Finanzas

Ejercicios de finanzas Ejercios de finanzas 1) For 2006, Treasury bonds with 5-year maturities offered a return about 8.65%; face value of $1,200; and 7.25% coupon rate. What would be the present value of this bond'. The present value of the bond is the present value of the interest and the principal discounted at the offered return of 8.65%. The annual interest is 1,200 X 7.25% = $87. Interest is an annuity and so the present value would be calculated using the PVIFA table PV of interest is 87 X PVIFA (5,8.65%) = 87 X 3.9252 = 341.50 The principal amount is $1,200 and is a lump sum. We use the PVIF table to get the PV factor PV of principal is 1,200 X PVIF (5,8.65%) = 1,200 X 0.6605 = 792.56 The PV of the bond = 341.50 + 792.56 = $1,134.06 2) Mrs. Smith has 20 common stocks from A&T Global Enterprises. If the A&T Global Enterprises’ board directors believe that the price at the end of the year, these common stocks will rise to $57.80 per common stock and the estimate dividend paid would be $2.15 per common stock, what would be the actual price for each common stock if the expected rate of return is 10.75%'. The actual price of the stock now will be the present value of the cash flows from the stock. The cash flows are price of $57.80 at the end of the year and a dividend of $2.15. Total cash flow at the end of the year is $59.95 The discounting rate is the expected return of 10.75% Price now = PV of 59.95 in year 1 = 59.95/(1+10.75%)^1 = $54.13 3) Simon bought a common stock from Monona Air Cleaners Inc. at $35 per share for January 5, 2006 and he expected that the price per share increase by $8 for December 31, 2006. If Monona Air Cleaners will pay $1.75 for dividend per share, what would be the expected rate of return of Simon’s shares. Expected rate of return = (Ending Price – Beginning Price + Dividends)/Beginning Price = (8 + 1.75)/35 = 27.86% The price increases by $8 so the difference of ending and beginning price is $8. 4) Four Possible Outcomes for Portfolio Return Outcome Possible Return Probability Expansion 60% 0.1 Normal 25% 0.5 Recession 5% 0.3 Other -15% 0.1 A) Calculate the following: 1) The Expected Portfolio Return; 2) Variability of Expected Return. 1. Expected return = Sum (Probability X Possible Return) = 0.1 X 60% + 0.5 X 25% + 0.3 X 5% + 0.1 X -15% = 18.5% 2. The variability of expected return = Standard Deviation Standard Deviation = Square root (Sum (Expected return – Possible Return)^2 X Probability) = Square root ((18.5%-60%)^2 X 0.1 + (18.5%-25%)^2X0.5 + (18.5%-5%)^2X0.3 + (18.5%--15%)^2X0.1) = 18.98% 5) Consider the following two-assets: Expected return Expected risk (σ) Company X – Japan 10% 12% Company X – Spain 20% 25% Correlation coefficient (ρJ-S) 0.45 A) Calculate the portfolio risk (expected return and variability) if you decide invest 35% of your profit in Spain and the other in Japan. Expected return = Proportion invested in Spain X Expected return of Spain + Proportion invested in Japan X Expected return of Japan = 0.35 X 20% + 0.65 X 10% = 13.5% Variability = Standard Deviation = Square root(Wa^2*SD(a)^2+Wb^2*SD(b)^2+2*Wa*Wb*SD(a)*Sd(b)*correlation) Wa = Weight of Spain = 35% SD(a) = Standard Deviation of Spain = 25% Wb = Weight of Japan = 1-0.35 = 65% SD(b) = Standard Deviation of Japan = 12% Correlation = 0.45 Variability = Square root (0.35^2 X 25%^2 + 0.65^2 X 12%^2 + 2 X 0.35 X 0.65 X 25% X 12% X 0.45) = 14.10% 6) By 2005 the rate of return of Treasury bill was 5.25% and market rate of return was 9.75%, with .85 of beta for J&M Warehouse’s common stock. What is the expected rate of return of its common stocks'. Using the CAPM equation Expected return = Rf + (Rm-Rf) beta Rf = risk free rate = 5.25% Rm = market return = 9.75% Beta = 0.85 Expected return = 5.25% + (9.75%-5.25%) 0.85 = 9.075% 7) Consider the previous exercise and calculate beta if the market rate of return is 12.25%. Using the CAPM equation Expected return = Rf + (Rm-Rf) beta Rf = risk free rate = 5.25% Rm = market return = 12.25% Beta = 0.85 Expected return = 5.25% + (12.25%-5.25%) 0.85 = 11.2%