## Finance order. Montecallo Analysis

MONTE CARLO PRACTICE QUESTION Company WTF will manufacture 1,000,000 copper widgets each year for the next two years. Each widget requires 1kg of copper. The required copper will be purchased at the start of each year (i.e., 1,000,000 kg of copper will be purchased at time-0, and 1,000,000 kg of copper will be purchased at time-1). The current (time-0) price of copper is 0 C ï€½ $10 / kg . The future price of copper is modelled by 2 0.3 0.145 0.3 2 1 , ~ (0,1) tz C Ce z N tt t ïƒ¦ ïƒ¶ ïƒ§ ïƒ· ï€ ï€« ïƒ¨ ïƒ¸ ï€½ ï€ , The current market price for copper widgets is 0 P ï€½ $15 each. The future market price for copper widgets is modelled by 2 0.2 0.3 0.145 0.3 2 1 1 1 , ~ (0,1) 2 wt t tt t t P PP e w N C ï€ ïƒ¦ ïƒ¶ ïƒ§ ïƒ· ï€ ï€« ï€ ïƒ¨ ïƒ¸ ï€ ï€ ïƒ¦ ïƒ¶ ï€½ ïƒ§ ïƒ· ïƒ¨ ïƒ¸ . The manufacturing process requires skilled technicians who earn an annual bonus dependant on the margin of the widget price over the copper price. Using the MS Excel “IF” function, the annual labour cost is modelled by L PC P C t tt t t ï€½ ï€«ï€¾ ï€ 3000000 IF 2 ,300000*( 2* ),0 ï€¨ ï€© . Annual fixed costs are $3,000,000. Upfront investment in plant and equipment is $2,000,000. Ignore taxes. The cost of capital is 13% per annum. a) Using a projection of the expected copper price, 0.145 E[ ] C Ce t t ï€½ ï€1 , and the expected widget price, 0.2 0.145 E[ ] ( / (2 )) P PP C e t tt t 11 1 ï€ ï€½ ï€ï€ ï€ , calculate the project NPV. b) Using Monte Carlo analysis with 10,000 simulations, calculate the project NPV. c) Present a histogram of the 10,000 Monte Carlo scenario NPV values. d) Present a scatter plot of the 10,000 Monte Carlo scenario NPV values versus the P C 2 1 ï€ state-of-the-world outcomes. e) Explain the difference between your answers for (a) and (b).

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