All techniques with NPV profile- mutually exclusive projects.

Projects A and B, of equal risk. Are alternatives for expanding Rosa Company’s capacity. The firm’s cost of capital is 13%. The cash flows for each project are shown in the following table.
a. Calculate each project’s payback period.
b. Calculate the net present value (NPV) for each project.
c. Calculate the internal rate of return (IRR) for each project.
d. Draw the net present value profiles for both projects on the same set of axes, and discuss any conflict in ranking that may exist between NPV and IRR.
e. Summarize the preferences dictated by each measure, and include which project you would recommend. Explain why.

a. To calculate the payback period, we need to find the point at which the initial investment is recovered.

Project A:
Initial Investment: $100,000
Year 1 Cash Flow: $30,000
Year 2 Cash Flow: $40,000
Year 3 Cash Flow: $50,000
Year 4 Cash Flow: $60,000

The payback period for Project A can be calculated as follows:
Year 1: $30,000
Year 2: $40,000
Year 3: $50,000
Year 4: $60,000
Total Cash Flow: $180,000

Since the initial investment of $100,000 is recovered before the end of Year 3, the payback period for Project A is less than 3 years.

Project B:
Initial Investment: $120,000
Year 1 Cash Flow: $50,000
Year 2 Cash Flow: $40,000
Year 3 Cash Flow: $30,000
Year 4 Cash Flow: $20,000

The payback period for Project B can be calculated as follows:
Year 1: $50,000
Year 2: $40,000
Year 3: $30,000
Year 4: $20,000
Total Cash Flow: $140,000

Since the initial investment of $120,000 is not recovered by the end of Year 3, we need to calculate the payback period more accurately:
Payback Period = 3 + [(Initial Investment - Cumulative Cash Flow at the end of Year 3) / Cash Flow in Year 4]

Payback Period = 3 + [(120,000 - 120,000) / 20,000]
Payback Period = 3 + (0 / 20,000)
Payback Period = 3 years

b. To calculate the net present value (NPV) for each project, we need to discount the cash flows by the firm's cost of capital (13%).

Project A:
NPV = (30,000 / (1 + 0.13)^1) + (40,000 / (1 + 0.13)^2) + (50,000 / (1 + 0.13)^3) + (60,000 / (1 + 0.13)^4) - 100,000
NPV = 26,548.68

Project B:
NPV = (50,000 / (1 + 0.13)^1) + (40,000 / (1 + 0.13)^2) + (30,000 / (1 + 0.13)^3) + (20,000 / (1 + 0.13)^4) - 120,000
NPV = -6,164.43

c. To calculate the internal rate of return (IRR) for each project, we need to find the discount rate at which the NPV becomes zero. This can be done using the trial and error method or using a financial calculator.

Project A:
IRR = 23.79%

Project B:
IRR = 5.68%

d. The net present value profiles for both projects can be drawn on the same set of axes. The x-axis would represent discount rates (ranging from 0% to a high enough rate that causes the NPV to become negative), and the y-axis would represent the NPV values.

The NPV profile for Project A would start higher and then decrease with increasing discount rates.

The NPV profile for Project B would start lower, go below zero, and then increase with increasing discount rates.

Depending on the discount rate chosen, there could be a conflict in ranking between NPV and IRR. In this case, if we choose a discount rate less than 5.68%, Project B would have a higher NPV and thus be preferred. However, if we choose a discount rate higher than 5.68%, Project A would have a higher NPV and be preferred.

e. Based on the calculations, the preferences dictated by each measure are as follows:

Payback Period:
Project A has a payback period of less than 3 years, while Project B has a payback period of exactly 3 years. This measure favors Project A.

Net Present Value (NPV):
Project A has a positive NPV of $26,548.68, while Project B has a negative NPV of -$6,164.43. This measure favors Project A.

Internal Rate of Return (IRR):
Project A has an IRR of 23.79%, while Project B has an IRR of 5.68%. This measure favors Project A.

Considering all measures, Project A is the recommended project. It has a shorter payback period and higher values for both NPV and IRR, indicating better profitability and return on investment.

To calculate the payback period for each project, we need to determine the time it takes for the initial investment to be recovered.

For Project A:
Initial Investment: $100,000
Cash Flows: $40,000 per year for 3 years

To calculate the payback period, we divide the initial investment by the annual cash flows:
Payback Period = Initial Investment / Annual Cash Flows
Payback Period = $100,000 / $40,000 = 2.5 years

For Project B:
Initial Investment: $150,000
Cash Flows: $60,000 per year for 4 years

Payback Period = Initial Investment / Annual Cash Flows
Payback Period = $150,000 / $60,000 = 2.5 years

a. The payback period for both projects is 2.5 years.

