Newport Mining has a lease, with two years remaining, in which it can extract copper ore on a remote Island in Indonesia. The company has completed the exploration phase and estimates that the mine contains 5 million pounds of ore that can be extracted. The ore deposit is particularly rich and contains 37.5% pure copper Newport can contract with a local mining company to develop the property in the coming year at a cost of $ 1.2 million. Three-fourths of the cost of development must be paid immediately and the remainder at the end of one year. Once the site is developed, Newport can contract with a mine operator to extract the ore for a cash payment equal to $ 0.60 per pound of ore processed or $ 1.60 per pound of copper produced. 11 The total cost must be paid in advance at the beginning of the second year of operations. This amounts to a cash payment in one year of $3 million. At the end of one year, Newport can contract to sell the copper ore for the prevailing spot price at that time. However, because the spot price at the end of the year is unknown today, the proceeds from the sale of the refined copper are uncertain. The current price is $ 2.20 per pound, and commodity analysts estimate that it will be $250 a pound at year-end. However, because the price of copper is highly volatile, industry analysts have estimated that it might be as high as S 2.80 or as low as $ 1.20 per pound by the end of the year. The price of copper is expected to stay at $ 2.80 or as low as $ 1.20 throughout the second year. As an alternative to selling the copper at the end-of-year spot price, Newport could sell the production today for the two year forward price of S 2.31 and eliminate completely the uncertainty surrounding the future price of copper. However, this strategy would require that the firm commit today to producing the copper. This, in turn, means that Newport's management would forfeit the option to shut down the plant should the price be less than the cost of producing the copper. Given the risk inherent in exploration, Newport requires a rate of return of 25% for investments at the exploration stage but requires only 15% for investments at the development stage. The risk-free rate of interest is currently only 5%. Build a binomial tree, using the starting value (525m) and a volatility for the project value of 12% to calculate the up and down factors (u and d) and the risk-neutral probabilities (p and 1-P), and then construct a tree in Excel. You can assume that the time horizon of the project is 3 years and the risk-free rate is 5%, but assume the development cost is $25m instead of $23m and that there is no convenience yleid. Once you have built your model, answer these questions: a) What are the up and down factors for the change in project value in each period? What are the risk- neutral probabilities? b) Would you invest in this project if there was no flexibility (l.e., develop now or never)? What would the NPV be in that case? c) What is the value of the project with flexibility (.e., with the option to develop the lease)? d) Use the Black-Scholes equation to calculate the value of the option to develop. How does this compare to your answer from part c)? What assumption are you making about the option to develop when you use this approach? Is this a valid assumption in this case? o) Suppose that there is a 4% lease penalty that accrues to the property owners for every year that you decide to delay(e, essentially a 4% convenience yield that reduces the value of the property). Update your binomial model and calculate the value with the flexibility to develop. (Hint: use the same approach you used for part a) but adjust the values for u and d by subtracting the convenience yield from the volatility, and the value for p by subtracting the convenience yield from r. What is the project value in this case? When would you exercise the option to develop in this case? G A 3 Solution Legend 4 5 B Value given in problem = Formula/Caloulation/Analysis required Qualitative analysis or Short answer required Goal Seek or Solver cell = Crystal Ball Input Crystal Ball Output B 10 11 12 13 14 15 Given VARIATION IN PROBLEM: High price of copper is 2.8 and low price is 12 Ce purity 0.375 De quants 5.000.000 Current price 220 p-high 3 2.80 P-low 1 120 Expected price $ 250 Forward price + 231 Development costs +1.200.000,00 Amount payable today 75.00 Amount duene year 25.00 Extraction contpelbol 1 160 copper) Costo Capitale ploration) 25.00 Cost of capital development 15.00 Raktreetste 5.00 17 18 19 Note: Extraction costs of $1.50 incurred at the beginning of the second year is shined to the end of the second year by multiplying by the risk free This makes all cash flows in the computation consistent with regard to timing of cash flows) 21 23 24 Solution a. Vue of the hedged lease Carta Equivalentoash flows NPV Pakoveral probability isknout probability NPV of project of Newport comes to production today and locko in a forward price 27 28 29 b. Value of the undhedged lase Without any option in the high price scenario In the low priceste Certainty equivalent NPV Use forward price to culoulate the risk neutral probability, ie Forward Ritual Probota H Price U todays' price to celovite the risk neutral probability, le 36 37 39 o, d. Value of the unbedged lease with option In the high price scenario in the low priceste Certaneguver NPV Value of the hedged) without Any real option 42 43 44 45 Value of the hedged) ase with rest option 47 48 43 50 e. Strategy of short positions on 1875mlbs cal options exercise price: $168.mauny 2 call premium-3070/b] and long ng DIGIGL Price $2.80 Price $120 Gainless on options Gaindloss on production Net payoffatt 2 Payoff from sale of option [atta Investment in project Mercantil 51 52 50 54 This Suaregrutin asure profiel IRIS Fale price of option Newport Mining has a lease, with two years remaining, in which it can extract copper ore on a remote Island in Indonesia. The company has completed the exploration phase and estimates that the mine contains 5 million pounds of ore that can be extracted. The ore deposit is particularly rich and contains 37.5% pure copper Newport can contract with a local mining company to develop the property in the coming year at a cost of $ 1.2 million. Three-fourths of the cost of development must be paid immediately and the remainder at the end of one year. Once the site is developed, Newport can contract with a mine operator to extract the ore for a cash payment equal to $ 0.60 per pound of ore processed or $ 1.60 per pound of copper produced. 