a. To determine if the purchase of the mine is a good investment using NPV, we need to calculate the net present value of the project.
First, let’s calculate the cash flows for each year:
Year 1: -$2,500,000 (initial investment) Year 2-6: $5,500,000 (annual profit) Year 7: $5,500,000 (annual profit) + $1,500,000 (salvage value) – $4,000,000 (closing cost)
Next, we need to discount these cash flows to their present value using the minimum rate of return of 15%.
Year 1: -$2,500,000 / (1 + 0.15)^1 = -$2,173,913.04 Year 2-6: $5,500,000 / (1 + 0.15)^2 = $3,804,347.83 Year 7: ($5,500,000 + $1,500,000 – $4,000,000) / (1 + 0.15)^7 = $2,225,272.73
Now we can calculate the net present value (NPV) by summing up the present values of the cash flows:
NPV = -$2,173,913.04 + $3,804,347.83 + $3,804,347.83 + $3,804,347.83 + $3,804,347.83 + $3,804,347.83 + $2,225,272.73 = $21,692,153.94
Since the NPV is positive ($21,692,153.94), the purchase of this mine is a good investment as it generates a positive return.
b. The Profitability Index (PVR) is calculated by dividing the present value of the future cash flows by the initial investment.
PVR = Present Value of Future Cash Flows / Initial Investment = ($3,804,347.83 * 5 + $2,225,272.73) / $2,500,000 = $21,692,153.94 / $2,500,000 = 8.68
The PVR for this investment is 8.68.
c. To draw a Cumulative NPV diagram for the project, we plot the cumulative NPV for each year.
Year 1: -$,173913.04 Year 2: -$2,173,913.04 + $3,804,347.83 = $1,630,434.78 Year 3: $1,630,434.78 + $3,804,347.83 = $5,434782.61 Year 4: $5,434782.61 + $3,804347.83 = $9,239130.44 Year 5: $9,239130.44 + $3,804347.83 = $13,043478.27 Year 6: $13,043478.27 + $3,804347.83 = $16,847826.10 Year 7: $16,847826.10 + $2,225272.73 = $19,073098.83
We can now plot these values on a graph with years on the x-axis and cumulative NPV on the y-axis.
d. The Discounted Payback is the time it takes for the cumulative discounted cash flows to equal or exceed the initial investment.
Cumulative NPV in Year 1: -$2,173913.04 Cumulative NPV in Year 2: -$2,173913.04 + $3,804347.83 = $1,630434.78 Cumulative NPV in Year 3: $1,630434.78 + $3,804347.83 = $5,434782.61 Cumulative NPV in Year 4: $5,434782.61 + $3,804347.83 = $9,239130.44 Cumulative NPV in Year 5: $9,239130.44 + $3,804347.83 = $13,043478.27 Cumulative NPV in Year 6: $13,043478.27 + $3,804347.83 = $16,847826.10 Cumulative NPV in Year 7: $16,847826.10 + $2,225272.73 = $19,073098.83
The discounted payback occurs in Year 4 since the cumulative NPV reaches and exceeds the initial investment of -$2,500000 before Year 5.
Therefore, a) The purchase of this mine is a good investment using NPV. b) The PVR is 8.68. c) Please refer to the attached Cumulative NPV diagram for the project. d) The discounted payback is in Year 4.
