Last Updated on March 23, 2024 by Qusai Ahmad

Managerial accounting is the branch of accounting that deals with providing financial information and analysis to managers for planning, controlling, and evaluating the companyâ€™s operations and performance. Managerial accounting uses various formulas and equations to calculate and present the relevant data to managers. In this blog post, you will learn:

## The Categories and Purposes of Managerial Accounting Formulas

Managerial accounting formulas can be classified into four main categories, according to their purposes and functions:

**Cost accounting formulas**: Cost accounting formulas are used to determine and allocate the costs of the companyâ€™s products and services. Cost accounting formulas help managers to understand the profitability and efficiency of the companyâ€™s operations and to make decisions regarding pricing, production, and inventory management.**Budgeting formulas**: Budgeting formulas are used to prepare and approve a plan for the companyâ€™s revenues and expenses for a given period. Budgeting formulas help managers to set goals and expectations for the company and its departments and to monitor and control the actual performance against the budget.**Variance analysis formulas**: Variance analysis formulas are used to compare the actual results of the companyâ€™s operations with the budgeted or expected results and to identify and explain the causes and effects of the differences. Variance analysis formulas help managers to evaluate the performance and effectiveness of the company and its departments and to take corrective actions if needed.**Capital budgeting formulas**: Capital budgeting formulas are used to evaluate and select the long-term investments and projects that the company will undertake. Capital budgeting formulas help managers to allocate the companyâ€™s scarce resources to the most profitable and strategic opportunities and to measure the return on investment and the risk of each project.

## The Common and Useful Managerial Accounting Formulas and Equations

Here are some of the most common and useful managerial accounting formulas and equations that you should know and understand:

### Cost accounting formulas:

**Cost of goods sold (COGS) =**Beginning inventory + Purchases – Ending inventory**Contribution margin (CM) =**Sales – Variable costs**Contribution margin ratio (CMR) =**Contribution margin / Sales**Break-even point (BEP) in units =**Fixed costs / Contribution margin per unit**Break-even point (BEP) in sales =**Fixed costs / Contribution margin ratio**Margin of safety (MOS) in units**= Budgeted sales in units – Break-even sales in units**Margin of safety (MOS) in sales**= Budgeted sales in sales – Break-even sales in sales**Margin of safety ratio (MOSR) =**Margin of safety / Budgeted sales**Cost-volume-profit (CVP) analysis =**Sales – Variable costs – Fixed costs = Net income

### Budgeting formulas:

**Sales budget =**Expected sales units x Expected sales price per unit**Production budget =**Expected sales units + Desired ending inventory units – Beginning inventory units**Direct materials budget = (**Expected production units x Direct materials required per unit) + Desired ending direct materials units – Beginning direct materials units**Direct labor budget =**Expected production units x Direct labor hours required per unit x Direct labor rate per hour**Manufacturing overhead budget =**Variable manufacturing overhead rate per unit x Expected production units + Fixed manufacturing overhead**Selling and administrative expense budget =**Variable selling and administrative expense rate per unit x Expected sales units + Fixed selling and administrative expense**Cash budget =**Beginning cash balance + Cash receipts – Cash payments – Minimum cash balance required = Ending cash balance

### Variance analysis formulas:

**Material price variance (MPV) =**(Actual price – Standard price) x Actual quantity**Material quantity variance (MQV) =**(Actual quantity – Standard quantity) x Standard price**Labor rate variance (LRV) = (**Actual rate – Standard rate) x Actual hours**Labor efficiency variance (LEV) =**(Actual hours – Standard hours) x Standard rate**Variable overhead spending variance (VOSV) =**(Actual rate – Standard rate) x Actual hours**Variable overhead efficiency variance (VOEV) =**(Actual hours – Standard hours) x Standard rate**Fixed overhead budget variance (FOBV) =**Actual fixed overhead – Budgeted fixed overhead**Fixed overhead volume variance (FOVV) =**Budgeted fixed overhead – (Standard hours x Standard rate)

### Capital budgeting formulas:

**Net present value (NPV) =**Present value of cash inflows – Present value of cash outflows**Internal rate of return (IRR) =**The discount rate that makes the NPV of a project equal to zero**Payback period (PP) =**The number of years required to recover the initial investment of a project**Profitability index (PI) =**Present value of cash inflows / Present value of cash outflows

