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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:Group of answer choices2.2 years2.1 years2.6 years3.0 years

Question

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.AthenaCorpanticipatescashinflowsfromthisventureasoutlinedbelow:YearOneYearTwoYearThreeYearFour450,000. AthenaCorp anticipates cash inflows from this venture as outlined below:Year OneYear TwoYear ThreeYear Four200,000225,000225,000275,000$200,000The appropriate discount rate for this project is 16%. The discounted payback period for this project is closest to:Group of answer choices2.2 years2.1 years2.6 years3.0 years

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Solution

The discounted payback period is the length of time it takes to break even from an investment, in terms of discounted cash flows. In this case, we need to calculate the present value of each year's cash inflow and then determine how long it takes for the sum of these present values to equal the initial investment of $450,000.

Here's how to calculate it:

  1. Calculate the present value (PV) of each year's cash inflow. The formula for PV is:

    PV = Future Value / (1 + r)^n

    where r is the discount rate (16% or 0.16 in this case) and n is the year.

    Year One: PV = 200,000/(1+0.16)1=200,000 / (1 + 0.16)^1 = 172,413.79 Year Two: PV = 225,000/(1+0.16)2=225,000 / (1 + 0.16)^2 = 166,284.16 Year Three: PV = 275,000/(1+0.16)3=275,000 / (1 + 0.16)^3 = 181,347.15 Year Four: PV = 200,000/(1+0.16)4=200,000 / (1 + 0.16)^4 = 118,248.17

  2. Add up the present values until the sum equals or exceeds the initial investment of $450,000.

    After Year One: 172,413.79AfterYearTwo:172,413.79 After Year Two: 172,413.79 + 166,284.16=166,284.16 = 338,697.95 After Year Three: 338,697.95+338,697.95 + 181,347.15 = $520,045.10

So, the discounted payback period is somewhere in the third year. To find the exact point, we can calculate the fraction of the third year needed to reach $450,000:

Fraction = (450,000−450,000 - 338,697.95) / $181,347.15 = 0.614

Therefore, the discounted payback period is approximately 2.6 years. So, the closest answer is 2.6 years.

This problem has been solved

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