Preston Corporation is evaluating its potential investment in a $225,660 piece of equipment with a three-year life and no salvage value. The company anticipates that pre-tax cash flows in each of the three years will equal to 22%, 44%, and 66%, respectively, of the investment’s face value. The tax rate is 28%. Pre-tax cash flows, discounted at 10 percent, are $427,697, undiscounted after-tax cash flows are $279,185, and after-tax cash flows, discounted at 10 percent, are $225,660. The internal rate of return is:
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Preston Corporation is evaluating its potential investment in a $225,660 piece of equipment with a three-year life and no salvage value. The company anticipates that pre-tax cash flows in each of the three years will equal to 22%, 44%, and 66%, respectively, of the investment's face value. The tax rate is 28%. Pre-tax cash flows, discounted at 10 percent, are $427,697, undiscounted after-tax cash flows are $279,185, and after-tax cash flows, discounted at 10 percent, are $225,660. The internal rate of return is:
a. 10%
b. 44%
c. 22%
d. 23.7%
To calculate the internal rate of return (IRR), we need to find the discount rate that makes the net present value (NPV) of the cash flows equal to zero. In this case, the NPV is already provided as $225,660.
We can use the NPV formula to solve for the IRR:
NPV = CF1 / (1+r)^1 + CF2 / (1+r)^2 + CF3 / (1+r)^3 - Initial Investment
where CF1, CF2, and CF3 are the cash flows in each year and r is the discount rate.
Given the cash flows and the NPV, we have the following equation:
$225,660 = $427,697 / (1+r)^1 + $279,185 / (1+r)^2 + $427,697 / (1+r)^3 - Initial Investment
Since the initial investment is $225,660, we can simplify the equation:
$0 = $427,697 / (1+r)^1 + $279,185 / (1+r)^2 + $427,697 / (1+r)^3 - $225,660
To solve this equation, we can use trial and error or numerical methods such as the Newton-Raphson method. However, since this is a complex equation, it is more practical to use financial software or a financial calculator to find the IRR.
To calculate the internal rate of return (IRR), we need to find the discount rate at which the present value of the cash inflows equals the initial investment. We can use trial and error or financial software to find the IRR.
However, in this case, we already have the undiscounted after-tax cash flows and the after-tax cash flows discounted at 10 percent, so we can use them to directly calculate the IRR without trial and error.
The undiscounted after-tax cash flows are $279,185, which is the total cash inflow over the three-year period.
The after-tax cash flows discounted at 10 percent are $225,660. This is the present value of the cash flows if we discount them at a rate of 10 percent per year.
Using these two values, we can calculate the IRR using the following formula:
IRR = (Discounted Cash Flows / Undiscounted Cash Flows)^(1 / number of periods) - 1
where:
- Discounted Cash Flows = $225,660
- Undiscounted Cash Flows = $279,185
- Number of periods = 3 (since we have cash flows for three years)
Plugging in the values, we get:
IRR = ($225,660 / $279,185)^(1 / 3) - 1
IRR = 0.924 - 1
IRR = -0.076
Therefore, the internal rate of return (IRR) is -0.076 or -7.6%.