The AthenaCorp is considering funneling resources into a fresh initiative. This entails acquiring state-of-the-art equipment with a price tag of $450,000. AthenaCorp anticipates cash inflows from this venture as outlined below:Year OneYear TwoYear ThreeYear Four$200,000$225,000$275,000$200,000The appropriate discount rate for this project is 16%. The discounted payback period for this project is closest to:
Question
The AthenaCorp is considering funneling resources into a fresh initiative. This entails acquiring state-of-the-art equipment with a price tag of 200,000275,000$200,000The appropriate discount rate for this project is 16%. The discounted payback period for this project is closest to:
Solution
To calculate the discounted payback period, we first need to calculate the present value of each year's cash inflow. The formula for present value is:
PV = CF / (1 + r)^n
where:
- PV is the present value
- CF is the cash inflow
- r is the discount rate
- n is the year
Let's calculate the present value for each year:
Year One: PV = 172,413.79
Year Two: PV = 166,284.48
Year Three: PV = 181,699.15
Year Four: PV = 118,248.17
Now, we add up these present values to get the total present value of the cash inflows:
Total PV = 166,284.48 + 118,248.17 = $638,645.59
The discounted payback period is the time it takes for the present value of the cash inflows to equal or exceed the initial investment. In this case, the initial investment is $450,000.
If we add up the present values year by year, we can see that the total present value exceeds the initial investment sometime during Year Three. Therefore, the discounted payback period is closest to three years.
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