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 (r_{debt} ): 8%

Number of shares of common stock: 10,000

Price per share: $50

Book value per share: $25

Expected rate of return on stock (r_{equity}): 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.

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