Final answer:
The profitability index for the project is calculated at 0.9985, which is less than 1. Therefore, according to the profitability index rule, the project should not be accepted since the present value of future cash inflows is not high enough to cover the initial investment when discounted at a 14% rate.
Step-by-step explanation:
The question asks whether a project with an upfront cost of $27,700 and cash inflows of $11,800 in year 1 and $24,600 in year 3 should be accepted based on the profitability index rule given a discount rate of 14 percent. To answer this, we need to calculate the present value of the cash inflows and then compute the profitability index.
- First, we discount the cash inflow of year 1: $11,800 / (1 + 0.14)1 = $10,351.75
- Next, we discount the cash inflow of year 3: $24,600 / (1 + 0.14)3 = $17,306.17
- We add these two present values: $10,351.75 + $17,306.17 = $27,657.92
- To find the profitability index, we divide the total present value of cash inflows by the cost of the investment: $27,657.92 / $27,700 = 0.9985
Since the profitability index is less than 1, the rule suggests the project should not be accepted.
For comparison, let's consider a two-year bond with an 8% interest rate issued at $3,000. The bond pays $240 each year in interest. Calculating the present value of these payments given different discount rates shows how discounting affects the present value of future cash inflows.