M14_MCDO8122_01_ISM_C14

# M14_MCDO8122_01_ISM_C14 - Chapter 14 Real Options n...

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Chapter 14 Real Options n Question 14.1 Note that, in order to get the answers exact, the up and down factors are 0 30 u e . = and 1 . d u = / The discount rate for the cash flows (which we use with real-world probabilities) is 0 07 2 (0 11 0 07) 15%. . + × . - . = The present value of the cash flow in Period 1 is 134 9859 0 532 74 0818 0 468 92 5937. 1 15 . × . + . × . = . . Since the prepaid forward price is 92.5937, the forward price is 92 5937 1 07 99 0753 . × . = . . For total cash flow analysis, as well as a summary, we have the following table: Project 1 Year 1 2 3 Cash Flows 134.9859 182.2119 245.9603 74.0818 100.0000 134.9859 54.8812 74.0818 40.6570 Probabilities 0.5320 0.2830 0.1506 0.4680 0.4980 0.3974 0.2190 0.3496 0.1025 Expected Cash Flow 106.4828 113.3858 120.7364 Discount Factor 1.1500 1.3225 1.5209 Total PV (sum) PV of Cash Flow 92.5937 85.7360 79.3861 257.7158 n Question 14.2 Denote next year’s two possible cash flows as u X and . d X The risk neutral probability is 1 99 0753 74 0818 0 4104. 134 9859 74 0818 d u d F X p X X - . - . = = = . - . - . The present value of the cash flow in Period 1 is

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165 McDonald • Fundamentals of Derivatives Markets 134 9859 0 4104 74 0818 5896 92 5937. 1 07 . × . + . ×. = . . Using risk neutral pricing, the forward price is the risk neutral expected value 1 134 9859 74 0818(1 ) 99 0753 F p p = . + . - = . Note that this is a circular argument, for this is how p is derived. We have the total value and a summary in the following table: Year 1 2 3 Cash Flows 134.9859 182.2119 245.9603 74.0818 100.0000 134.9859 54.8812 74.0818 40.6570 Risk Neutral 0.4104 0.1684 0.0691 Probabilities 0.5896 0.4839 0.2979 0.3477 0.4280 0.2050 Expected Cash Flow 99.0753 98.1591 97.2514 Discount Factor 1.0700 1.1449 1.2250 Total PV (sum) PV of Cash Flow 92.5937 85.7360 79.3861 257.7158 n Question 14.3 Using risk neutral methodology, we can simply repeat Problem 14.2 with the new cash flows. We have the following: Year 1 2 3 Cash Flows 44.9859 92.2119 155.9603 –15.9182 10.0000 44.9859 –35.1188 –15.9182 –49.3430 Risk Neutral 0.4104 0.1684 0.0691 Probabilities 0.5896 0.4839 0.2979 0.3477 0.4280 0.2050 Risk neutral expected value 9.0753 8.1591 7.2514 Discount Factor 1.0700 1.1449 1.2250 Total PV (sum) PV of Cash Flow 8.4816 7.1265 5.9193 21.5274 Note that if we tried using the traditional DCF approach as in Problem 14.1, we’d have to determine a new risk adjusted discount rate for each period due to the different leverage. Alternatively, we could subtract the present value of \$90 for all three years from the answers to Problems 14.1 and 14.2. Specifically,
Chapter 14 Real Options 166 2 3 1 1 1 Project 2 value 257 7158 90 21 5274.

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