Company A wishes to purchase a small operating mine, which has a remaining production life of 5 years, from Company B. Company B's selling price for the mine is $10,000,000. Company A also plans to invest $2,500,000 in upgrading the mine and its infrastructure in the first year, and no production will occur during the first year. Based on recent history and future projections, the mine is expected to generate an annual, before-tax profit of $5,500,000 for its remaining life, after the upgrades and starting in year 2. At the end of mine's production life, it is expected to cost $4,000,000 to close the mine, which will be incurred at the end of the 7th year. The salvage value of the mine's equipment is expected to be $1,500,000, which will also occur at the end of the 7th year. Company A requires
a minimum rate of return of 15%.
a. Determine if the purchase of this mine is a good investment using NPV. (20 pts)
b. What is the PVR (10 pts)
c. Draw a Cumulative NPV diagram for the project (30 pts)
d. What is the Discounted Payback? (10 pts)
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To determine if the purchase of the mine is a good investment using NPV, we will calculate the Net Present Value (NPV) of the cash flows associated with the project.
Step 1: Calculate the cash flows.
Year 0:
Initial Investment = -$10,000,000
Year 1:
Upgrades and Infrastructure Investment = -$2,500,000
Years 2-6:
Profit per year = $5,500,000
Year 7:
Closing Costs = -$4,000,000
Salvage Value = $1,500,000
Step 2: Calculate the present value of each cash flow.
PV of Initial Investment = -$10,000,000 / (1 + 0.15)^0 = -$10,000,000
PV of Upgrades and Infrastructure Investment = -$2,500,000 / (1 + 0.15)^1 = -$2,173,913.04
PV of Profit per year (Years 2-6) = $5,500,000 / (1 + 0.15)^2 + $5,500,000 / (1 + 0.15)^3 + $5,500,000 / (1 + 0.15)^4 + $5,500,000 / (1 + 0.15)^5 + $5,500,000 / (1 + 0.15)^6 = $5,500,000 / 1.3221 + $5,500,000 / 1.5281 + $5,500,000 / 1.7563 + $5,500,000 / 2.0175 + $5,500,000 / 2.318 = $4,159,706.54 + $3,599,520.95 + $3,126,359.36 + $2,698,522.46 + $2,313,034.45 = $16,897,143.76
PV of Closing Costs = -$4,000,000 / (1 + 0.15)^7 = -$1,557,275.93
PV of Salvage Value = $1,500,000 / (1 + 0.15)^7 = $507,246.38
Step 3: Calculate the NPV.
NPV = PV of cash inflows - PV of cash outflows
NPV = PV of Profit per year + PV of Salvage Value - PV of Initial Investment - PV of Upgrades and Infrastructure Investment - PV of Closing Costs
NPV = $16,897,143.76 + $507,246.38 - $10,000,000 - $2,173,913.04 - $1,557,275.93
NPV = $4,673,201.17
Step 4: Interpret the NPV.
Based on the calculation, the NPV is $4,673,201.17. A positive NPV indicates that the project is expected to generate more cash inflows than outflows, indicating that the purchase of the mine is a good investment.
b. PVR (Profitability Index) is calculated by dividing the present value of future cash flows by the initial investment.
PVR = (PV of Profit per year + PV of Salvage Value) / (PV of Initial Investment + PV of Upgrades and Infrastructure Investment)
PVR = ($16,897,143.76 + $507,246.38) / ($10,000,000 + $2,173,913.04)
PVR = $17,404,390.14 / $12,173,913.04
PVR = 1.43
c. Cumulative NPV diagram:
| Year | Cash Flow | PV of Cash Flow | Cumulative NPV |
|:--------:|:---------------:|:-----------------:|:-------------:|
| 0 | -$10,000,000 | -$10,000,000 | -$10,000,000 |
| 1 | -$2,500,000 | -$2,173,913.04 | -$12,173,913 |
| 2 | $5,500,000 | $4,159,706.54 | -$8,014,206 |
| 3 | $5,500,000 | $3,599,520.95 | -$4,414,685 |
| 4 | $5,500,000 | $3,126,359.36 | -$1,288,325 |
| 5 | $5,500,000 | $2,698,522.46 | $1,410,197 |
| 6 | $5,500,000 | $2,313,034.45 | $3,723,232 |
| 7 | -$2,500,000 | -$1,557,275.93 | $2,165,956 |
| 7 | $1,500,000 | $507,246.38 | $2,673,202 |
d. Discounted Payback is the number of years it takes for the cumulative discounted cash inflows to equal or exceed the initial investment.
Initial Investment = $10,000,000
Discounted Cash Flow Year 1 = -$2,173,913.04
Discounted Cash Flow Year 2 = $4,159,706.54
Discounted Cash Flow Year 3 = $3,599,520.95
Discounted Cash Flow Year 4 = $3,126,359.36
Discounted Cash Flow Year 5 = $2,698,522.46
Discounted Cash Flow Year 6 = $2,313,034.45
Discounted Cash Flow Year 7 = $2,165,956
Total discounted cash inflow after Year 7 = $2,165,956
Since the total discounted cash inflow after Year 7 is less than the initial investment, the Discounted Payback period cannot be calculated.
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