1. From the information below, calculate the impact of discount rate changes on the present-value break-even point. Fixed costs are $2500 per year. The initial investment is $2000.

Variable costs: $8/unit

Depreciation: $500/year

Price: $25/unit

Initial Discount rate: 10%

Project life: 4 years.

Tax rate: 34%

If the discount rate were 15% or 5% what would be the present-value break-even points?

  • PV Break-even(10%) = 630.94 + (2500*.66-500*.34)/(25-8)(.66) = 188.14 (EAC@10%=630.94)
  • PV Break-even(15%) = 700.53 + (2500*.66-500*.34)/(25-8)(.66) = 194.34
  • PV Break-even(5%) = 564.02 + (2500*.66-500*.34)/(25-8)(.66) = 182.17

Not very sensitive; a 50% increase or decrease in the discount rate causes only a 3.3% increase in break-even units or a 3.2% decrease in break-even units necessary respectively.

2.

Returns (%)

Year / X / Y
1 / 15 / 18
2 / 4 / -3
3 / -9 / -10
4 / 8 / 12
5 / 9 / 5
  1. What is the mean return for asset X? For asset Y? 5.4%, 4.5%
  2. What is the five-year holding period return for asset X? For asset Y?

[(1.15)(1.04)(.91)(1.08)(1.09)]-1=.2812=28.1%; 21.14%

  1. What is the variance of the return for asset X? For asset Y?

Var(X)=(.032120/4)=.00803; Var(Y)=.012630 (.032120 is the squared deviations)

  1. What is the standard deviation of the return for asset X? For asset Y?

Square root of the variance: SD(X)=.089610=8.96%; SD(Y)=.112383=11.24%

  1. What is the covariance between the returns for assets X and Y?

Cov(Rx,Ry)=(.03720/4)=.009255 (.03720 is the product of the deviations)

  1. What is the correlation between the returns for assets X and Y?

Corr(Rx,Ry)=Cov(Rx,Ry)/xy=(.009255)/(.08961)(.112383)=.9190

  1. Assume that the three stocks listed below plot on the SML. The standard deviation for the market is 22%. What is the equation for the SML? Fill in the missing correlations and betas in the table.

Security / E(Ri) / Var(Ri) / Corr(Ri,Rm) / Betai
1 / .07 / .0225
2 / .14 / .0400 / .80
3 / .10 / .1225 / .60
4 / .07 / .0000

Stock 4 has a 7%expected return and zero variance; thus the risk-free rate is 7%. The correlation of Security with the market is zero since the return for Security 4 does not vary. The beta for Security 4 is also zero.

Security 1 has the same 7% return, so Security 1 must have a zero beta and thus zero correlation with the market.

Security 2 has a beta of .8. A portfolio invested 80% in the market and 20% in the risk-free asset also has a beta of .8 and must have a return of 14%. This implies a market return of .8[E(Rm)]+.2(7%)=14%, so the market expected return must be 15.75%. Based on these numbers, the SML equation is: E(Ri)=7%+8.75%i.

Or use the information on Security 2 and the SML equation: .14=.07+(.80)(Rm-.07)

Solve for Rm.

Security 3 has an expected return of 10%, so its beta must be [(.10-.07)/.0875]=.343.

Rm-Rf = .08975 (This is a plug in to the SML equation - you know all but beta) (If you solve for beta from the equation used below, you do not get the correct answer. The number given for the correlation (.6) is incorrect – correlation should be .2156).

For Security 2, the beta is .8. Since the market standard deviation is .22, the covariance of Security 2 with the market must satisfy the following equation: .8=[Cov(R2,Rm)]/(.0484). Therefore, Cov(R2,Rm)=.03872. The correlation is [.038721(.20*.22)]=.88.

3. Given the following information on 3 stocks:

Stock A / Stock B / Stock C / T-Bills / Market Portfolio
E(r) / 0.19 / 0.15 / 0.09 / 0.07 / 0.18
2 / 0.02 / 0.1196 / 0.0205 / 0.0000 / 0.0064
i,M / 0.007 / 0.0045 / 0.0013 / 0.0000 / 0.0064

i,M = covariance of the security with the market portfolio.

Using the CAPM, calculate the expected return for stocks A, B, and C. Which stocks would you recommend purchasing?

E(RA) = .07 + [(.007)/(.0064)][.18-.07] = 19.03% A = .007/.0064 = 1.0938

E(RB) = .07 + B [.18-.07] = 14.73% B = .0045/.0064 = .7031

E(RC) = .07 + C [.18-.07] = 9.23% C = .0013/.0064 = .2031