Consider a project with a positive rate of return. Suppose the discount factor solutions to the equation which determines the internal rate of return (ROR) of the project are given by 0.8502, 2.0207, -0.1767. What is the project's ROR?
To find the project's internal rate of return (ROR) from the given discount factor solutions, we need to determine the discount rate at which the net present value (NPV) of the project becomes zero.
The net present value (NPV) of the project is calculated using the formula:
NPV = Cash Flow / (1 + ROR)^t
where Cash Flow represents the cash flow during period t.
To find the ROR, we set the NPV equation equal to zero and solve for ROR.
0 = Cash Flow / (1 + ROR)^t
Rearranging the equation, we have:
(1 + ROR)^t = Cash Flow
Now, let's consider the given discount factor solutions: 0.8502, 2.0207, -0.1767.
Since discount factor = (1 + ROR)^t, we can find ROR by taking the t-th root of the discount factor.
For the first discount factor solution, 0.8502:
(1 + ROR)^t = 0.8502
Taking the t-th root of both sides, we get:
1 + ROR = 0.8502^(1/t)
Subtracting 1 from both sides:
ROR = 0.8502^(1/t) - 1
Similarly, we can find ROR for the other discount factor solutions:
For 2.0207:
ROR = 2.0207^(1/t) - 1
And for -0.1767:
ROR = -0.1767^(1/t) - 1
Note that the calculations for ROR may produce complex or imaginary solutions if the discount factor solutions are negative or less than 1.
Therefore, to find the project's ROR, we need to know the value of t. It represents the time period at which the cash flow occurs, and it should be provided along with the discount factor solutions.