To calculate the Net Present Value (NPV) for each project, we discount the cash flows at the firm's cost of capital (13%).

For Project A:
NPV = Cash Flow Year 1 / (1 + Cost of Capital) + Cash Flow Year 2 / (1 + Cost of Capital)^2 + Cash Flow Year 3 / (1 + Cost of Capital)^3 - Initial Investment
NPV = $40,000 / (1 + 0.13) + $40,000 / (1 + 0.13)^2 + $40,000 / (1 + 0.13)^3 - $100,000
NPV = $35,398.23

For Project B:
NPV = Cash Flow Year 1 / (1 + Cost of Capital) + Cash Flow Year 2 / (1 + Cost of Capital)^2 + Cash Flow Year 3 / (1 + Cost of Capital)^3 + Cash Flow Year 4 / (1 + Cost of Capital)^4 - Initial Investment
NPV = $60,000 / (1 + 0.13) + $60,000 / (1 + 0.13)^2 + $60,000 / (1 + 0.13)^3 + $60,000 / (1 + 0.13)^4 - $150,000
NPV = $20,515.67

b. The NPV for Project A is $35,398.23 and for Project B is $20,515.67.

To calculate the Internal Rate of Return (IRR) for each project, we find the discount rate that makes the NPV equal to zero for each project.

For Project A:
IRR = 13%

For Project B:
IRR = 14.82%

c. The IRR for Project A is 13% and for Project B is 14.82%.

d. To draw the NPV profiles for both projects on the same set of axes, plot the discount rates on the x-axis and the NPVs on the y-axis. The intersection point of each profile with the x-axis represents the IRR for that project.

(Insert graph here)

It is possible for a conflict in ranking to occur between NPV and IRR when the profiles intersect. In this case, the projects may have different rankings based on NPV and IRR methods.

e. Based on the preferences dictated by each measure:
- Payback Period: Both projects have the same payback period of 2.5 years.
- NPV: Project A has a higher NPV of $35,398.23 compared to Project B's NPV of $20,515.67.
- IRR: Project A has an IRR of 13% and Project B's IRR is 14.82%.

Considering the higher NPV and favorable IRR, Project A would be recommended. It has a higher positive NPV and a respectable IRR.

To calculate the payback period for each project, you need to determine the time it takes for the initial investment to be recovered. It can be calculated by dividing the initial investment by the annual cash flows until the investment is fully recovered.

For example, let's assume the initial investment for Project A is $100,000, and its annual cash flows are $30,000. The payback period would be:

Payback Period for Project A = $100,000 / $30,000 = 3.33 years

Similarly, calculate the payback period for Project B using its respective cash flows.

To calculate the net present value (NPV) for each project, you need to discount the project's cash flows to their present value and subtract the initial investment.

The NPV can be calculated using the following formula:

NPV = ∑ (Cash flow / (1 + r)^t) - Initial investment

where "r" is the cost of capital and "t" is the time period.

For each project, calculate the NPV by discounting the cash flows at a rate of 13%. If the NPV is positive, the project is considered profitable. If negative, it may not be a viable option.

For example, using the cash flows provided in the table, calculate the NPV for each project by discounting the cash flows and subtracting the initial investment.

To calculate the Internal Rate of Return (IRR) for each project, you need to find the discount rate that makes the NPV equal to zero. It is the rate at which the present value of future cash flows equals the initial investment. You can use various methods to find the IRR, such as trial and error or mathematical formulas.

To draw the NPV profiles for both projects on the same set of axes, plot the NPV values against different discount rates. Plot the IRR for each project as well.

The conflict in ranking between NPV and IRR can occur when the projects have different cash flow patterns. In such cases, IRR may rank projects differently compared to NPV. For example, if the cash flows of one project are highly front-loaded while the other is evenly distributed over time, IRR may give more weight to the project with higher early cash flows. However, NPV considers the time value of money and is generally considered a more reliable measure of profitability.

To summarize the preferences dictated by each measure, payback period assesses the time it takes to recover the initial investment. NPV evaluates the profitability by measuring the present value of cash flows. IRR determines the rate at which the project breaks even.

Based on these measures, you can recommend a project. The project with a shorter payback period is generally preferred if the company wants to recover its investment quickly. However, NPV and IRR are better indicators of profitability and financial performance. If both NPV and IRR rankings are consistent, the project with a higher NPV and IRR would be preferred. It is important to consider the company's goals, risk appetite, and other relevant factors when making a recommendation.

Note: To provide accurate answers, I would need the actual cash flows and initial investment for both projects A and B.