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1. In December 2008, your company faces a decision to bid for a eightyear lease on a coal mine offered by the government. The lease gives the winner of the auction the right to actually develop the mine for two years. Once development takes place (if ever at all), the leaseholder can extract 25 million tons of coal per year for exactly four years with the xed extraction cost of $4 per ton. Development of the mine costs $50 million. There are reclamation costs of $2 million at the end of the life of the mine. If development did not take place by December 2012 (four years down the road), then the lease would end at that time. At the time of the auction, the spot price of coal was $4.58. The riskfree rate of interest is 6% per year and the net convenience yield on coal is 3.5% per year, both of which are constant and compounded continuously. The standard deviation of log changes in coal prices is 15% per year. Development costs are depreciated on a straightline basis over four years. There are no net working capital requirements. The marginal tax rate of your company is 40%. There is no ination. (a) Suppose that your company commits to an immediate development of the mine. What is the maximum amount that your company should bid in the auction for the lease? (b) Build a fourstep binomial tree with a time step set equal to one year, taking the adjustments of the convenience yield into account. Calculate the value of the lease by the real options approach. (c) Build a fourstep binomial tree with a time step set equal to one year, ignoring the convenience yield. Calculate the value of the lease by the real options approach. (d) Are the values in parts (b) and (c) dierent? Why and why not? 4. A 15-year, y.25% coupon Dona, priced at by8U.UU. (Note: all the above bonds are non-callable, investment-grade, nonconvertible, annual coupon bonds). Questions: a). Given the information provided, find the current yield and the promised yield-to-maturity for each bond in her portfolio. b). Given the following Macaulay durations: Bond 1: 8.07 years Bond 3: 6.89 years Bond 4: 8.41 years and your own calculation for the Macaulay duration for Bond 2, calculate the modified durations of each bond in the portfolio. c). Indicate how each bond will change if rates were to rise by 75 basis-points. How each bond will change if rates were to fall by 75 basis-points? d). Find the duration of her entire bond portfolio. Given the 7-year target that she has set, would you consider this an immunized portfolio? Explain. e). Using 1 or more of the 4 bonds, put together an $200,000 immunized portfolio for Grace.Grace 5. is extremely Successful in managing her own investment portfolios. Grace has been playing with the idea of immunizing her trond portfolio. She will like to cash out her bond portfolio in 3" years and use the proceeds to buy a vacation home in Nova Scotia. To do this she intends to use $2, she now has invested in the flowing corporate bonds (she currently has $5D, invested in each one]: 1.15. 12yearIr ?.5% coupon bond currently priced at $895.. 1A iiiyear, zerocoupon bond priced at $495.[i. 3.15s iiiyear, 13% coupon bond priced at $1B3. 4. A 15yearF 9.25% coupon bond, priced at $9Eli]. (Note: all the above bonds are noncallable, investmentgrade, nonconvertible, annual coupon bonds]. Questions: a]. Given the information provided, find the current yield and the promised yieldtomaturity for each bond in her portfolio. ti]. Given the following Macaulay durations: Bond 1: 8.11]? years Bond 3: 6.89 years Bond 4: 8.41 years I I I a' f LI I. I I n.' r I'll IF\\ I I I. II :I'r