Finance and Accounting Problem Solving Guide

This article provides a structured template for solving common accounting and finance problems involving budgeting, interest calculations, direct labor costs, overhead rates, and cash flows.

1. Cash Budgeting

Calculate the ending cash balance or required borrowing based on beginning balance, collections, and disbursements:

Formula:

\[ \text{Ending Cash Balance} = \text{Beginning Cash Balance} + \text{Collections} - \text{Disbursements} \]

If the ending cash balance is less than the minimum required cash balance, calculate the borrowing amount:

Required Borrowing (rounded to nearest increment):

\[ \text{Required Borrowing} = \text{Minimum Required Cash Balance} - \text{Ending Cash Balance} \]

Example:

Let’s say the beginning balance is $B$, collections are $C$, and disbursements are $D$ with a required minimum cash balance of $M$. The required borrowing will be:

\[ \text{Required Borrowing} = \max(0, M - (B + C - D)) \]

2. Interest Calculation

For calculating the total interest due on a borrowed amount over a period of months:

Monthly Interest Calculation:

\[ \text{Interest} = \text{Principal} \times \text{Interest Rate} \times \text{Number of Months} \]

Example:

Suppose $P$ is the principal amount borrowed, $r$ is the monthly interest rate, and $n$ is the duration in months. The interest is:

\[ \text{Interest} = P \times r \times n \]

3. Direct Labor Cost Calculation

To determine the direct labor rate per hour or total cost:

Formula:

\[ \text{Total Labor Cost} = \text{Direct Labor Hours} \times \text{Labor Rate per Hour} \]

To find the hourly labor rate if given the total labor cost and hours:

\[ \text{Labor Rate per Hour} = \frac{\text{Total Labor Cost}}{\text{Total Labor Hours}} \]

Example:

Given $T$ as the total labor cost and $H$ as the total hours worked, the labor rate per hour is:

\[ \text{Labor Rate per Hour} = \frac{T}{H} \]

4. Overhead Rate Calculation

For predetermined overhead rates based on total budgeted overhead (fixed and variable) and direct labor hours:

Formula:

\[ \text{Predetermined Overhead Rate} = \frac{\text{Total Overhead}}{\text{Total Direct Labor Hours}} \]

Example:

Suppose the variable overhead rate is $v$, total labor hours are $H$, and fixed overhead is $F$. Then:

\[ \text{Total Overhead} = (v \times H) + F \]

\[ \text{Predetermined Overhead Rate} = \frac{(v \times H) + F}{H} \]

5. LaTeX Examples

Here are some useful LaTeX expressions to help with formatting:

• **Basic Math**: \( a + b = c \)
• **Fractions**: \( \frac{a}{b} \)
• **Summations**: \( \sum_{i=1}^n i \)
• **Products**: \( \prod_{i=1}^n i \)
• **Square Roots**: \( \sqrt{x} \)
• **Exponents**: \( x^n \)

Using these formulas, you can approach each type of accounting problem with a consistent method. Modify the variables as needed for each scenario, and apply these principles to solve similar questions.