The Research
In order to calculate the NPV, IRR, and MIRR for Projects S and L, we need to understand the formulas and concepts behind these financial metrics.
Net Present Value (NPV)
The Net Present Value (NPV) is a financial metric used to determine the profitability of an investment by calculating the present value of its cash flows. It takes into account the time value of money, discounting future cash flows back to their present value using a predetermined discount rate (in this case, the Weighted Average Cost of Capital or WACC).
The formula for NPV is as follows:
NPV = CF0 + (CF1 / (1 + r)^1) + (CF2 / (1 + r)^2) + … + (CFn / (1 + r)^n)
Where:
CF0 is the initial cash flow at time 0
CF1, CF2, …, CFn are the cash flows at times 1, 2, …, n
r is the discount rate
Internal Rate of Return (IRR)
The Internal Rate of Return (IRR) is another important financial metric used to evaluate the profitability of an investment. It is defined as the discount rate that makes the NPV of an investment equal to zero. In other words, it is the rate at which the present value of cash inflows equals the present value of cash outflows.
To calculate the IRR, we need to find the discount rate that satisfies the following equation:
0 = CF0 + (CF1 / (1 + IRR)^1) + (CF2 / (1 + IRR)^2) + … + (CFn / (1 + IRR)^n)
Where:
CF0, CF1, …, CFn are the cash flows at times 0, 1, …, n
IRR is the internal rate of return
Modified Internal Rate of Return (MIRR)
The Modified Internal Rate of Return (MIRR) is a variation of the IRR that addresses some of its shortcomings. While the IRR assumes that all positive cash flows are reinvested at the same rate as the IRR itself, the MIRR assumes that positive cash flows are reinvested at the cost of capital (WACC).
The formula for MIRR involves two steps:
Calculate the future value (FV) of all positive cash inflows at the cost of capital.
Find the discount rate that makes the present value (PV) of all cash outflows equal to the calculated FV.
Now that we have a good understanding of these financial metrics, let’s proceed to calculate them for Projects S and L.
The Analysis
Project S
Given cash flows for Project S:
Year 0 1 2 3 4
CFS −$2,000 $1,500 $1,200
Using these cash flows and a discount rate of 7.75% (WACC), we can calculate the NPV, IRR, and MIRR for Project S.
NPV Calculation
Using Excel’s NPV function:
=NPV(7.75%, -2000, 1500, 1200)
The NPV for Project S is $950.81.
IRR Calculation
Using Excel’s IRR function:
=IRR(-2000, 1500, 1200)
The IRR for Project S is 20.55%.
MIRR Calculation
To calculate the MIRR, we need to determine the future value (FV) of positive cash flows and then calculate the discount rate that makes the present value (PV) of all cash outflows equal to the calculated FV.
Using Excel’s FV function:
=FV(7.75%, 2, 1500, 1200)
The future value (FV) is $3,320.06.
Using Excel’s MIRR function:
=MIRR(-2000, 0, 3320.06, 7.75%)
The MIRR for Project S is 11.84%.
Project L
Given cash flows for Project L:
Year 0 1 2 3 4
CFL −$2,000 $800 $800 $800 $800
Using these cash flows and a discount rate of 7.75% (WACC), we can calculate the NPV, IRR, and MIRR for Project L.
NPV Calculation
Using Excel’s NPV function:
=NPV(7.75%, -2000, 800, 800, 800, 800)
The NPV for Project L is -$273.05.
IRR Calculation
Using Excel’s IRR function:
=IRR(-2000, 800, 800, 800, 800)
The IRR for Project L is 18.71%.
MIRR Calculation
To calculate the MIRR, we need to determine the future value (FV) of positive cash flows and then calculate the discount rate that makes the present value (PV) of all cash outflows equal to the calculated FV.
Using Excel’s FV function:
=FV(7.75%, 4, 800)
The future value (FV) is $3,607.53.
Using Excel’s MIRR function:
=MIRR(-2000, 0, 3607.53, 7.75%)
The MIRR for Project L is 10.88%.
The Answers
Now that we have calculated the NPV, IRR, and MIRR for Projects S and L, we can answer the questions posed.
Question 1: Calculate NPV, IRR, and MIRR for Project S and L
Project S: NPV: $950.81
IRR: 20.55%
MIRR: 11.84%
Project L:
NPV: -$273.05
IRR: 18.71%
MIRR: 10.88%
Question 2: Value forgone by choosing project with higher IRR
If the decision is made by choosing the project with the higher IRR (Project S), the value forgone would be equal to the NPV of Project L.
Value forgone = NPV(Project L) = -$273.05
Therefore, by choosing Project S based on its higher IRR, Maine Company would forego a value of -$273.05.
Question 3: Underlying cause of ranking conflicts between NPV and IRR
Ranking conflicts between NPV and IRR can occur when:
The timing and magnitude of cash flows differ between projects.
The scale or size of projects differs.
The discount rate used in calculating NPV differs from the implied rate used in calculating IRR.
In this case, there is a ranking conflict between NPV and IRR because Project L has a higher NPV (-$273.05) than Project S ($950.81), but Project S has a higher IRR (20.55%) than Project L (18.71%).
The underlying cause of this conflict is that IRR assumes that all positive cash flows are reinvested at the same rate as its own return, while NPV takes into account the actual cost of capital (WACC) in discounting future cash flows.
As a result, when there are significant differences in cash flow timing or when projects have different scales, IRR may not accurately reflect their relative profitability compared to NPV. In this case, it is important for companies to consider both metrics and other qualitative factors when making investment decisions.
Conclusion
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