## The Examples and Applications of Managerial Accounting Formulas and Equations

To illustrate how managerial accounting formulas and equations can be used in practice, letâ€™s look at some numerical examples and applications:

### Cost accounting formulas:

- Suppose a company sells a product for $100 per unit and has the following costs:
- Beginning inventory: 500 units at $40 per unit
- Purchases: 2,000 units at $50 per unit
- Ending inventory: 300 units
- Variable costs: $20 per unit
- Fixed costs: $50,000
**The cost of goods sold for the company is:**- COGS = 500 x 40 + 2,000 x 50 – 300 x 50
- COGS = 20,000 + 100,000 – 15,000
- COGS = $105,000

**The contribution margin for the company is:**- CM = Sales – Variable costs
- CM = (2,200 – 300) x 100 – (2,200 – 300) x 20
- CM = 190,000 – 38,000
- CM = $152,000

**The contribution margin ratio for the company is:**- CMR = Contribution margin / Sales
- CMR = 152,000 / 190,000
- CMR = 0.8 or 80%

**The break-even point in units for the company is:**- BEP in units = Fixed costs / Contribution margin per unit
- BEP in units = 50,000 / (100 – 20)
- BEP in units = 50,000 / 80
- BEP in units = 625 units

**The break-even point in sales for the company is:**- BEP in sales = Fixed costs / Contribution margin ratio
- BEP in sales = 50,000 / 0.8
- BEP in sales = $62,500

**The margin of safety in units for the company is:**- MOS in units = Budgeted sales in units – Break-even sales in units
- MOS in units = 1,900 – 625
- MOS in units = 1,275 units

**The margin of safety in sales for the company is:**- MOS in sales = Budgeted sales in sales – Break-even sales in sales
- MOS in sales = 190,000 – 62,500
- MOS in sales = $127,500

**The margin of safety ratio for the company is:**- MOSR = Margin of safety / Budgeted sales
- MOSR = 127,500 / 190,000
- MOSR = 0.67 or 67%

**The net income for the company is:**- Net income = Sales – Variable costs – Fixed costs
- Net income = 190,000 – 38,000 – 50,000
- Net income = $102,000

### Budgeting formulas:

- Suppose a company has the following information for the next year:
- Expected sales units: 10,000
- Expected sales price per unit: $100
- Desired ending inventory units: 500
- Beginning inventory units: 300
- Direct materials required per unit: 2 kg
- Desired ending direct materials units: 1,000 kg
- Beginning direct materials units: 800 kg
- Direct labor hours required per unit: 0.5 hour
- Direct labor rate per hour: $20
- Variable manufacturing overhead rate per unit: $5
- Fixed manufacturing overhead: $30,000
- Variable selling and administrative expense rate per unit: $10
- Fixed selling and administrative expense: $40,000
- Minimum cash balance required: $10,000
- Beginning cash balance: $15,000
- Cash receipts: $120,000
- Cash payments: $100,000
**The sales budget for the company is:**- Sales budget = Expected sales units x Expected sales price per unit
- Sales budget = 10,000 x 100
- Sales budget = $1,000,000

**The production budget for the company is:**- Production budget = Expected sales units + Desired ending inventory units – Beginning inventory units
- Production budget = 10,000 + 500 – 300
- Production budget = 10,200 units

**The direct materials budget for the company is:**- Direct materials budget =
- (Expected production units x Direct materials required per unit) + Desired ending direct materials units – Beginning direct materials units – Direct materials budget = (10,200 x 2) + 1,000 – 800 – Direct materials budget = 20,400 + 1,000 – 800 – Direct materials budget = 20,600 kg

**The direct labor budget for the company is:**- Direct labor budget = Expected production units x Direct labor hours required per unit x Direct labor rate per hour
- Direct labor budget = 10,200 x 0.5 x 20
- Direct labor budget = 5,100 x 20
- Direct labor budget = $102,000

**The manufacturing overhead budget for the company is:**- Manufacturing overhead budget = Variable manufacturing overhead rate per unit x Expected production units + Fixed manufacturing overhead
- Manufacturing overhead budget = 5 x 10,200 + 30,000
- Manufacturing overhead budget = 51,000 + 30,000
- Manufacturing overhead budget = $81,000

