ECN 134: Probabilities, NPV & Budgets with Normal Distribution - Solution Key - Prof. Klau, Assignments of Economics

Download ECN 134: Probabilities, NPV & Budgets with Normal Distribution - Solution Key - Prof. Klau and more Assignments Economics in PDF only on Docsity! ECN 134 SOLUTION KEY #1 1. (i) μ = .06 and σ = .10 : Find P (X < 0) = P ¡ Z < 0−.06 .10 ¢ = P (Z < −.6) . Turning to the normal tables we find that the probability associated with the critical value of −.6 is 27.43%. That is 27.43% of the time, and thus approximately 13 years , the return on corporate bonds was less than 0%. (ii) μ = .11 and σ = .16 : Find out what the rate of return is for the worst five years of the S&P. That is: what was the rate of return for the worst 10% of the last 48 years. We must solve for a : .10 = P (X < a) = P ¡ Z < a−.11 .16 ¢ . Turning to the normal tables we find that the critical value leading to a .10 outcome is −1.28 . Thus find a such that −1.28 = a− .11 .16 a = −.09 This tells us (approximately) that in the worst 5 years of the last 48 years the S&P lost 9% or more . 2. r = 0.12. i) NPV = -75,000 + 140,000/(1+r)5 = -75,000 + 79,439.76 = 4,439.76 . ii) Yes , since Venkatesh can borrow against the return from selling the land. iii) Keeping future consumption unchanged means Venkatesh borrows against the entirety of his return, i.e., he borrows 140,000/(1+0.12)5 = 79,439.76 at t=0. So C0=Y0 - 75,000 + 79,439.76 = Y0 + 4439.76. The effect on C0 is 4439.76 = NPV. iv) Venkatesh is willing to pay up to the PV of his returns on the land, or $ 79,439.8 . 1