《财务管理：理论与实践》（Brigham）的教学PPTCh 15 Show.ppt

Financial Option Analysis: Inputs X = exercise price = cost of implement project = $75 million. kRF = risk-free rate = 6%. t = time to maturity = 3 years. Estimating P: First, find the value of future CFs at exercise year. Example: $111.91 = $45/1.1 + $45/1.12 + $45/1.13. See Ch 15 Mini Case.xls for calculations. Now find the expected PV at the current date, 2001. PV2001=PV of Exp. PV2004 = [(0.3* $111.91) +(0.4*$74.61) +(0.3*$37.3)]/1.13 = $56.05. See Ch 15 Mini Case.xls for calculations. The Input for P in the Black-Scholes Model The input for price is the present value of the project’s expected future cash flows. Based on the previous slides, P = $56.05. Estimating s2: Find Returns from the Present until the Option Expires Example: 25.9% = ($111.91/$56.05)(1/3) - 1. See Ch 15 Mini Case.xls for calculations. E(Ret.)=0.3(0.259)+0.4(0.10)+0.3(-0.127) E(Ret.)= 0.080 = 8.0%. ?2 = 0.3(0.259-0.08)2 + 0.4(0.10-0.08)2 + 0.3(-0.1275-0.08)2 ?2 = 0.023 = 2.3%. Use these scenarios, with their given probabilities, to find the expected return and variance of return. Why is s2 so much lower than in the investment timing example? s2 has fallen, because the dispersion of cash flows for replication is the same as for the original project, even though it begins three years later. This means the rate of return for the replication is less volatile. We will do sensitivity analysis later. Estimating s2 with the Indirect Method From earlier slides, we know the value of the project for each scenario at the expiration date. E(PV)=.3($111.91)+.4($74.61)+.3($37.3) E(PV)= $74.61. Use these scenarios, with their given probabilities, to find the project’s expected PV and ?PV. ?PV = [.3($111.91-$74.61)2 + .4($74.61-$74.61)2 + .3($37.30-$74.61)2]1/2 ?PV = $28.90. Now use the indirect formula to estimate ?2. CVPV = $28.90 /$74.61 = 0.39. The option expires in 3 years, t=3. Use the Black-Scholes Model: P = $56.06; X = $75; kRF = 6%;t = 3 years: ?2 = 0.047