**The selling and administrative expense budget for the company is:**- Selling and administrative expense budget = Variable selling and administrative expense rate per unit x Expected sales units + Fixed selling and administrative expense
- Selling and administrative expense budget = 10 x 10,000 + 40,000
- Selling and administrative expense budget = 100,000 + 40,000
- Selling and administrative expense budget = $140,000

**The cash budget for the company is:**- Cash budget = Beginning cash balance + Cash receipts – Cash payments – Minimum cash balance required = Ending cash balance
- Cash budget = 15,000 + 120,000 – 100,000 – 10,000 = Ending cash balance
- Cash budget = 25,000 = Ending cash balance

### Variance analysis formulas:

- Suppose a company has the following information for a month:
- Actual output: 8,000 units
- Actual price: $105 per unit
- Actual quantity: 16,000 kg
- Actual rate: $52 per kg
- Actual hours: 4,000 hours
- Actual rate: $22 per hour
- Actual fixed overhead: $35,000
- Standard output: 10,000 units
- Standard price: $100 per unit
- Standard quantity: 18,000 kg
- Standard price: $50 per kg
- Standard hours: 5,000 hours
- Standard rate: $20 per hour
- Budgeted fixed overhead: $30,000
**The material price variance for the company is:**- MPV = (Actual price – Standard price) x Actual quantity
- MPV = (52 – 50) x 16,000
- MPV = 2 x 16,000
- MPV = $32,000 unfavorable

**The material quantity variance for the company is:**- MQV = (Actual quantity – Standard quantity) x Standard price
- MQV = (16,000 – 18,000) x 50
- MQV = -2,000 x 50
- MQV = -$100,000 favorable

**The labor rate variance for the company is:**- LRV = (Actual rate – Standard rate) x Actual hours
- LRV = (22 – 20) x 4,000
- LRV = 2 x 4,000
- LRV = $8,000 unfavorable

**The labor efficiency variance for the company is:**- LEV = (Actual hours – Standard hours) x Standard rate
- LEV = (4,000 – 5,000) x 20
- LEV = -1,000 x 20
- LEV = -$20,000 favorable

**The variable overhead spending variance for the company is:**- VOSV = (Actual rate – Standard rate) x Actual hours
- VOSV = (22 – 20) x 4,000
- VOSV = 2 x 4,000
- VOSV = $8,000 unfavorable

**The variable overhead efficiency variance for the company is:**- VOEV = (Actual hours – Standard hours) x Standard rate
- VOEV = (4,000 – 5,000) x 20
- VOEV = -1,000 x 20
- VOEV = -$20,000 favorable

**The fixed overhead budget variance for the company is:**- FOBV = Actual fixed overhead – Budgeted fixed overhead
- FOBV = 35,000 – 30,000
- FOBV = $5,000 unfavorable

**The fixed overhead volume variance for the company is:**- FOVV = Budgeted fixed overhead – (Standard hours x Standard rate)
- FOVV = 30,000 – (5,000 x 20)
- FOVV = 30,000 – 100,000
- FOVV = -$70,000 favorable

### Capital budgeting formulas:

- Suppose a company has the following information for a project:
- Initial investment: $200,000
- Cash inflows: $50,000 for year 1, $60,000 for year 2, $70,000 for year 3, and $80,000 for year 4
- Discount rate: 10%
**The net present value for the project is:**- NPV = Present value of cash inflows – Present value of cash outflows
- NPV = (50,000 / 1.1) + (60,000 / 1.1^2) + (70,000 / 1.1^3) + (80,000 / 1.1^4) – 200,000
- NPV = 45,455 + 49,587 + 52,140 + 53,350 – 200,000
- NPV = $532

**The internal rate of return for the project is:**- IRR = The discount rate that makes the NPV of a project equal to zero
- IRR = 10.03% (using a financial calculator or an online tool)

**The payback period for the project is:**- PP = The number of years required to recover the initial investment of a project
- PP = 3.67 years (using a financial calculator or an online tool)

**The profitability index for the project is:**- PI = Present value of cash inflows / Present value of cash outflows
- PI = 200,532 / 200,000
- PI = 1.003

I hope you find these examples and applications helpful and interesting. Please let me know if you have any feedback or suggestions. Thank you for your time and attention. ðŸ˜Š