## Assignment problems – Investments

1(a) Lonesome Gulch Mines has a standard deviation of 42% per year and a beta of 0.10. Amalgamated Copper has a standard deviation of 31% a year and a beta of 0.66. Which is a safer investment? Why?

**SAMPLE ANSWER:**

**In the context of a well-diversified portfolio, one of the risk characteristics underlying single security that matters is security’s contribution to overall portfolio risk. This security’s contribution is measured by beta (β).**

**The safer investment here is lonesome Gulch Mines because when we compare the beta of Lonesome Gulch Mines and Amalgamated Copper,**

(b) In class we called NPV the “gold standard” of investment decision rules. What makes this so? IRR is closely related to NPV.. Why not use that instead?

2 (a) RBC has 100 loans outstanding, each for $1 million, which it expects to be repaid today. Each loan has a 5% probability of default, in which case the bank is not repaid anything. The chance of default is independent across all the loans. BMO has only one loan of $100 million outstanding, which it also expects will be repaid today. It also has a 5% probability of not being repaid. Explain the difference between the types of risk each bank faces. Which bank faces less risk? Why?

(b) Explain why the risk premium of a stock does not depend on its diversifiable risk.

3 (a) A Company has the following capital structure:

Debt: $2,000,000

Preferred: $1,000,000

Common: $4,000,000

Retained Earnings: $3,000,000

The amounts shown represent book values. The market values and the after-tax cost of the components are as follows;

Debt: $1,800,000 .06

Preferred: $700,000 .11

Common: $12,500,000 .15

Calculate the weighted-average cost of capital.

(b) Define and explain the two methods of calculating the cost of equity

4. Big Joe’s is replacing a piece of equipment. The equipment will cost $5,000 and has a 5 year life. The equipment can be leased for annual payment of $1,295 paid at the beginning of each year, or it can be purchased and financed at an interest rate of 10% with annual loan payments of $1,319. There is zero salvage value. Big Joe’s tax rate is 40%. The equipment has a 20% CCA rate. What should Big Joe do?

5. Telematrix Limited is considering two mutually exclusive projects – cable and satellite. The possible NPVs for each project and their associated probabilities are as follows:

Cable: Satellite:

NPV ($’000) Probability NPV ($’000) Probability

10 10% 15 60%

20 50% 20 20%

25 40% 40 20%

Calculate the standard deviation for each project. Which project has the higher level of risk?

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