Stone Inc. is evaluating a project with an initial cost of $8,450. Cash inflows are expected to be $1,000, $1,000 and $10,000 in the three years over which the project will produce cash flows. If the discount rate is 13%, what is the net present value of the project?
Between 0 and $400
To calculate the net present value (NPV) of the project, we need to discount the cash inflows back to their present value and subtract the initial cost.
Step 1: Calculate the present value of each cash inflow:
PV1 = $1,000 / (1 + 0.13)^1
PV2 = $1,000 / (1 + 0.13)^2
PV3 = $10,000 / (1 + 0.13)^3
Step 2: Add up the present values of the cash inflows:
PV_total = PV1 + PV2 + PV3
Step 3: Calculate the net present value by subtracting the initial cost:
NPV = PV_total - $8,450
Now let's calculate each step:
PV1 = $1,000 / (1 + 0.13)^1 = $884.96
PV2 = $1,000 / (1 + 0.13)^2 = $783.98
PV3 = $10,000 / (1 + 0.13)^3 = $7,092.81
PV_total = PV1 + PV2 + PV3 = $884.96 + $783.98 + $7,092.81 = $8,761.75
NPV = PV_total - $8,450 = $8,761.75 - $8,450 = $311.75
Therefore, the net present value (NPV) of the project is $311.75.
To calculate the net present value (NPV) of a project, you need to discount the cash inflows by the discount rate and subtract the initial cost of the project.
The formula for NPV is:
NPV = (Cash inflow year 1 / (1 + Discount rate)^1) + (Cash inflow year 2 / (1 + Discount rate)^2) + ... + (Cash inflow year N / (1 + Discount rate)^N) - Initial cost
In this case, let's calculate the NPV of the project.
1. Discount the cash inflows for each year:
- Cash inflow year 1 = $1,000 / (1 + 0.13)^1 ≈ $884.96
- Cash inflow year 2 = $1,000 / (1 + 0.13)^2 ≈ $782.81
- Cash inflow year 3 = $10,000 / (1 + 0.13)^3 ≈ $7,910.79
2. Calculate the NPV by summing the discounted cash inflows and subtracting the initial cost:
NPV = $884.96 + $782.81 + $7,910.79 - $8,450
So, the net present value of the project is:
NPV = -$871.44
The negative NPV suggests that the project is not financially attractive as it is expected to generate less value than its initial cost, and implies a net loss.