Option 1
Question 1: Portfolio Risk
Golden Eagle invests 60% of their funds in stock I and the balance in stock J. The standard deviation of returns on I is 10%, and on J it is 20%. Calculate the variance of portfolio returns, assuming
60% of the money is invested in Stock I
40% of the money is invested in stock J
- The correlation between the returns is 1.0
(0.60^2 * 0.10^2) + (0.40^2 * 0.20^2) + 2 (0.60 * 0.40 * 1.0 * 0.10 * 0.20)
= 0.0036 + 0.0064 + 2 (0.0048)= 0.0196
- The correlation is .5.
(0.60^2 * 0.10^2) + (0.40^2 * 0.20^2) + 2 (0.60 * 0.40 * 0.5 * 0.10 * 0.20)
=0.0036 + 0.0064 + 2(0.0024)= 0.0148
- The correlation is 0.
Portfolio Variance = 60%^2 * 10%^2 + 40%^2 * 20%^2 + 2*60%*40%*10%*20%*0
Portfolio Variance = 0.01 or 1%
Question 2: Certainty Equivalents
A project has the following forecasted cash flows:
Cash Flows ($ Thousands)
| C 0 | C 1 | C 2 | C 3 |
| -100 | +40 | +60 | +50 |
The estimated project beta is 1.5. The market return r m is 16%, and the risk-free rate rf is 7%.
- Estimate the opportunity cost of capital and the project’s PV (using the same rate to discount each cash flow).
Opportunity Cost of Capital = rf + (rm – rf) x Beta
7% + (16% – 7%) x 1.5
7% + 13.5%
Opportunity Cost of Capital = 20.5%
Project PV = [(C0 + C1) /(1 + r) ^1] + [C2/(1 + r) ^2] + [C3/(1 + r) ^3]
[(-100 + 40) /(1 + 0.205) ^1] + [60/(1 + 0.205) ^2] + [50/(1 +.0.205) ^3]
60/(1.205^1) + 60/(1.205^2) + 50/(1.205^3)
Project PV = $3.09
- What are the certainty-equivalent cash flows in each year?
- What is the ratio of the certainty-equivalent cash flow to the expected cash flow in each year?
- Explain why this ratio declines.
Question 3: Measuring Risk
The following table shows estimates of the risk of two well-known Canadian stocks:
| Standard Deviation (%) | R 2 | Beta | Standard Error of Beta | |
| TDM | 13 | 0.49 | 0.83 | 0.11 |
| LLW | 21 | 0.01 | 0.21 | 0.25 |
- What proportion of each stock’s risk was market risk, and what proportion was specific risk?
- What is the variance of TDM Bank? What is the specific variance?
- What is the confidence interval on LLW’s beta?
- If the CAPM is correct, what is the expected return on TDM Bank? Assume a risk-free interest rate of 5% and an expected market return of 12%.
- Suppose that next year the market provides a zero return. Knowing this, what return would you expect from TDM Bank?
Question 4: Company Cost of Capital
You are given the following information for GFF Financial:
Long-term debt outstanding: $300,000
Current yield to maturity (rdebt ): 8%
Number of shares of common stock: 10,000
Price per share: $50
Book value per share: $25
Expected rate of return on stock (requity): 15%
Calculate GFF Financial’s company cost of capital. Ignore taxes.
References
Project Management Institute. (2017). The PMI Guide to Business Analysis. Project Management Institute.
