What is the discounted payback period of a five-year project that costs $18,000 today and pays an annual cash flow of $7,500? Assume the cost of capital is 15%.

Question

Quizplus · Accepted Answer

To calculate the discounted payback period, we need to first calculate the present value of each cash flow using the formula:

Present Value = Future Cash Flow / (1 + Cost of Capital)^Number of Years

Year 1: $7,500 / (1 + 0.15)^1 = $6,521.74
Year 2: $7,500 / (1 + 0.15)^2 = $5,668.35
Year 3: $7,500 / (1 + 0.15)^3 = $4,923.38
Year 4: $7,500 / (1 + 0.15)^4 = $4,269.47
Year 5: $7,500 / (1 + 0.15)^5 = $3,691.29

Next, we calculate the cumulative present value of cash flows for each year:

Year 1: $6,521.74
Year 2: $12,190.09 ($6,521.74 + $5,668.35)
Year 3: $17,113.47 ($6,521.74 + $5,668.35 + $4,923.38)
Year 4: $21,382.94 ($6,521.74 + $5,668.35 + $4,923.38 + $4,269.47)
Year 5: $25,074.23 ($6,521.74 + $5,668.35 + $4,923.38 + $4,269.47 + $3,691.29)

The discounted payback period is the point at which the cumulative present value of cash flows equals the initial investment, which in this case is $18,000. From the calculations above, we can see that this point falls between year 3 and year 4. To find the exact point, we can use linear interpolation:

Year 3: $17,113.47
Year 4: $21,382.94
Proportion of year 4 needed to reach discounted investment: ($18,000 - $17,113.47) / ($21,382.94 - $17,113.47) = 0.2403

The discounted payback period is therefore: year 3 + 0.2403 years = 3.2403 years, or approximately 3.20 years.

What Is the Discounted Payback Period of a Five-Year Project