following information is provided:

Long-term interest rates = 6%

Short-term interest rates =11%

Earnings before interest and taxes = $996,000

Tax rate = 40%

Calculation of interest expense 

The interest expense is $302,000.

$$\begin{gathered} \mathbf{Interest}\mathbf{}\mathbf{}\mathbf{expenses}\mathbf{}\mathbf{=}\mathbf{}\mathbf{Long}\mathbf{-}\mathbf{term}\mathbf{}\mathbf{interest}\mathbf{}\mathbf{expense}\mathbf{}\mathbf{+}\mathbf{}\mathbf{Short} \\ \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{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{}\mathbf{=}\mathbf{(}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{6}\mathbf{\%}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{11}\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{192}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{+}\mathbf{}\mathbf{\$}\mathbf{110}\mathbf{,}\mathbf{00} \\ \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{302}\mathbf{,}\mathbf{000}\mathbf{} \end{gathered}$$

Calculation of earnings after taxes 

The earning after taxes is $416,400.

$$\begin{gathered} \mathbf{Earnings}\mathbf{}\mathbf{after}\mathbf{}\mathbf{taxes}\mathbf{}\mathbf{=}\mathbf{}\mathbf{Earnings}\mathbf{}\mathbf{before}\mathbf{}\mathbf{interest}\mathbf{}\mathbf{and}\mathbf{}\mathbf{taxes}\mathbf{} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{-}\mathbf{}\mathbf{Interest}\mathbf{}\mathbf{expenses}\mathbf{-}\mathbf{Taxes} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{996}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{302}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{277}\mathbf{,}\mathbf{600} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{416}\mathbf{,}\mathbf{400} \end{gathered}$$