FREE IGNOU MCO-07 SOLVED ASSIGNMENT 2023

Question 3: A company is considering the following investment projects. Find out payback period, net present value, and rank the projects according to them. Assume discount rate 10% and 20%.

To find the payback period and net present value (NPV) for each project, we need to calculate the cash flows for each period and then apply the respective formulas. The payback period is the time taken to recover the initial investment, and the NPV represents the present value of the project’s cash flows after discounting them at the given rates. Let’s calculate the payback period and NPV for each project using the provided data and discount rates:

Project A: Initial Investment = ₹10,00,000 Cash Flows (₹) = ₹12,00,000, ₹8,00,000, ₹0

Payback Period (PB) for Project A: PB = Initial Investment / Cash Inflows in the first period PB = ₹10,00,000 / ₹12,00,000 = 0.833 years

Net Present Value (NPV) for Project A: Discount Rate (r) = 10% NPV = (Cash Flow Year 1 / (1 + r) + Cash Flow Year 2 / (1 + r)^2) – Initial Investment NPV = (₹12,00,000 / (1 + 0.10) + ₹8,00,000 / (1 + 0.10)^2) – ₹10,00,000 NPV = ₹10,90,909.09 (approx)

NPV at 20% discount rate: Discount Rate (r) = 20% NPV = (Cash Flow Year 1 / (1 + r) + Cash Flow Year 2 / (1 + r)^2) – Initial Investment NPV = (₹12,00,000 / (1 + 0.20) + ₹8,00,000 / (1 + 0.20)^2) – ₹10,00,000 NPV = ₹9,17,355.37 (approx)

Project B: Initial Investment = ₹10,00,000 Cash Flows (₹) = ₹8,00,000, ₹10,00,000, ₹12,00,000

Payback Period (PB) for Project B: PB = Initial Investment / Cash Inflows in the first period PB = ₹10,00,000 / ₹8,00,000 = 1.25 years

Net Present Value (NPV) for Project B: Discount Rate (r) = 10% NPV = (Cash Flow Year 1 / (1 + r) + Cash Flow Year 2 / (1 + r)^2 + Cash Flow Year 3 / (1 + r)^3) – Initial Investment NPV = (₹8,00,000 / (1 + 0.10) + ₹10,00,000 / (1 + 0.10)^2 + ₹12,00,000 / (1 + 0.10)^3) – ₹10,00,000 NPV = ₹13,14,462.81 (approx)

NPV at 20% discount rate: Discount Rate (r) = 20% NPV = (Cash Flow Year 1 / (1 + r) + Cash Flow Year 2 / (1 + r)^2 + Cash Flow Year 3 / (1 + r)^3) – Initial Investment NPV = (₹8,00,000 / (1 + 0.20) + ₹10,00,000 / (1 + 0.20)^2 + ₹12,00,000 / (1 + 0.20)^3) – ₹10,00,000 NPV = ₹9,54,545.45 (approx)

Project C: Initial Investment = ₹10,00,000 Cash Flows (₹) = ₹3,00,000, ₹5,00,000, ₹5,00,000

Payback Period (PB) for Project C: PB = Initial Investment / Cash Inflows in the first period PB = ₹10,00,000 / ₹3,00,000 = 3.33 years

Net Present Value (NPV) for Project C: Discount Rate (r) = 10% NPV = (Cash Flow Year 1 / (1 + r) + Cash Flow Year 2 / (1 + r)^2 + Cash Flow Year 3 / (1 + r)^3) – Initial Investment NPV = (₹3,00,000 / (1 + 0.10) + ₹5,00,000 / (1 + 0.10)^2 + ₹5,00,000 / (1 + 0.10)^3) – ₹10,00,000 NPV = -₹3,19,669.42 (approx)

NPV at 20% discount rate: Discount Rate (r) = 20% NPV = (Cash Flow Year 1 / (1 + r) + Cash Flow Year 2 / (1 + r)^2 + Cash Flow Year 3 / (1 + r)^3) – Initial Investment NPV = (₹3,00,000 / (1 + 0.20) + ₹5,00,000 / (1 + 0.20)^2 + ₹5,00,000 / (1 + 0.20)^3) – ₹10,00,000 NPV = -₹3,63,636.36 (approx)

Project D: Initial Investment = ₹10,00,000 Cash Flows (₹) = ₹10,00,000, ₹6,00,000, ₹3,00,000

Payback Period (PB) for Project D: PB = Initial Investment / Cash Inflows in the first period PB = ₹10,00,000 / ₹10,00,000 = 1 year

Net Present Value (NPV) for Project D: Discount Rate (r) = 10% NPV = (Cash Flow Year 1 / (1 + r) + Cash Flow Year 2 / (1 + r)^2 + Cash Flow Year 3 / (1 + r)^3) – Initial Investment NPV = (₹10,00,000 / (1 + 0.10) + ₹6,00,000 / (1 + 0.10)^2 + ₹3,00,000 / (1 + 0.10)^3) – ₹10,00,000 NPV = ₹4,50,413.22 (approx)

NPV at 20% discount rate: Discount Rate (r) = 20% NPV = (Cash Flow Year 1 / (1 + r) + Cash Flow Year 2 / (1 + r)^2 + Cash Flow Year 3 / (1 + r)^3) – Initial Investment NPV = (₹10,00,000 / (1 + 0.20) + ₹6,00,000 / (1 + 0.20)^2 + ₹3,00,000 / (1 + 0.20)^3) – ₹10,00,000 NPV = ₹2,16,528.93 (approx)

Ranking of Projects based on NPV:

At 10% discount rate:

1. Project B: ₹13,14,462.81
2. Project A: ₹10,90,909.09
3. Project D: ₹4,50,413.22
4. Project C: -₹3,19,669.42 (Negative NPV indicates unprofitable project)

At 20% discount rate:

1. Project B: ₹9,54,545.45
2. Project A: ₹9,17,355.37
3. Project D: ₹2,16,528.93
4. Project C: -₹3,63,636.36 (Negative NPV indicates unprofitable project)

In conclusion, Project B is the most favorable investment option, yielding the highest positive NPV, while Project C shows a negative NPV, making it an unfavorable choice. The ranking of projects changes with the discount rate, highlighting the sensitivity of NPV to the discount rate used in the analysis.