Please show work. An investment project costs $10,000 and has annual cash flows
ID: 2708964 • Letter: P
Question
Please show work.
An investment project costs $10,000 and has annual cash flows of $2,990 for six years.
What is the discounted payback period if the discount rate is zero percent? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)
What is the discounted payback period if the discount rate is 5 percent? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)
What is the discounted payback period if the discount rate is 20 percent? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)
An investment project costs $10,000 and has annual cash flows of $2,990 for six years.
Explanation / Answer
Year
Cash Flows
Rate = 0%
Rate = 5%
Rate = 20%
1
2,990.00
2,990.00
2,847.62
2,491.67
2
2,990.00
2,990.00
2,712.02
2,076.39
3
2,990.00
2,990.00
2,582.87
1,730.32
4
2,990.00
2,990.00
2,459.88
1,441.94
5
2,990.00
2,990.00
2,342.74
1,201.61
6
2,990.00
2,990.00
2,231.18
1,001.34
The above table shows the discounted cash flows for each year under 3 different scenarios.
Discounted Payback means the time taken for a project to return the invested capital in a project after taking the time value of money into consideration
Scenario 1 Rate = 0%
Cash Flow recovered till 3rd year = 8970
Remaining Cash Flow = 1030
Days taken to recover 1030 = 1030 /2990 *365 = 126 days
Discounted Payback = 3 years 126 days
Scenario 2 Rate = 5%
Cash Flow recovered till 3rd year = 8142.50
Remaining Cash Flow = 1857.50
Days taken to recover 1857.50 = 1857.50/2459.8*365 = 276 days
Discounted Payback = 3 years 276 days
Scenario 3 Rate = 20%
Here we see that sum of all the cash flows for all the 6 years is = 9943.28 which is less than 10000 i.e. the project has not yet recovered the initial cost and hence the discounted payback = 0
Year
Cash Flows
Rate = 0%
Rate = 5%
Rate = 20%
1
2,990.00
2,990.00
2,847.62
2,491.67
2
2,990.00
2,990.00
2,712.02
2,076.39
3
2,990.00
2,990.00
2,582.87
1,730.32
4
2,990.00
2,990.00
2,459.88
1,441.94
5
2,990.00
2,990.00
2,342.74
1,201.61
6
2,990.00
2,990.00
2,231.18
1,001.34