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Let's solve the problem step by step:

### Problem Breakdown:
1. **Inputs**:
   - Cost of capital = 10%
   - Projects A and B have an investment of ₹2,00,000 each.
   - Cash inflows for 5 years are provided for both projects.
   
2. **Tasks**:
   - Compute **Net Present Value (NPV)** at 10% for both projects.
   - Compute **Internal Rate of Return (IRR)** for both projects.
   - Evaluate IRR when the discount rate is 10% and 15%.

---

### Formulas:
1. **Net Present Value (NPV)**:
   \[
   NPV = \sum \frac{\text{Cash Inflow}_t}{(1 + r)^t} - \text{Initial Investment}
   \]
   where \( r \) is the discount rate, and \( t \) is the year.

2. **Internal Rate of Return (IRR)**:
   IRR is the discount rate (\( r \)) that makes the NPV = 0:
   \[
   NPV = \sum \frac{\text{Cash Inflow}_t}{(1 + r)^t} - \text{Initial Investment} = 0
   \]
   This is typically solved iteratively.

---

### Step 1: Cash Flows
#### Project A:
- Investment: ₹2,00,000
- Cash inflows (years 1-5): ₹40,000, ₹60,000, ₹80,000, ₹1,00,000, ₹1,20,000

#### Project B:
- Investment: ₹2,00,000
- Cash inflows (years 1-5): ₹90,000, ₹80,000, ₹60,000, ₹20,000, ₹16,000

---

### Step 2: Compute NPV for Both Projects at 10% Discount Rate

Let's compute the NPV for both projects. I'll calculate it step by step now. Data for calculations
# Constants
investment_A = 200000  # Initial investment for Project A
investment_B = 200000  # Initial investment for Project B
discount_rate = 0.10  # Discount rate for NPV calculation

# Cash inflows for Project A and Project B
cash_inflows_A = [40000, 60000, 80000, 100000, 120000]
cash_inflows_B = [90000, 80000, 60000, 20000, 16000]

# Function to calculate NPV
def calculate_npv(investment, cash_inflows, discount_rate):
    npv = -investment  # Start with the negative investment
    for t, cash_inflow in enumerate(cash_inflows, start=1):
        npv += cash_inflow / (1 + discount_rate) ** t  # Discounted cash inflows
    return npv

# Calculate NPVs for Project A and Project B
npv_A = calculate_npv(investment_A, cash_inflows_A, discount_rate)
npv_B = calculate_npv(investment_B, cash_inflows_B, discount_rate)

npv_A, npv_B### NPV Results:
1. **Project A**: ₹88,867.50  
2. **Project B**: ₹16,607.78  

These are the Net Present Values (NPVs) at a 10% discount rate.

---

### Step 3: Compute IRR for Both Projects
Now, let's calculate the Internal Rate of Return (IRR) for both projects. scipy.optimize import irr

# Function to calculate IRR
def calculate_irr(cash_flows):
    return irr(cash_flows)  # Uses cash flows to calculate IRR

# Cash flows for IRR calculations (investment is negative cash outflow)
cash_flows_A = [-investment_A] + cash_inflows_A
cash_flows_B = [-investment_B] + cash_inflows_B

# Calculate IRRs for Project A and Project B
irr_A = calculate_irr(cash_flows_A)
irr_B = calculate_irr(cash_flows_B)

irr_A, irr_BIt

A firm whose cost of capital is 10% is considering two projects A and B. Compute the Net Present Value (NPV) at 10% and Internal Rate of Return (IRR) for Project A by 20% and Project B by 10% and 15%. The initial investments and cash inflows for 5 years are provided for both projects.

Step-by-step calculation of Net Present Value (NPV) and Internal Rate of Return (IRR) for two projects at a 10% discount rate. Learn how to analyze cash flows and evaluate project profitability in financial decision-making.

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