Wednesday, 9 July 2014

An investment project has annual cash inflows of $4,400, $3,900, $5,100, and $4,300, and a discount rate of 14 percent.

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))

  Discounted payback period years  

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))

  Discounted payback period years  

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))
  
  Discounted payback period years  


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 / 1.142 = $3,000.92
Value today of Year 3 cash flow = $5,100 / 1.143 = $3,442.35
Value today of Year 4 cash flow = $4,300 / 1.144 = $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