# Aje Corporation Project AnalysisThis analysis covers- Calculation of **Optimistic** and **Pessimistic** NPV - **Accounting Break-even Point** - **Financial Break-even Point** --- ## 1. **Data Summary** | Item | Base Value | Optimistic | Pessimistic | |-------------------------------|---------------|------------|-------------| | Initial Investment | Rs. 30,000 | | | | Cost of Capital | 10% | | | | Quantity Sold (units/year) | 1,400 | 1,800 | 800 | | Price per Unit | Rs. 30 | Rs. 50 | Rs. 20 | | Variable Cost per Unit | Rs. 20 | Rs. 15 | Rs. 40 | | Fixed Costs (per year) | Rs. 3,000 | | | | Depreciation (per year) | Rs. 2,000 | | | | Tax Rate | 50% | | | | Project Life | 5 years | | | | Salvage Value | Nil | | | --- ## 2. **NPV Calculation Structure** ### **Steps for Each Scenario** 1. **Sales Revenue = Quantity × Price** 2. **Variable Costs = Quantity × Variable Cost per Unit** 3. **Total Costs = Variable Costs + Fixed Costs + Depreciation** 4. **EBIT = Sales Revenue – Variable Costs – Fixed Costs – Depreciation** 5. **EBT = EBIT** 6. **Tax = EBT × Tax Rate** 7. **PAT = EBT – Tax** 8. **Add Depreciation (non-cash expense) to PAT to get Annual Cash Flow** 9. **NPV = Sum of Present Value of Cash Flows (discounted at 10%) – Initial Investment** --- ### **A. Pessimistic Case** #### **Calculate Annual Cash Flow** - Quantity = 800 - Price = Rs. 20 - Variable Cost = Rs. 40 **1. Sales Revenue:** \( 800 \times 20 = Rs. 16,000 \) **2. Variable Costs:** \( 800 \times 40 = Rs. 32,000 \) **3. Fixed Costs:** Rs. 3,000 **4. Depreciation:** Rs. 2,000 **5. EBIT:** \( 16,000 - 32,000 - 3,000 - 2,000 = -Rs. 21,000 \) **6. EBT:** \(-Rs. 21,000\) **7. Tax (savings):** Tax shield on loss: \( 21,000 \times 50\% = Rs. 10,500 \) (since loss, this is tax saving) **8. PAT:** \(-21,000 + 10,500 = -Rs. 10,500\) **9. Add Depreciation:** \(-10,500 + 2,000 = -Rs. 8,500\) (annual cash outflow) #### **Calculate NPV** - Cash flow each year = **\(-8,500\)** - Discount rate = 10% - 5 years **Present Value of Annuity Factor (PVAF, 10%, 5 years):** \[ PVAF = \frac{1 - (1 + r)^{-n}}{r} = \frac{1 - (1+.1)^{-5}}{.1} \approx 3.7908 \] \[ \text{NPV} = (-8,500) \times 3.7908 - 30,000 = -32,221.8 - 30,000 = -Rs. 62,221.8 \] --- ### **B. Optimistic Case** #### **Calculate Annual Cash Flow** - Quantity = 1,800 - Price = Rs. 50 - Variable Cost = Rs. 15 **1. Sales Revenue:** \( 1,800 \times 50 = Rs. 90,000 \) **2. Variable Costs:** \( 1,800 \times 15 = Rs. 27,000 \) **3. Fixed Costs:** Rs. 3,000 **4. Depreciation:** Rs. 2,000 **5. EBIT:** \( 90,000 - 27,000 - 3,000 - 2,000 = Rs. 58,000 \) **6. EBT:** Rs. 58,000 **7. Tax:** \( 58,000 \times 50\% = Rs. 29,000 \) **8. PAT:** \( 58,000 - 29,000 = Rs. 29,000 \) **9. Add Depreciation:** \( 29,000 + 2,000 = Rs. 31,000 \) (annual cash inflow) #### **Calculate NPV** \[ \text{NPV} = 31,000 \times 3.7908 - 30,000 = 117,514.8 - 30,000 = Rs. 87,514.8 \] --- ## 3. **Break-Even Points** ### **A. Accounting Break-Even Point** Set **EBIT = ** (no profit, no loss before tax). \[ \text{Sales} - \text{Total Variable Cost} - \text{Fixed Cost} - \text{Depreciation} = \] Let \( Q \) = break-even quantity, \( P \) = price per unit, \( V \) = variable cost per unit \[ Q(P - V) = \text{Fixed Cost} + \text{Depreciation} \] Given: \( P = 30 \), \( V = 20 \), Fixed Cost = 3,000, Depreciation = 2,000 \[ Q = \frac{3,000 + 2,000}{30 - 20} = \frac{5,000}{10} = 500 \text{ units} \] --- ### **B. Financial Break-Even Point** Set **NPV = ** (find annual cash flow required for NPV = ). Let \( C \) = annual cash flow required. \[ NPV = C \times PVAF(10\%, 5) - 30,000 = \] \[ C = \frac{30,000}{3.7908} \approx Rs. 7,918.6 \] This is the **post-tax annual cash flow** required. #### **Find Corresponding Quantity** Annual cash flow = \( (Q \times (P - V) - \text{Fixed Cost}) \times (1 - t) + \text{Depreciation} \times t \) Let \( Q \) = financial break-even quantity. - \( t = .5 \), \( P - V = 10 \), Fixed = 3,000, Depreciation = 2,000 \[ \text{After-tax OCF} = [Q \times 10 - 3,000] \times .5 + 1,000 \] Set equal to required cash flow: \[ .5(Q \times 10 - 3,000) + 1,000 = 7,918.6 \] \[ .5(Q \times 10 - 3,000) = 6,918.6 \] \[ Q \times 10 - 3,000 = 13,837.2 \] \[ Q \times 10 = 16,837.2 \] \[ Q = 1,683.72 \text{ units} \] --- ## **Summary Table** | Scenario | NPV (Rs.) | Break-even Quantity (units) | |------------------|-------------|-----------------------------| | Pessimistic | \(-62,221.8\) | | | Optimistic | \(87,514.8\) | | | Accounting BEP | | 500 | | Financial BEP | | 1,684 (rounded) | --- ## **Conclusion** - **NPV can swing widely depending on scenario**: - *Pessimistic*: Large negative NPV - *Optimistic*: Large positive NPV - **Accounting Break-even**: 500 units - **Financial Break-even**: ~1,684 units (rounded) --- ### **Image: Break-even Chart**  *Alt text: Break-even chart showing total costs and revenues, with accounting and financial break-even quantities marked.* --- If you need further breakdowns or a sensitivity table, let me know!