Capital Budgeting – Numerical Problems for Practice
The "Big Question" (15 Marks) in exams usually involves calculating NPV for a 5-year project.
The Problem
Question: XYZ Ltd plans to set up a plant.
- Initial Investment: ₹ 1,00,000.
- Life: 5 Years.
- Scrap Value: ₹ 10,000.
- Annual Sales: ₹ 80,000.
- Annual Variable Cost: ₹ 30,000.
- Fixed Cost: ₹ 10,000 (excluding Depreciation).
- Tax Rate: 30%.
- Cost of Capital (k): 10%.
- Calculate NPV.
The Solution
Step 1: Calculate Annual Cash Flow (CFAT)
Calculation of Annual Cash Inflow
| A. Sales Revenue | 80,000 |
| Add: B. Less: Variable Cost | (30,000) |
| Add: C. Less: Fixed Cost | (10,000) |
| D. Cash Profit Before Tax (EBITDA) | 40,000 |
| Add: E. Less: Depreciation (Cost-Scrap)/5 | (18,000) |
| Add: F. Profit Before Tax (PBT) | 22,000 |
| Add: G. Less: Tax @ 30% | (6,600) |
| Add: H. Profit After Tax (PAT) | 15,400 |
| Add: I. Add Back Depreciation | + 18,000 |
| Add: J. Annual Cash Inflow (CFAT) | 33,400 |
Step 2: Calculate PV of Inflows
- Annuity Factor for 10% for 5 years =
3.791. - PV of Operating Inflows = 33,400 * 3.791 = 1,26,619.
- PV of Scrap Value (Received at end of Year 5):
- Value = 10,000.
- PV Factor (Year 5) = 0.621.
- PV = 10,000 * 0.621 = 6,210.
- Total PV of Inflows = 1,26,619 + 6,210 = 1,32,829.
Step 3: Calculate NPV
NPV = PV Inflows - Initial InvestmentNPV = 1,32,829 - 1,00,000- Answer: NPV = + ₹ 32,829. (Accept the project).
Exam Notes: Common Mistakes
- Depreciation: Students forget to add back depreciation at the end. Remember: Tax is calculated after depreciation, but Cash Flow includes depreciation.
- Scrap Value: Often forgotten. It is an inflow in the last year. Discount it using the single year factor, not annuity factor.
- Working Capital: If Working Capital is introduced at start, it is an Outflow. It is usually recovered at the end (Inflow).
Quiz Time! 🎯
Test Your Knowledge
Question 1 of 4
1. To calculate Operating Cash Flow from PAT, we must: