Question

Question 4 (20 marks) (a) You need to invest $10M in two assets: a risk-free asset with an expected return of 5% and a risky asset with an expected return of 12% and a standard deviation of 40%. You face a cap of 30% on the portfolio's standard deviation. What is the maximum expected return you can achieve on your portfolio? (6 marks) (b) Which of the following portfolios can not be on the Markowitz efficient frontier? Explain briefly. Portfolio Expected Return Standard Deviation 10% 10.5% 11.5% 12.5% 15% 16.5% 18.5% 20% (7 marks) (c) You are a consultant to a large manufacturing corporation that is considering a project with the following net after-tax cash flows (in millions of dollars) Years from Now After-Tax Cash Flow 40 15 1-10 The project's beta is 1.8. Assuming that rf-8% and E(n) = 16%; what is the net present value of the project? What is the highest possible beta estimate for the project before its NPV becomes negative? (7 marks)

Answer 1

A) Given Rf = 5%

Return on Risky asset = 12%

SD of asset = 40%

Max cap on SD = 30%

Weights in which amount is to be invested to maintain SD = W1 * SD of Rf + (1 - W1) * SD of Risky Asset

30 = W1 * 0 + (1 - W1) *40

30 = 40 - 40 W1

40 W1 = 40 - 30

W1 = 10/40

W1 = 25%

So Weight of Risk Free Asset = 25%

Weight of Risky Asset = 75%

Expected Maximum Return = 0.25 * 5% + 0.75 * 12%

=1.25 + 9

= 10.25

B) Portfolio S and T will not be on Markowitz Efficient Frontier as they have less return than their respective Standard Deviation.

C) As per CAPM, Cost of Project - Rf + Beta * (Rm-Rf)

= 8 + 1.8 (16-8)

= 22.4%

NPV of the Project = -40 * 1 + 15 * (PVIFA,22.4,10)

= -40 *1 + 15 * 3.8728

= -40 + 58.092

= 18.092