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 required rate of return 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 calculate the payback period, we need to find out in which year the accumulated cash inflows equal the initial investment of $150,000. We can use a table to track the cumulative cash inflows:

| Year  | Cash Inflows | Cumulative Inflows |
|-------|-------------|--------------------|
|   1   |     30,000  |      30,000        |
|   2   |     30,000  |      60,000        |
|   3   |     30,000  |      90,000        |
|   4   |     30,000  |     120,000        |
|   5   |     35,000  |     155,000        |
|   6   |     35,000  |     190,000        |
|   7   |     35,000  |     225,000        |
|   8   |     35,000  |     260,000        |
|   9   |     35,000  |     295,000        |
|   10  |     40,000  |     335,000        |

The payback period is the time it takes for the cumulative cash inflows to equal the initial investment. It looks like this occurs between Years 4 and 5, since the cumulative inflows are $120,000 after Year 4 and increase to $155,000 after Year 5. To get a more precise estimate, we can use linear interpolation:

Payback Period = Year 4 + (150,000 - Cumulative Inflows at end of Year 4) / Cash Inflows in Year 5
Payback Period = 4 + (150,000 - 120,000) / 35,000
Payback Period = 4.86 years

Therefore, the answer is B (4.86 years).

The Seattle Corporation Has Been Presented with an Investment Opportunity