Key Financial Metrics and Cost Accounting Methods for Business
Payback Period (PP)
The time it takes for an initial investment to be repaid from the net cash inflows of a project.
Characteristics
- Does not consider the time value of money.
- Ignores cash flows that occur after the investment has been repaid.
Formula: Year Before Full Repayment + (Unpaid Amount / Net Cash Flow in Repayment Year)
Interpretation: “I will have to wait X years to recuperate the initial investment.”
Accounting Rate of Return (ARR)
Expresses the average accounting operating profit an investment will generate as a percentage of the average investment made over the project’s life.
Characteristics
- Does not consider the time value of money.
- Based on profit, not actual cash flow.
- Does not account for risk.
Formula: Average Annual Operating Profit / Average Investment
Interpretation: “On average, for each euro invested, we are getting a return of X cents in the form of operating income after depreciation.”
Net Present Value (NPV)
The primary objective is to maximize profits. NPV is considered one of the most important investment appraisal techniques.
Characteristics
- Pros: Considers the time value of money and applies the principle of additivity.
- Assumptions: Assumes a flat yield curve and that the reinvestment rate of positive cash flows is equal to the discount rate.
Interpretation: “The implementation of this investment will create an additional value of X euros for the company and its shareholders.”
Decision Rule
- NPV > 0: Accept the project.
- NPV = 0: Indifferent to the project.
- NPV < 0: Reject the project.
If projects are mutually exclusive, the one that provides the highest positive NPV should be selected.
Internal Rate of Return (IRR)
The discount rate at which the Net Present Value (NPV) of all cash flows from a project equals zero. It represents the maximum cost of capital a company can have for a project to be acceptable.
Characteristics
Unlike NPV, IRR does not apply the principle of additivity. It can also yield multiple or no conclusive answers with non-conventional cash flows.
Decision Rule
- IRR > r (Cost of Capital): Accept the project.
- IRR < r (Cost of Capital): Reject the project.
For mutually exclusive projects, the one with the highest IRR should generally be chosen, but this can sometimes conflict with the NPV rule.
Profitability Index (PI)
Measures the benefit per unit of cost, calculated as the ratio of the present value of future cash flows to the initial investment.
Formula: Present Value of Future Cash Flows / |Initial Investment|
- Present Value of Future Cash Flows (PVofFCF): The sum of the discounted cash flows from year 1 onwards.
- Initial Investment: The initial outlay in Year 0.
Interpretation: “For each monetary unit invested, the project is expected to return X units in present value terms.”
Discounted Payback Period (DPP)
The length of time it takes for the initial investment to be repaid from the discounted net cash flows of a project. This method accounts for the time value of money.
Calculation Steps
- Calculate the Discount Factor (DF) for each period: DF = 1 / (1 + r)^t
- Calculate the Discounted Net Cash Flow (DNCF) for each period: DNCF = Cash Flow x DF
- Calculate the Accumulated Discounted Cash Flow (ADCF) by summing the DNCF period by period.
- Use a table to track the ADCF and apply the formula.
Formula: Year Before Full Repayment + (|Accumulated Discounted Cash Flow Before Repayment| / Discounted Cash Flow in Repayment Year)
Present Value (PV) and Future Value (FV)
The formulas for Present Value and Future Value are reciprocal. The first formula represents simple annual compounding, while the second is for compounding multiple times within a period.
- m
- Number of compounding periods per year.
- t or n
- Number of years.
- r
- Annual interest rate.
Financial vs. Managerial Accounting
Financial Accounting
Communicates economic information to individuals and organizations external to the company’s direct operations. It is the process of recording, summarizing, and reporting the multitude of transactions resulting from business operations over a period of time.
Managerial Accounting
A method of accounting that creates statements and reports to help internal managers make better decisions to improve business performance.
Fundamental Cost Concepts
Definition of Cost
Generally, the price paid or resources sacrificed to achieve a specific objective. Costs are measured and used for specific purposes, and the intended use defines how they should be computed. Managerial accountants use various systems and classifications to prepare cost information.
GAAP Definition
GAAP defines cost as the monetary value of goods and services expended to achieve current or future benefits. Expenses are the costs of goods and services that have expired or been consumed.
Product Costs (Overheads)
These are indirect costs associated with production. Examples include:
- Indirect materials
- Indirect labor
- Maintenance and repair
- Supplies
- Utilities
- Depreciation (loss of an asset’s value over time)
- Salaries (of non-production staff)
- Occupancy costs (rent)
- Other fixed costs
Cost Classifications
- By Nature: Materials, labor, etc.
- By Function: Production, sales, administration, etc.
- By Traceability: Direct or indirect.
- By Variability: Fixed or variable.
- By Controllability: Controllable or uncontrollable.
- By Occurrence: Normal or abnormal.
Cost-Volume-Profit (CVP) Analysis
An analysis of how a firm’s income and profitability depend on its cost structure, sales volume, and pricing.
Break-Even Point (BEP)
The point at which total sales revenue exactly covers total costs (both fixed and variable). The company does not make a profit but also does not incur a loss (Return on Sales = 0). This analysis typically excludes financing costs like interest.
