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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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