1. Q1 The discount rate for the value of the option is the expected return on the stock: E(s) =r=0.02+3(0.1-0.02)=0.26 The call option has a positive value if (up, up) occurs. This happens with probability: Pr(up,up)=0.6^2=0.36 The present value of the option is: PV=0.36[50(1.15^2)-55]/(1.26 2 )=2.52

2. Q2 The present value of the cost for r=EAIR=(1.005)^12-1=0.061678 is: PV=80/(1+r) 21 +80/(1+r) 22 +80/(1+r) 23 +80/(1+r) 24 +90/(1+r) 24 +90/(1+r) 25 +90/(1+r) 26 +90/(1+r) 27 =161.84 The present value of the deposits for the same discount rate: PV=100/(1+r) 2 +x/(1+r) 10 Set the present value of the cost equal to the value of the deposits and solve of x 161.84=88.19+x/(1+r) 10 X=133,052

3. Q3 Calculate the present value of the cash value of dividends for each year and add them together: PV 1/2 =5.5/1.16 1/2 + PV 3/2 =5.5(1.15)/1.16 3/2 + PV 5/2 =5.5(1.15 )2/ 1.16 5/2 + PV 7/2 =5.5(1.15) 3 /1.16 7/2 PV 9/2 =5.5(1.15 )4/ 1.16 9/2 + PV 11/2 =5.5(1.15 )5/ 1.16 11/2 + PV 13/2 =5.5(1.15 )5/ (0.16*1.16 11/2 ) =60.55

4. Q4 You can find the covariance of the portfolio by multiplying the correlation by the standard deviations of both stocks: Cov(x,y)=0.04*0.12*0.18=0.000864 Then use the formula for the portfolio variance and take the square root to find the portfolio’s standard deviation: Var p =0.8 2 *0.12 2 +2*0.8*0.2*0.000864+0.2 2 *0.18 2 =0.010788 Std=(0.010788) 1/2 =0.10387

5. Q5 Use the weighted cost of capital equation from Modigliani and Miller (1958) proposition II: R S =0.12+0.4/0.6(0.12-0.3)=0.18

6. Q6 Use the condition that IRR is the discount rate (r) that would make the projects NPV=0. Then solve for r using the quadratic formula. 1.Let x=1+r NPV=0 -500-600/x+1500/x 2 =0 5x 2 +6x-15=0 2. Using the quadratic formula x is either x 1 = 1.233 x 2 =-2.34 3.Ignore any negative rates of return r=x 1 -1=0.23

7. Q7 The yield on a bond is the discount rate (r) that would make the NPV of the bond equal to zero. Use that condition and solve for r using the quadratic formula. 1.Let x=1+r NPV=0 1320/x 2 +120/x+120-800=0 17x 2 -3x-33=0 2. Using the quadratic formula x is either x 1 = 1.484 x 2 =-1.307 3.Ignore any negative rates of return 4.Currently r is the 6 month discount rate. Transform it to an effective annual interest rate: EAIR=(x 1 ) 2 -1=0.203 = 20.3%