Should Pickins Mining take the contract and open the mine? Explain in detail, showing calculations, so the instructor can follow your thoughts.

Pickins Mining’s case was solved by the calculation of the payback time, profitability index and net present value.

Payback period: The time taken to return the original investment and repay it is called the payback period.

For the calculation of payback periods, it is necessary to first determine cumulative cash flows over each year.

• Year 1: Cash flow = (770,000 x \$82) – (770,000 x \$26) – \$3.9 million – (\$65 million x 0.05) = \$14.8 million
• Year 2: Cash flow = (830,000 x \$82) – (830,000 x \$26) – \$3.9 million = \$19.1 million
• Year 3: Cash flow = (850,000 x \$82) – (850,000 x \$26) – \$3.9 million = \$19.7 million
• Year 4: Cash flow = (740,000 x \$82) – (740,000 x \$26) – \$3.9 million = \$16.3 million
• Year 5: Cashflow = -\$5.5million (costs of reclamation).
• Year 6 Cashflow = -\$7.5 Million (tax deductions for charitable expenses)

You can calculate the payback time by multiplying the initial investment and the annual cashflow.

Initial investment = \$5.4 million + \$46 million = \$51.4 million

Payback period: \$51.4million / \$14.8million = 3.47 years

Profitability index: This is the measure of how profitable an investment is. The profitability index calculates the value of future cash flows multiplied by the initial investment.

For profitability index calculations, it is necessary to first determine the value of future cash flows and use the required rate return of 12.

• Year 1: Cashflow = \$14.8million / (1+0.12) 1 = \$12.2 million
• Year 2 Cashflow = \$19.1 Million / (1+0.12) 2 = \$16.4 Million
• Year 3, Cash flow = \$19.7 Million / (1+0.12)3 = 16.7 Million
• Year 4: Cashflow = \$16.3 Million / (1+0.12)4 = 13.5 million
• Year 5 Cashflow = -\$5.5 Million / (1+0.12)5 = \$-4.1 Million
• Year 6: Cash flow = USD7.5million / (1+0.12)6 = USD5.3million

Calculating the profitability index involves adding future cash flow value to your initial investment and subtracting it from the present value.

Profitability index = (\$13.2 million + \$16.4 million + \$16.7 million + \$13.5 million – \$4.1 million – \$5.3 million) / \$51.4 million = 0.9

Net present Value: This is the value of the future cash flows at a discounted rate that takes into account the return required. It can be subtracted from your initial investment.

Net present value = (\$13.2 million + \$16.4 million + \$16.7 million + \$13.5 million – \$4.1 million – \$5.3 million) – \$51.4 million = -\$4.6 million

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