11 The total cost must be paid in advance at the beginning of the second year of operations. This amounts to a cash payment in one year of $3 million. At the end of one year, Newport can contract to sell the copper ore for the prevailing spot price at that time. However, because the spot price at the end of the year is unknown today, the proceeds from the sale of the refined copper are uncertain. The current price is $ 2.20 per pound, and commodity analysts estimate that it will be $250 a pound at year-end. However, because the price of copper is highly volatile, industry analysts have estimated that it might be as high as S 2.80 or as low as $ 1.20 per pound by the end of the year. The price of copper is expected to stay at $ 2.80 or as low as $ 1.20 throughout the second year. As an alternative to selling the copper at the end-of-year spot price, Newport could sell the production today for the two year forward price of S 2.31 and eliminate completely the uncertainty surrounding the future price of copper. However, this strategy would require that the firm commit today to producing the copper. This, in turn, means that Newport's management would forfeit the option to shut down the plant should the price be less than the cost of producing the copper. Given the risk inherent in exploration, Newport requires a rate of return of 25% for investments at the exploration stage but requires only 15% for investments at the development stage. The risk-free rate of interest is currently only 5%. Build a binomial tree, using the starting value (525m) and a volatility for the project value of 12% to calculate the up and down factors (u and d) and the risk-neutral probabilities (p and 1-P), and then construct a tree in Excel. You can assume that the time horizon of the project is 3 years and the risk-free rate is 5%, but assume the development cost is $25m instead of $23m and that there is no convenience yleid. Once you have built your model, answer these questions: a) What are the up and down factors for the change in project value in each period? What are the risk- neutral probabilities? b) Would you invest in this project if there was no flexibility (l.e., develop now or never)? What would the NPV be in that case? c) What is the value of the project with flexibility (.e., with the option to develop the lease)? d) Use the Black-Scholes equation to calculate the value of the option to develop. How does this compare to your answer from part c)? What assumption are you making about the option to develop when you use this approach? Is this a valid assumption in this case? o) Suppose that there is a 4% lease penalty that accrues to the property owners for every year that you decide to delay(e, essentially a 4% convenience yield that reduces the value of the property). Update your binomial model and calculate the value with the flexibility to develop. (Hint: use the same approach you used for part a) but adjust the values for u and d by subtracting the convenience yield from the volatility, and the value for p by subtracting the convenience yield from r. What is the project value in this case? When would you exercise the option to develop in this case? G A 3 Solution Legend 4 5 B Value given in problem = Formula/Caloulation/Analysis required Qualitative analysis or Short answer required Goal Seek or Solver cell = Crystal Ball Input Crystal Ball Output B 10 11 12 13 14 15 Given VARIATION IN PROBLEM: High price of copper is 2.8 and low price is 12 Ce purity 0.375 De quants 5.000.000 Current price 220 p-high 3 2.80 P-low 1 120 Expected price $ 250 Forward price + 231 Development costs +1.200.000,00 Amount payable today 75.00 Amount duene year 25.00 Extraction contpelbol 1 160 copper) Costo Capitale ploration) 25.00 Cost of capital development 15.00 Raktreetste 5.00 17 18 19 Note: Extraction costs of $1.50 incurred at the beginning of the second year is shined to the end of the second year by multiplying by the risk free This makes all cash flows in the computation consistent with regard to timing of cash flows) 21 23 24 Solution a. Vue of the hedged lease Carta Equivalentoash flows NPV Pakoveral probability isknout probability NPV of project of Newport comes to production today and locko in a forward price 27 28 29 b. Value of the undhedged lase Without any option in the high price scenario In the low priceste Certainty equivalent NPV Use forward price to culoulate the risk neutral probability, ie Forward Ritual Probota H Price U todays' price to celovite the risk neutral probability, le 36 37 39 o, d. Value of the unbedged lease with option In the high price scenario in the low priceste Certaneguver NPV Value of the hedged) without Any real option 42 43 44 45 Value of the hedged) ase with rest option 47 48 43 50 e. Strategy of short positions on 1875mlbs cal options exercise price: $168.mauny 2 call premium-3070/b] and long ng DIGIGL Price $2.80 Price $120 Gainless on options Gaindloss on production Net payoffatt 2 Payoff from sale of option [atta Investment in project Mercantil 51 52 50 54 This Suaregrutin asure profiel IRIS Fale price of option