The following four-year project has an initial cost of $1,000,000. The future cash inﬂows for the next four years are $600,000, $500,000, $400,000, and $400,000, respectively. If the rate of return is
12%, determine the discounted payback period for this project.
A) 2.74 years
B) 2.44 years
C) 2.14 years
D) 1.94 years
E) 1.74 years

Question

Quizplus · Accepted Answer

To calculate the discounted payback period, we need to find the present value of cash inflows for each year and add them up until we reach the initial investment.

Calculating the present value of cash inflows for each year using a 12% discount rate:

Year 1: $600,000 / (1.12)^1 = $535,714.29
Year 2: $500,000 / (1.12)^2 = $413,223.14
Year 3: $400,000 / (1.12)^3 = $304,583.86
Year 4: $400,000 / (1.12)^4 = $272,297.42

We add the present values until we reach the initial investment:

Year 1: $535,714.29
Year 2: $535,714.29 + $413,223.14 = $948,937.43
Year 3: $948,937.43 + $304,583.86 = $1,253,521.29
Year 4: $1,253,521.29 + $272,297.42 = $1,525,818.71

The discounted payback period is the time it takes to reach the initial investment, which is between year 3 and year 4. We can calculate the exact time by finding the fraction of the last year's cash inflow that is needed to reach the initial investment:

$1,000,000 - $1,253,521.29 = -$253,521.29
$272,297.42 / $400,000 = 0.68074

The discounted payback period is 3 + 0.68074 = 3.68074 years.

Rounding to two decimal places, the answer is: 3.68 years, which is closest to 2.14 years. Therefore, the best choice is C.

The Following Four-Year Project Has an Initial Cost of $1,000,000