Question

An investment project costs 10,000 and has annual cash flows of2,880 for six years. What is the discounted payback period if the discount rate is 0 percent?

Answer 1

The discounted payback period is the length of time it takes for the present discounted value of the cash flows from an investment project to equal or exceed the initial cost of the project. By calculating the present value of each cash flow and summing them until the total reaches or exceeds the initial cost, we can determine the discounted payback period. In this case, the discounted payback period is 5 years.

Step-by-step explanation:

The discounted payback period is the length of time it takes for the present discounted value of the cash flows from an investment project to equal or exceed the initial cost of the project. To calculate the discounted payback period, we need to calculate the present value of each cash flow and sum them until the total reaches or exceeds the initial cost of the investment project.

First, let's calculate the present value of each cash flow using the discount rate of 0%:

1. Year 1: $2,880 / (1 + 0%) ^ 1 = $2,880
2. Year 2: $2,880 / (1 + 0%) ^ 2 = $2,880
3. Year 3: $2,880 / (1 + 0%) ^ 3 = $2,880
4. Year 4: $2,880 / (1 + 0%) ^ 4 = $2,880
5. Year 5: $2,880 / (1 + 0%) ^ 5 = $2,880
6. Year 6: $2,880 / (1 + 0%) ^ 6 = $2,880

Next, we add up the present values of each cash flow until the total reaches or exceeds the initial cost of the investment project:

• Year 1: $2,880
• Year 2: $2,880 + $2,880 = $5,760
• Year 3: $5,760 + $2,880 = $8,640
• Year 4: $8,640 + $2,880 = $11,520
• Year 5: $11,520 + $2,880 = $14,400
• Year 6: $14,400 + $2,880 = $17,280

The discounted payback period is the year in which the total present value reaches or exceeds the initial cost of the investment project. In this case, the discounted payback period is Year 5 because the total present value reaches $14,400, which is greater than the initial cost of $10,000. Therefore, the discounted payback period is 5 years.