Final answer:
The discounted payback period for the project is 4 years, and the project will be accepted based on the criteria.
Step-by-step explanation:
The discounted payback period measures the time required for a project to recoup the initial investment, taking into account the time value of money. To calculate it, we need to find the present value of each cash flow using the discount rate. In this case, the discount rate is 6%.
First, we find the present value of each cash flow:
- Year 1: $14,000 / (1 + 0.06) = $13,207.55
- Year 2: $20,000 / (1 + 0.06)^2 = $17,694.21
- Year 3: $15,000 / (1 + 0.06)^3 = $12,010.19
- Year 4: $15,000 / (1 + 0.06)^4 = $10,727.92
- Year 5: $20,000 / (1 + 0.06)^5 = $14,910.82
Next, we calculate the discounted cumulative cash flow for each year:
- Year 1: $13,207.55
- Year 2: $13,207.55 + $17,694.21 = $30,901.76
- Year 3: $30,901.76 + $12,010.19 = $42,911.95
- Year 4: $42,911.95 + $10,727.92 = $53,639.87
- Year 5: $53,639.87 + $14,910.82 = $68,550.69
The discounted payback period is the earliest year in which the discounted cumulative cash flow surpasses the initial investment. In this case, it is year 4 since the cumulative cash flow at the end of year 4 ($53,639.87) is greater than the initial investment ($40,000).
Therefore, the discounted payback period is 4 years. Since it is less than 4 years, the project will be accepted.