The Seattle Corporation has been presented with an investment opportunity which will yield cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost the firm $150,000 today, and the firm's cost of capital is 10 percent. Assume cash flows occur evenly during the year, 1/365th each day. What is the payback period for this investment?

Question

Quizplus · Accepted Answer

To find the payback period, we need to calculate how long it takes for the initial investment to be fully repaid by the cash flows. We can use a cumulative cash flow approach to find this:

Year 1: -$150,000 + $30,000 = -$120,000
Year 2: -$120,000 + $30,000 = -$90,000
Year 3: -$90,000 + $30,000 = -$60,000
Year 4: -$60,000 + $30,000 = -$30,000
Year 5: -$30,000 + $35,000 = $5,000
Year 6: $5,000 + $35,000 = $40,000
Year 7: $40,000 + $35,000 = $75,000
Year 8: $75,000 + $35,000 = $110,000
Year 9: $110,000 + $35,000 = $145,000
Year 10: $145,000 + $40,000 = $185,000

The payback period is the time it takes for the cumulative cash flow to reach zero or turn positive, which is in Year 4. To be more precise, we can calculate the fraction of the final year's cash flow needed to reach zero:

$30,000 / $40,000 = 0.75

So the total payback period is 3.75 years plus 0.75 years, or 4.50 years. Since cash flows are evenly distributed throughout the year, we can divide the payback period by 365 to get the payback period in days:

4.50 years / 365 = 0.0123 years per day

Finally, we can convert this to years by dividing by 1.0123, the factor needed to compound at 10% per year:

0.0123 / 1.0123 = 0.0121 years per day at a 10% discount rate

Therefore, the payback period is approximately:

365 / 0.0121 = 30,124 days

or about 4.86 years. So the answer is B.

The Seattle Corporation Has Been Presented with an Investment Opportunity