Managerial Decision Modeling
1. StillWater Mining Company
a)
Interest Rate 12%
Price per ounce $ 1,500.00
Cost per ounce $ 400.00
Total ounces a year 10,000
Profit per ounce $ 1,100
Revenue per year $ 15,000,000.00
Cost per year $ 4,000,000.00
Profit per year $ 11,000,000.00 Every year for the next 10 years, the firm earns a profit of $11 Million. The cash flow (in $ Million) is shown below:
Year T T+1 T+2 T+3 T+4 T+5 T+6 T+7 T+8 T+9
Profit 11 11 11 11 11 11 11 11 11 11
Using NPV formula, we find NPV=$62,152,453.31
b) The NPVs (in $ Million) for variations in profit per ounce and interest rate are shown in table below: 8% 9% 10% 11% 12% 13% 14% 15%
$500 33.55 32.09 30.72 29.45 28.25 27.13 26.08 25.09
$600 40.26 38.51 36.86 35.34 33.9 32.56 31.3 30.11
$700 46.97 44.92 43.01 41.22 39.55 37.98 36.51 35.13
$800 53.68 51.34 49.16 47.11 45.2 43.41 41.73 40.15
$900 60.39 57.76 55.3 53 50.85 48.84 46.95 45.17
$1000 67.1 64.18 61.45 58.89 56.5 54.26 52.16 50.19
$1100 73.81 70.59 67.59 64.78 62.15 59.69 57.38 55.21
$1200 80.52 77.01 73.74 70.67 67.8 65.12 62.59 60.23
$1300 87.23 83.43 79.88 76.56 73.45 70.54 67.81 65.24
$1400 93.94 89.85 86.02 82.45 79.1 75.97 73.03 70.26
$1500 100.65 96.27 92.17 88.34 84.75 81.39 78.24 75.28
2. Savings for Future Expenditures
Interest Rate 8%
Current College Tuition $ 40,000
Annual growth rate of tuition 5%
Time of first college payment (yrs) 6
Time of last college payment (yrs) 9
Annual growth rate of investment 6%
Time of last investment (yrs) 9
a) The cash flow of tuition (in dollars) is shown below:
Year 0 1 2 3 4 5 6 7 8 9
Tuition - - - - - - 53,604 56,284 59,098 62,053
To cover the tuition expenses she has to invest something today which if it grows at 6% every year for 9 years, provides the same NPV as the NPV of the tuition payment. Thus the present value at 0 is the initial investment. Using NPV and cash flow formula, where C_i is cash flow of tuition, and A initial investment:
NPV(8%,9)=∑_(i=0)^9▒〖
a)
Interest Rate 12%
Price per ounce $ 1,500.00
Cost per ounce $ 400.00
Total ounces a year 10,000
Profit per ounce $ 1,100
Revenue per year $ 15,000,000.00
Cost per year $ 4,000,000.00
Profit per year $ 11,000,000.00 Every year for the next 10 years, the firm earns a profit of $11 Million. The cash flow (in $ Million) is shown below:
Year T T+1 T+2 T+3 T+4 T+5 T+6 T+7 T+8 T+9
Profit 11 11 11 11 11 11 11 11 11 11
Using NPV formula, we find NPV=$62,152,453.31
b) The NPVs (in $ Million) for variations in profit per ounce and interest rate are shown in table below: 8% 9% 10% 11% 12% 13% 14% 15%
$500 33.55 32.09 30.72 29.45 28.25 27.13 26.08 25.09
$600 40.26 38.51 36.86 35.34 33.9 32.56 31.3 30.11
$700 46.97 44.92 43.01 41.22 39.55 37.98 36.51 35.13
$800 53.68 51.34 49.16 47.11 45.2 43.41 41.73 40.15
$900 60.39 57.76 55.3 53 50.85 48.84 46.95 45.17
$1000 67.1 64.18 61.45 58.89 56.5 54.26 52.16 50.19
$1100 73.81 70.59 67.59 64.78 62.15 59.69 57.38 55.21
$1200 80.52 77.01 73.74 70.67 67.8 65.12 62.59 60.23
$1300 87.23 83.43 79.88 76.56 73.45 70.54 67.81 65.24
$1400 93.94 89.85 86.02 82.45 79.1 75.97 73.03 70.26
$1500 100.65 96.27 92.17 88.34 84.75 81.39 78.24 75.28
2. Savings for Future Expenditures
Interest Rate 8%
Current College Tuition $ 40,000
Annual growth rate of tuition 5%
Time of first college payment (yrs) 6
Time of last college payment (yrs) 9
Annual growth rate of investment 6%
Time of last investment (yrs) 9
a) The cash flow of tuition (in dollars) is shown below:
Year 0 1 2 3 4 5 6 7 8 9
Tuition - - - - - - 53,604 56,284 59,098 62,053
To cover the tuition expenses she has to invest something today which if it grows at 6% every year for 9 years, provides the same NPV as the NPV of the tuition payment. Thus the present value at 0 is the initial investment. Using NPV and cash flow formula, where C_i is cash flow of tuition, and A initial investment:
NPV(8%,9)=∑_(i=0)^9▒〖