NET PRESENT VALUE (NPV) AND DISCOUNTED CASH FLOW (DCF)

1. What is Net Present Value (NPV)? 
Net Present Value (NPV) measures the profitability of an investment by comparing the present value of cash inflows to the initial investment cost. 
- If NPV > 0 → The investment is profitable. 
- If NPV < 0 → The investment will result in a loss. 
- If NPV = 0 → The investment will break even (no profit, no loss). 

➡️ NPV accounts for the time value of money, meaning that money received today is more valuable than the same amount received in the future due to inflation and opportunity cost. 

Formula: 
PV = CFt / (1 + r)^t 

Where: 
- PV = Present Value 
- CFt = Cash Flow in year t 
- r = Discount Rate (reflects the uncertainty and cost of capital) 
- t = Time period (in years) 

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2. Example: Should You Buy a Lawnmower? 

You are considering buying a lawnmower for your landscaping business: 
- Initial Cost = $2,000 
- Expected Annual Cash Flow = $1,000 
- Discount Rate = 10% 
- Duration = 5 years 

Step 1: Calculate Present Value for Each Year 

PV (Year 1) = 1000 / (1 + 0.10)^1 = 909.09 
PV (Year 2) = 1000 / (1 + 0.10)^2 = 826.45 
PV (Year 3) = 1000 / (1 + 0.10)^3 = 751.31 
PV (Year 4) = 1000 / (1 + 0.10)^4 = 683.01 
PV (Year 5) = 1000 / (1 + 0.10)^5 = 620.92 

Step 2: Total Present Value of Cash Flows 
Total PV = 909.09 + 826.45 + 751.31 + 683.01 + 620.92 
Total PV = 3,790.79 

Step 3: Net Present Value (NPV) 
NPV = Total PV - Initial Investment 
NPV = 3,790.79 - 2,000 = 1,790.79 

➡️ Since NPV > 0, the investment is profitable. ✅ 

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3. Example: Cable Business Investment 

You are considering investing in a new cable production machine: 
- Initial Cost = $100,000 
- Expected Annual Profit = $25,000 
- Discount Rate = 8% 
- Duration = 5 years 

Step 1: Present Value of Each Cash Flow 

PV (Year 1) = 25,000 / (1 + 0.08)^1 = 23,148.15 
PV (Year 2) = 25,000 / (1 + 0.08)^2 = 21,437.18 
PV (Year 3) = 25,000 / (1 + 0.08)^3 = 19,842.76 
PV (Year 4) = 25,000 / (1 + 0.08)^4 = 18,370.15 
PV (Year 5) = 25,000 / (1 + 0.08)^5 = 17,013.11 

Step 2: Total Present Value of Cash Flows 
Total PV = 23,148.15 + 21,437.18 + 19,842.76 + 18,370.15 + 17,013.11 
Total PV = 99,811.35 

Step 3: Net Present Value (NPV) 
NPV = 99,811.35 - 100,000 
NPV = -188.65 

➡️ Since NPV < 0, the investment is NOT profitable. ❌ 

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4. Why NPV and DCF Matter 
- Helps compare projects with different cash flow patterns. 
- Accounts for the time value of money. 
- Useful for capital budgeting and investment decisions. 

✅ Example: If you have multiple project options, NPV helps identify which project provides the highest return. 
✅ Example: If cash flows are uncertain, adjusting the discount rate can reflect that risk. 

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5. Common Mistakes to Avoid 
❌ Ignoring the discount rate → Leads to overestimating future cash flows. 
❌ Using the wrong discount rate → Higher rates reflect higher risk and uncertainty. 
❌ Ig