MBA
643: Managerial Finance
Problem Set #2
Please turn in a soft copy of your answers via Blackboard by 7:20pm on Monday, May 3rd. Please name
your submission file ‘groupX_ps2’ and submit one per group. Late submissions will NOT be accepted!
Please make sure that you show all your work when solving the problems.
1) Consider the following expectations for the market and two stocks in two possible equally
likely states:
State Market Return Stock A Stock B
Boom 25% 38% 12%
Recession 5% -2% 6%
a. What is the expected return on each stock?
Expected Return on A = 0.5*(38% + -2%) = 18%
Expected Return on B = 0.5*(12% + 6%) = 9%
b. Given that the risk-free rate is 6%, draw the Security Market Line (SML) for this
economy, and plot the two securities on the graph given that you have computed
Stock A has a β of 2 and Stock B has a β of 0.3.
Expected market return is = (0.5*0.25) + (0.5*0.05) = 15%
Given that rf =6%; the equation of the line will be:
6%+ β*(15%-6%)
Plotting the graph of expected returns against beta
1
, SML
35
30
Expected returns % 25
20
18
15
10 9
5
0
0 0.5 1 1.5 2 2.5 3 3.5
Beta
c. Assuming that the CAPM holds, state for each of the two stocks if the stock is
overvalued, correctly priced, or undervalued according to CAPM?
Stock A is below the SML and hence this stock is overvalued. Stock B is
above the SML and therefore stock B is undervalued.
2) Assume CAPM holds and you have the following information regarding three investment
opportunities:
Project 1 has a project beta of 2.0 and you have estimated that the project’s NPV using a cost
of capital of 20% equals zero. Project 2 has a project beta of 1.5 and its NPV using a cost of
capital of 10% equals zero. Lastly, project 3 has a project beta of 1.0 and its NPV equals zero
using a cost of capital of 6%. None of these projects are ‘scale-enhancing’ for the firm, i.e.
they are different than the regular operations the firm currently maintains. As the head of
the capital budgeting department you are trying to decide which projects should be accepted.
The company has a levered equity beta of 0.8 and a debt-to-equity ratio of 0.5, which the
company is planning to maintain for the foreseeable future. The company currently faces a
40% tax rate. Given that the expected return on the market portfolio is 8% and the risk-free
rate is 3%, which projects would you accept and why? (Assume there is no capital rationing
and the projects are going to be financed with 100% equity.)
2
643: Managerial Finance
Problem Set #2
Please turn in a soft copy of your answers via Blackboard by 7:20pm on Monday, May 3rd. Please name
your submission file ‘groupX_ps2’ and submit one per group. Late submissions will NOT be accepted!
Please make sure that you show all your work when solving the problems.
1) Consider the following expectations for the market and two stocks in two possible equally
likely states:
State Market Return Stock A Stock B
Boom 25% 38% 12%
Recession 5% -2% 6%
a. What is the expected return on each stock?
Expected Return on A = 0.5*(38% + -2%) = 18%
Expected Return on B = 0.5*(12% + 6%) = 9%
b. Given that the risk-free rate is 6%, draw the Security Market Line (SML) for this
economy, and plot the two securities on the graph given that you have computed
Stock A has a β of 2 and Stock B has a β of 0.3.
Expected market return is = (0.5*0.25) + (0.5*0.05) = 15%
Given that rf =6%; the equation of the line will be:
6%+ β*(15%-6%)
Plotting the graph of expected returns against beta
1
, SML
35
30
Expected returns % 25
20
18
15
10 9
5
0
0 0.5 1 1.5 2 2.5 3 3.5
Beta
c. Assuming that the CAPM holds, state for each of the two stocks if the stock is
overvalued, correctly priced, or undervalued according to CAPM?
Stock A is below the SML and hence this stock is overvalued. Stock B is
above the SML and therefore stock B is undervalued.
2) Assume CAPM holds and you have the following information regarding three investment
opportunities:
Project 1 has a project beta of 2.0 and you have estimated that the project’s NPV using a cost
of capital of 20% equals zero. Project 2 has a project beta of 1.5 and its NPV using a cost of
capital of 10% equals zero. Lastly, project 3 has a project beta of 1.0 and its NPV equals zero
using a cost of capital of 6%. None of these projects are ‘scale-enhancing’ for the firm, i.e.
they are different than the regular operations the firm currently maintains. As the head of
the capital budgeting department you are trying to decide which projects should be accepted.
The company has a levered equity beta of 0.8 and a debt-to-equity ratio of 0.5, which the
company is planning to maintain for the foreseeable future. The company currently faces a
40% tax rate. Given that the expected return on the market portfolio is 8% and the risk-free
rate is 3%, which projects would you accept and why? (Assume there is no capital rationing
and the projects are going to be financed with 100% equity.)
2
