Practice Question
If a project has a cost of $80,000 and annual cash flows of $25,000 for 4 years, what is the discounted payback period at a discount rate of 10%?
Answer +
B
Step-by-step solutions +
Step 1: Calculate the discounted cash flows for each year:
Year 1: $25,000 / (1.10)^1 = $22,727.27
Year 2: $25,000 / (1.10)^2 = $20,661.16
Year 3: $25,000 / (1.10)^3 = $18,783.78
Year 4: $25,000 / (1.10)^4 = $17,075.25
Step 2: Accumulate discounted cash flows:
Year 1 total: $22,727.27
Year 2 total: $43,388.43
Year 3 total: $62,172.21
Year 4 total: $79,247.46
Step 3: Find the point where the cumulative discounted cash flow exceeds $80,000. This happens slightly after year 4.
Since it reaches about $79,247 by year 4, the discounted payback period is approximately 3.5 to 4 years.
Year 1: $25,000 / (1.10)^1 = $22,727.27
Year 2: $25,000 / (1.10)^2 = $20,661.16
Year 3: $25,000 / (1.10)^3 = $18,783.78
Year 4: $25,000 / (1.10)^4 = $17,075.25
Step 2: Accumulate discounted cash flows:
Year 1 total: $22,727.27
Year 2 total: $43,388.43
Year 3 total: $62,172.21
Year 4 total: $79,247.46
Step 3: Find the point where the cumulative discounted cash flow exceeds $80,000. This happens slightly after year 4.
Since it reaches about $79,247 by year 4, the discounted payback period is approximately 3.5 to 4 years.