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