An investment project has annual cash inflows of $3,400, $4,300, $5,500, and $4,
ID: 2646531 • Letter: A
Question
An investment project has annual cash inflows of $3,400, $4,300, $5,500, and $4,700, and a discount rate of 13 percent.
What is the discounted payback period for these cash flows if the initial cost is $6,100? (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 $8,200? (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 $11,200? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
An investment project costs $10,000 and has annual cash flows of $2,820 for six years.
What is the discounted payback period if the discount rate is 0 percent? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))
What is the discounted payback period if the discount rate is 4 percent? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))
What is the discounted payback period if the discount rate is 19 percent? (Enter 0 if the project never pays back. Do not round intermediate calculations and round your answer to 2 decimal places. (e.g., 32.16))
An investment project has annual cash inflows of $3,400, $4,300, $5,500, and $4,700, and a discount rate of 13 percent.
Explanation / Answer
Year PV Factor @ 13% Cashflow 1 Discounted Cashflow Cumulative Discounted Cashflow 0 1 (6,100.00) (6,100.00) (6,100.00) 1 0.884955752 3,400.00 3,008.85 (3,091.15) 2 0.783146683 4,300.00 3,367.53 276.38 3 0.693050162 5,500.00 3,811.78 4,088.16 4 0.613318728 4,700.00 2,882.60 6,970.75 Discounted Payback Period = A + B/C Where A = Last period with a negative discounted cumulative cashflow = 1 B = Absolute value of discounted cumulative cash flow at the end of the period A = 3091.15 C = Discounted cash flow during the period after A = 3367.53 Discounted Payback Period = A + B/C = 1 + 3091.15/3367.53 = 1.92 Year PV Factor @ 13% Cashflow 2 Discounted Cashflow Cumulative Discounted Cashflow 0 1 (8,200.00) (8,200.00) (8,200.00) 1 0.884955752 3,400.00 3,008.85 (5,191.15) 2 0.783146683 4,300.00 3,367.53 (1,823.62) 3 0.693050162 5,500.00 3,811.78 1,988.16 4 0.613318728 4,700.00 2,882.60 4,870.75 Discounted Payback Period = A + B/C Where A = Last period with a negative discounted cumulative cashflow = 2 B = Absolute value of discounted cumulative cash flow at the end of the period A = 1823.62 C = Discounted cash flow during the period after A = 3811.78 Discounted Payback Period = A + B/C = 1 + 1823.62/3811.78 = 2.48 Year PV Factor @ 13% Cashflow 3 Discounted Cashflow Cumulative Discounted Cashflow 0 1 (11,200.00) (11,200.00) (11,200.00) 1 0.884955752 3,400.00 3,008.85 (8,191.15) 2 0.783146683 4,300.00 3,367.53 (4,823.62) 3 0.693050162 5,500.00 3,811.78 (1,011.84) 4 0.613318728 4,700.00 2,882.60 1,870.75 Discounted Payback Period = A + B/C Where A = Last period with a negative discounted cumulative cashflow = 3 B = Absolute value of discounted cumulative cash flow at the end of the period A = 1011.84 C = Discounted cash flow during the period after A = 2882.60 Discounted Payback Period = A + B/C = 3 + 1011.84/2882.60 = 3.35 Year PV Factor @ 0% Cashflow Discounted Cashflow Cumulative Discounted Cashflow 0 1 (10,000.00) (10,000.00) (10,000.00) 1 1 2,820.00 2,820.00 (7,180.00) 2 1 2,820.00 2,820.00 (4,360.00) 3 1 2,820.00 2,820.00 (1,540.00) 4 1 2,820.00 2,820.00 1,280.00 5 1 2,820.00 2,820.00 4,100.00 6 1 2,820.00 2,820.00 6,920.00 Discounted Payback Period = A + B/C Where A = Last period with a negative discounted cumulative cashflow = 3 B = Absolute value of discounted cumulative cash flow at the end of the period A = 1540 C = Discounted cash flow during the period after A = 2820 Discounted Payback Period = A + B/C = 3 + 1540/2820 = 3.55 Year PV Factor @ 4% Cashflow Discounted Cashflow Cumulative Discounted Cashflow 0 1 (10,000.00) (10,000.00) (10,000.00) 1 0.961538462 2,820.00 2,711.54 (7,288.46) 2 0.924556213 2,820.00 2,607.25 (4,681.21) 3 0.888996359 2,820.00 2,506.97 (2,174.24) 4 0.854804191 2,820.00 2,410.55 236.30 5 0.821927107 2,820.00 2,317.83 2,554.14 6 0.790314526 2,820.00 2,228.69 4,782.83 Discounted Payback Period = A + B/C Where A = Last period with a negative discounted cumulative cashflow = 3 B = Absolute value of discounted cumulative cash flow at the end of the period A = 2174.24 C = Discounted cash flow during the period after A = 2410.55 Discounted Payback Period = A + B/C = 3 + 2174.24/2410.55 = 3.90 Year PV Factor @ 19% Cashflow Discounted Cashflow Cumulative Discounted Cashflow 0 1 (10,000.00) (10,000.00) (10,000.00) 1 0.840336134 2,820.00 2,369.75 (7,630.25) 2 0.706164819 2,820.00 1,991.38 (5,638.87) 3 0.593415814 2,820.00 1,673.43 (3,965.43) 4 0.498668751 2,820.00 1,406.25 (2,559.19) 5 0.419049371 2,820.00 1,181.72 (1,377.47) 6 0.352142329 2,820.00 993.04 (384.43) The Cumulative Discounted Cashflow < 0 at the end of the project. This means the project does not break-even.Related Questions
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