Break Even Point saat Initial Investment sudah terbayar kembali

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Derivation of the Break-Even Point (BEP) Formula

The Break-Even Point (BEP) is the level of sales where Total Revenue (TR) equals Total Cost (TC), meaning profit is zero.

Step 1: Define Key Equations

1. Total Revenue (TR)

   $$TR=\text{Selling Price per Unit}\times \text{Quantity Sold | TR = P × Q}$$

   Where:

   • $P$ = Price per unit
   • $Q$ = Quantity sold (break-even quantity)

2. Total Cost (TC)

   $$TC=\text{Fixed Costs}+\text{Variable Costs | TC = FC + (VC × Q)}$$

   Where:

   • $FC$ = Fixed Costs (rent, salaries, insurance, etc.)
   • $VC$ = Variable Cost per unit

Step 2: Set Revenue Equal to Total Cost at Break-Even

$$P \times Q = FC + (VC \times Q)$$

Step 3: Solve for Break-Even Quantity ($Q$)

Rearrange the equation:

$$P \times Q - VC \times Q = FC$$

Factor out $Q$:

$$Q \times (P - VC) = FC$$ $$Q = \frac{FC}{P - VC}$$

Final Break-Even Point Formula

$$Q_{BEP} = \frac{FC}{P - VC}$$

Interpretation:

• $P - VC$ is called the Contribution Margin per Unit.
• The break-even point is the number of units that must be sold to cover all fixed and variable costs.

ANALYSIS

Ketika sudah beberapa waktu Perusahaan menghasilkan keuntungan, akumulasi keuntungan bisa diperbandingkan dengan investasi awal dengan PayBack Period

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The Payback Period is the time it takes for an investment to generate enough cash flows to recover its initial cost. It is a simple method used to evaluate investment decisions by determining how quickly an investor can expect to break even.

Formula for Payback Period:

$$\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflows}}$$

Example Calculation:

If a project requires an initial investment of $50,000 and generates annual cash inflows of $10,000, the payback period would be:

$$\frac{50,000}{10,000} = 5 \text{ years}$$

Advantages:

✔️ Simple and easy to understand
✔️ Useful for assessing liquidity and risk
✔️ Helps compare multiple investment options

Disadvantages:

❌ Ignores the time value of money (does not consider discounted cash flows)
❌ Ignores cash flows beyond the payback period
❌ May not consider overall project profitability

For a more accurate evaluation, methods like Net Present Value (NPV) or Internal Rate of Return (IRR) should be used alongside the payback period.

Hal sama bisa juga digambarkan dan atau dianalogikan sebagai berikut:

Initial Investment = Accumulated Cash Inflows x Payback Period

Fixed Cost = Accumulated Cash Inflow x Certain time Accumulated Period

Jadi bisa dikatakan Fixed Cost dianggap sudah "0" atau sudah tercover secara Full Amount of Fixed Asset

Total Cost = Fixed Cost + Variable Cost

Fixed Cost sudah "0" aka sudah tercover 

Total Cost =         0          + Variable Cost

 Total Cost = Variable Cost

Melompat ke rumus Profit  disadur kembali dr ChatGPT:

$$\text{Profit }=(\text{Price per Unit }\times \text{Quantity Sold})-[\text{Fixed Costs }+(\text{Cost per Unit }\times \text{Quantity Produced})]$$

Break-Even Poin terjadi saat Profit mencapai titik impas yaitu bernilai 0

Dan dr pembahasan diatas, Fixed Cost jg diasumsikan "sudah" 0

Sehingga:

Profit = (Price per Unit × Quantity Sold) − [Fixed Costs + (Cost per Unit × Quantity Produced)]

   0   = (Price per Unit × Quantity Sold) − [         0        + (Cost per Unit × Quantity Produced)]

   0   = (Price per Unit × Quantity Sold) −  (Cost per Unit × Quantity Produced)

(Price per Unit × Quantity Sold) =  (Cost per Unit × Quantity Produced)

Break Even Point jg terjadi saat Quantity Sold ~ aka | sama dengan ~ Quantity Produced  

Jadi saat terjadi BEP adalah (setelah mengignore Fixed Cost):

Price per Unit =  Cost per Unit atau Variable Cost 

Dalam hal ini karena Cost per Unit hanya berunsur Variable Cost 

Jadi untuk menentukan Harga Jual utk mencapai Break Even sudah hanya memperhitungkan Biaya Variabel