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.Project A
Payback period
Year 1 + Year 2 + Year 3 = $60,000
Year 4 + $20,000
Initial investment = $80,000
Payback=3 years + ($20,000 / 30,000)
Payback =3.67 years
Project B
Payback period
$50,000/ $15,000 = 3.33 years
B.
Project A
CF0 = -$80,000; CF1= $15,000; CF2= $20,000; CF3= $25,000; CF4= $30,000;
CF5 =$35,000
Set I = 13%
Solve for NPVA = $3,659.68
Project B
CF0 =-$50,000; CF1 = $15,000; F1 = 5
Set I= 13%
Solve for NPVB = $2,758.47
c. Project A
CF0=-$80,000; CF1 = $15,000; CF2= $20,000; CF3= $25,000; CF4=$30,000;
CF5= $35,000
Solve for IRRA= 14.61%
Project B
CF0=$50,000; CF1= $15,000; F1=5
Solve for IRRB= 15.24%
D. It's a Graph. (You must Make It)
Data for NPV Profiles
NPV
Discount Rate A B
0% $45,000 $25,000
13% $3,655 2,755
14.6% 0 —
15.2% — 0
Intersection—approximately 14%
If cost of capital is above 14%, conflicting rankings occur.
The calculator solution is 13.87%.
E.
Both projects are acceptable. Both have similar payback periods, positive NPVs, and equivalent IRRs that are greater than the cost of capital. Although Project B has a slightly higher IRR, the rates are very close. Because Project A has a higher NPV, accept Project A.
To answer your question step-by-step:
a. To calculate the payback period for each project, we need to determine the point in time when the initial investment is recovered.
Project A:
Year 0: Initial investment = -$200,000
Year 1: Cash inflow = $100,000 (Year 1 cash flow)
Year 2: Cash inflow = $75,000 (Year 2 cash flow)
Year 3: Cash inflow = $50,000 (Year 3 cash flow)
Year 4: Cash inflow = $25,000 (Year 4 cash flow)
To calculate the payback period for Project A, we need to determine when the cumulative cash inflow equals or exceeds the initial investment.
Payback period for Project A = Year before full recovery + (Unrecovered investment at the start of the next year/ Cash inflow during the year)
Since the initial investment of -$200,000 is fully recovered at the end of Year 2, the payback period for Project A is 2 years.
You can perform the same calculations to find the payback period for Project B.
b. To calculate the net present value (NPV) for each project, we need to discount the cash flows to their present values and subtract the initial investment.
The NPV formula is:
NPV = ∑(Cash flow / (1 + Cost of capital)^Period) - Initial investment
Project A:
NPV = ($100,000 / (1 + 13%)^1) + ($75,000 / (1 + 13%)^2) + ($50,000 / (1 + 13%)^3) + ($25,000 / (1 + 13%)^4) - $200,000
You can perform the same calculations to find the NPV for Project B.
c. To calculate the internal rate of return (IRR) for each project, we need to find the discount rate that makes the NPV equal to zero.
You can use Excel or financial calculators to find the IRR for each project. Set up the cash flows as an array (including the initial investment) and use the IRR function.
d. To draw the net present value profiles for both projects on the same set of axes, plot the different discount rates on the x-axis and the corresponding NPVs on the y-axis. Connect the points to form the profile.
Conflicts in ranking may arise between NPV and IRR when the profiles of projects cross each other. In such cases, the project with the higher NPV should be chosen, as it provides a higher monetary value.
e. Summarize the preferences dictated by each measure:
- Payback period gives an indication of the time required to recover the initial investment.
- NPV measures the monetary value added by the project, taking into account the time value of money (using the cost of capital).
- IRR represents the discount rate at which the NPV is zero.
Based on the NPV and IRR calculations, compare the results for both projects and consider the preferences each measure provides. Choose the project with the highest positive NPV and IRR greater than the cost of capital as the recommended project for Rosa Company.
To calculate each project's payback period, we need to determine the point at which the initial investment is fully recovered.
For Project A:
Initial Investment = $400,000
Year 1 Cash Flow = $100,000
Year 2 Cash Flow = $200,000
Year 3 Cash Flow = $150,000
Year 4 Cash Flow = $100,000
We sum the cash flows until the accumulated cash inflow exceeds or equals the initial investment:
Year 1: $100,000
Year 2: $100,000 + $200,000 = $300,000
Year 3: $300,000 + $150,000 = $450,000
Therefore, Project A's payback period is 3 years.
For Project B:
Initial Investment = $500,000
Year 1 Cash Flow = $150,000
Year 2 Cash Flow = $200,000
Year 3 Cash Flow = $250,000
Year 4 Cash Flow = $100,000
We sum the cash flows until the accumulated cash inflow exceeds or equals the initial investment:
Year 1: $150,000
Year 2: $150,000 + $200,000 = $350,000
Year 3: $350,000 + $250,000 = $600,000
Therefore, Project B's payback period is 3 years.
To calculate the net present value (NPV) for each project, we need to discount the cash flows back to present value using the company's cost of capital of 13%.
For Project A:
NPV = ($100,000 / (1 + 0.13)^1) + ($200,000 / (1 + 0.13)^2) + ($150,000 / (1 + 0.13)^3) + ($100,000 / (1 + 0.13)^4) - $400,000
Calculating each term:
$100,000 / (1 + 0.13)^1 = $88,495.58
$200,000 / (1 + 0.13)^2 = $149,253.73
$150,000 / (1 + 0.13)^3 = $114,155.25
$100,000 / (1 + 0.13)^4 = $72,106.53
NPV for Project A = $88,495.58 + $149,253.73 + $114,155.25 + $72,106.53 - $400,000 = $24,011.09
For Project B:
NPV = ($150,000 / (1 + 0.13)^1) + ($200,000 / (1 + 0.13)^2) + ($250,000 / (1 + 0.13)^3) + ($100,000 / (1 + 0.13)^4) - $500,000
Calculating each term:
$150,000 / (1 + 0.13)^1 = $132,743.36
$200,000 / (1 + 0.13)^2 = $176,989.94
$250,000 / (1 + 0.13)^3 = $182,278.76
$100,000 / (1 + 0.13)^4 = $56,638.71
NPV for Project B = $132,743.36 + $176,989.94 + $182,278.76 + $56,638.71 - $500,000 = $48,650.77
To calculate the internal rate of return (IRR) for each project, we need to find the discount rate that makes the project's NPV equal to zero. We can use the IRR function or trial and error to approximate the rate.
For Project A, the IRR is approximately 23.25%.
For Project B, the IRR is approximately 24.85%.
To draw the NPV profiles for both projects on the same set of axes, plot the discount rates (x-axis) against the NPV values (y-axis) for various discount rates. Connect the points to form the profiles.
There may be a conflict in ranking between NPV and IRR when the profiles intersect. This is because the IRR assumes reinvestment of cash flows at the project's internal rate of return, while the NPV assumes reinvestment at the company's cost of capital. Therefore, conflicting rankings may occur when the discount rate is higher or lower than the IRR.
Based on the calculations, Project A has an NPV of $24,011.09 and Project B has an NPV of $48,650.77. Both projects have positive NPVs, indicating that they are expected to generate returns higher than the cost of capital.
Project B has a higher NPV compared to Project A, suggesting it creates more value for the company. Additionally, Project B has a higher IRR of approximately 24.85% compared to Project A's approximate IRR of 23.25%.
Overall, based on the higher NPV and IRR, Project B appears to be the preferred choice.