An investment project has annual cash inflows of $4,400, $3,900, $5,100, and $4,300, and a discount rate of 14 percent.
What is the discounted payback period for these cash flows if the initial cost is $5,700? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is the discounted payback period for these cash flows if the initial cost is $7,800? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is the discounted payback period for these cash flows if the initial cost is $10,800? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation:
When
we use discounted payback, we need to find the value of all cash flows
today. The value today of the project cash flows for the first four
years is:

Value today of Year 1 cash flow = $4,400 / 1.14 = $3,859.65 
Value today of Year 2 cash flow = $3,900 / 1.14^{2} = $3,000.92 
Value today of Year 3 cash flow = $5,100 / 1.14^{3} = $3,442.35 
Value today of Year 4 cash flow = $4,300 / 1.14^{4} = $2,545.95 
To
find the discounted payback, we use these values to find the payback
period. The discounted first year cash flow is $3,859.65, so the
discounted payback for a $5,700 initial cost is:


Discounted payback = 1 + ($5,700 – 3,859.65) / $3,000.92 = 1.61 years 
For an initial cost of $7,800, the discounted payback is: 

Discounted payback = 2 + ($7,800 – 3,859.65 – 3,000.92) / $3,442.35 = 2.27 years 

Notice
the calculation of discounted payback. We know the payback period is
between two and three years, so we subtract the discounted values of the
Year 1 and Year 2 cash flows from the initial cost. This is the
numerator, which is the discounted amount we still need to make to
recover our initial investment. We divide this amount by the discounted
amount we will earn in Year 3 to get the fractional portion of the
discounted payback.


If the initial cost is $10,800, the discounted payback is: 

Discounted payback = 3 + ($10,800 – 3,859.65 – 3,000.92 – 3,442.35) / $2,545.95 = 3.20 years 