BEP Formulas
- BEP in Units: BEP = Fixed Costs / (Price per unit – Variable Cost per unit)
- Sales for a Target Profit: Sales in Units = (Fixed Costs + Target Profit) / (Price per unit – Variable Cost per unit)
- Price to Achieve Target Profit: Total Revenue (TR) = Total Costs (TC) + Target Profit (TP), where TR = Price × Units and TC = (Variable Cost × Units) + Fixed Costs.
Interpretation: “The company will need to sell X units to break even.”
Break-Even Point for Multiple Products
Calculation Steps
- Determine the Product Mix: Establish the sales ratio of products (e.g., for every 3 units of A, 1 unit of B is sold).
- Calculate Contribution per Unit (CPU): For each product, CPU = Price – Variable Cost.
- Calculate Weighted-Average CPU: Multiply each product’s CPU by its proportion in the sales mix and sum the results.
- Identify Total Fixed Costs.
- Calculate BEP in “Mix” Units: BEP (Mix) = Total Fixed Costs / Weighted-Average CPU.
- Calculate BEP per Product: Multiply the BEP (Mix) result by each product’s ratio in the sales mix.
- Verification: Check if Total Revenue equals Total Costs at the calculated break-even sales levels.
Margin of Safety
The extent to which the current or projected volume of sales lies above the break-even point. It indicates how much sales can decline before the company starts incurring a loss.
Formulas
- In Monetary Terms: MS = Total Sales Revenue – Break-Even Sales Revenue
- In Percentage: MS % = (Total Sales Revenue – Break-Even Sales Revenue) / Total Sales Revenue
- In Unit Terms: MS = Total Sales in Units – Break-Even Sales in Units
- In Percentage: MS % = (Total Sales in Units – Break-Even Sales in Units) / Total Sales in Units
Related Formulas
- Net Income = Total Revenue – Total Costs
- Gross Margin = Sales Revenue – Variable Costs
- Sales Revenue = Price × Units Sold
- Contribution Margin = Gross Margin – Fixed Costs
Opportunity Cost and Production Decisions
Definition of Opportunity Cost
The sacrifice made when a resource is used for one purpose instead of its next-best alternative. Opportunity costs are implicit costs that do not appear in accounting records but are crucial for decision-making.
Example: Maximizing Profit with Limited Resources
To determine the optimal product combination for the highest profit when resources (e.g., machine hours) are limited:
- Calculate the Contribution per Unit (CPU) for each product: CPU = Price – Variable Cost.
- Determine the Contribution per Unit of the Limiting Resource (e.g., Contribution per Machine Hour) for each product.
- Rank the products from highest to lowest based on the Contribution per Unit of the Limiting Resource.
- Allocate the limited resource to the products according to their rank, starting with the highest-ranked product, until the resource is fully utilized or demand is met.
- Calculate the total contribution margin from the optimal product mix to find the maximum profit.
Full Costing (Absorption Costing)
A costing method that calculates the total amount of resources sacrificed to achieve an objective. From a business perspective, it includes all costs related to making a product or providing a service. To derive the full cost, all cost elements are accumulated and then assigned to the specific product or service.
Direct vs. Indirect Costs
Direct Costs
Costs that can be specifically and exclusively identified with a particular cost object (e.g., a product or job). Examples include raw materials, direct labor, and other variable costs directly connected to production.
Indirect Costs (Overheads)
All other cost elements that cannot be directly measured or traced to a specific cost unit. These are costs of resources acquired to be used by more than one cost object.
Formula
Full Cost = Total Direct Costs + Total Indirect Costs
Note: When determining a recommended price for a job, it is essential to first define and calculate all direct costs (materials, labor) and allocate a portion of the indirect costs.
Activity-Based Costing (ABC)
In traditional full costing, direct costs are charged to a product, and overheads are allocated from a single cost pool, often using a simple basis like machine hours. In contrast, ABC identifies that overheads are caused by various activities. Therefore, the cost units that drive those activities must be charged with the costs they cause.
Methodology
Under ABC, an overhead cost pool is established for each significant activity. A specific cost driver for that activity is then identified to allocate the costs more accurately.
Example: Comparing Full Costing and ABC
Given indirect costs, production weeks, units, and machine hours, we need to determine the overhead cost per unit using both methods.
A) Traditional Full Costing (Based on Machine Hours)
- Calculate the predetermined overhead rate: Rate = Total Indirect Costs / Total Machine Hours.
- Calculate machine hours per unit for each product: Hours per Unit = Total Machine Hours for Product / Total Units of Product.
- Calculate the indirect cost per unit for each product: Indirect Cost per Unit = Rate × Hours per Unit.
B) Activity-Based Costing
- Create cost pools for different activities (e.g., machine setup, quality inspection).
- Identify a cost driver for each pool (e.g., number of setups, number of inspections).
- Calculate an allocation rate for each activity pool: Rate = Total Cost in Pool / Total Cost Driver Volume.
- Allocate costs to products based on their consumption of each activity’s cost driver.