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Answer :
The project that maximizes shareholder value is Project Y, which has a MIRR of 24.50%.
In order to calculate the MIRR of the project that maximizes shareholder value, we will use the following steps:
Calculate the present value of all cash inflows of both the projects separately. This will give us the NPV of each project. Calculate the MIRR of each project. Choose the project with the highest MIRR, as it will maximize shareholder value.
Calculations of Project X:
We will first calculate the NPV of Project X. Using the formula, we get:
NPV of Project X = -1000 + (110/(1+0.12)¹) + (300/(1+0.12)²) + (370/(1+0.12)³) + (750/(1+0.12)⁴)= $378.94
We will now calculate the MIRR of Project X. We will use the following formula:
Using trial and error method, we can find the value of r which makes the present value of all negative cash flows equal to the present value of all positive cash flows, i.e., $0 = -1000 + 110/(1+r)¹ + 300/(1+r)² + 370/(1+r)³ + 750/(1+r)⁴.
Using Excel or a financial calculator, we can find that the MIRR of Project X is 23.15%.
Calculations of Project Y:
We will now calculate the NPV of Project Y. Using the formula, we get:
NPV of Project Y = -1000 + (1000/(1+0.12)¹) + (100/(1+0.12)²) + (55/(1+0.12)³) + (50/(1+0.12)⁴)= $201.90
We will now calculate the MIRR of Project Y. Using the same formula, we get:
Using trial and error method, we can find that the value of r which makes the present value of all negative cash flows equal to the present value of all positive cash flows, i.e., $0 = -1000 + 1000/(1+r)¹ + 100/(1+r)² + 55/(1+r)³ + 50/(1+r)⁴.
Using Excel or a financial calculator, we can find that the MIRR of Project Y is 24.50%.
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