MGFB10H3 (Principles of Finance) Assignment 2

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MGFB10H3 (Principles of Finance)

Assignment 2

 Question 1 (Stock Valuation)

Conlins Limited always pays dividend annually and it has just paid out $4 dividend per share today (t=0). The earnings per share of this firm is expected to be $5 at t=1 (one year from today). Suppose it has some investment opportunities at t=1(one year from today) and t=2 (two years from today). Therefore, at t=1 and t=2, Conlins only distributes 60% of its earnings out as dividends and reinvest the remaining earnings into these investment opportunities. The rate of return of these new investments is 30% and the proper risk-adjusted discount rate for dividend payments is 15% forever. After that (starting from t=3, three years from today), this firm will not have any good projects to reinvest its earnings so that all earnings will be paid out as dividends.

1. What is the annual growth rate for Conlins dividends after the first reinvestment?

2. What is the theoretical stock price of Conlins today?

3. If Conlins does NOT ever do any reinvestments of earnings, what is the stock price of Conlins today?

4. Explain the difference of stock prices that you have computed in Part (2) and Part (3) by calculating the net present values (NPVs) of re-investments of earnings in t=1 and t=2. Show that the sum of NPVs of these investments equals the difference between your answers in Part (2) and Part (3).

Question 2 (Capital Budgeting 1)

Weihu Corporation is considering building a new factory to manufacture bicycles. Weihu has already spent 300,000 in the R&D expense. The new factory will cost $1,500,000. The expected number of bikes produced and sold is 4000 for the first year, 5000 for the second year and 5500 for the third year. The sales price is $250 per bike in the first year in nominal terms. This price is expected to grow at 3% per year in real terms. The variable costs per bike are $120 in the first year in nominal terms. These costs are expected to increase at 2.5% per year in real terms. The factory requires temporary additional personnel, which will result in additional labor costs of

$50,000 per year (in nominal terms), which remains constant in real terms. All costs and sales are incurred at the end of each year. Additional net working capital requirements at the beginning of each year are 15% of expected sales for that same year. The market value of the factory after three years is $1,300,000 in real terms. The asset class is closed upon selling the factory. The CCA rate is 4%, the tax rate is 35%, the expected inflation rate is 2.5% and the required rate of return is 10% in real terms. Calculate the project’s NPV.


Question 3 (Capital Budgeting 2)

GoodEat Restaurant Inc. is considering replacing their refrigerators. They currently have five small fridges, which they purchased for $1100 each, four years ago. Today, they would be able to sell them for $500 each. The estimated market value three years from now is $240 per fridge. The new refrigerator is much larger, and the restaurant would need only two new fridges to keep all their food at the right temperature. The new model costs $2000 each and its estimated market value three years from now is $800. The new model is also more energy efficient and each fridge will save the restaurant in their annual energy costs. However, after two years, an additional maintenance service is required, which will cost $640 in total. The fridges are in the asset class with a CCA rate of 20%. Assume the asset class remains open. The tax rate is 39% and the opportunity cost of capital is 12% per year.

For which level of annual energy cost savings per fridge would the restaurant be indifferent between replacing the fridges and keeping the old ones?

Question 4 (Risk and Return1)

Following is the information on a portfolio of 3 stocks held by Bay Street Investment Management Inc.:

State of

Economy

 

Probability

Salma Ltd Rate

of Return

Aleena Corp Rate

of Return

Ayra Inc Rate

of Return

Boom

0.20

20%

40%

100%

Normal

0.50

15

20

50

Bust

0.30

10

-20

-80

1. If Bay Street’s portfolio is invested 50% in Salma, 25% in Aleena, and 25% in Ayra, what is the portfolio expected return? The variance? The standard deviation?

2. If the expected T-Bill rate is 4%, what is the expected risk premium on the portfolio?

3. If the expected inflation rate is 2%, what is the expected real return on the portfolio? What is the expected real risk premium on the portfolio?

4. What is the required rate of return on the portfolio, if the market risk premium is 6%, and portfolio beta is 1.8?

5. According to your calculation in Part (1) and Part (4), is this portfolio correctly priced? If not, is this portfolio overpriced or underpriced? What will happen to prices and expected returns of mispriced assets in this portfolio subsequently?


Question 5 (Risk and Returns 2)

Note: Part a, b and c are not related to each other.

a. PortfolioMan wants to create a portfolio as risky as the market and he has $1,000,000 to invest. Given this information, fill in the three missing values of the following table:

Asset

Investment

Beta

A

$170,000

1.6

B

$140,000

1.5

C

$130,000

1.1

D

$200,000

?

Risk-free asset

?

?

b. An asset’s reward-to-risk ratio is defined as its risk premium divided by its standard deviation. It is a useful statistic to summarize the asset’s risk-return trade-off.

Consider the following information:

Stock A has a reward-to-risk ratio of 0.4 and stock B has a reward-to-risk ratio of 0.33. Stock A’s risk premium is 8%, stock B’s risk premium is 10% and the market risk premium is 7%. The correlation between stocks A and B is 0.6. Assume the CAPM holds.

A portfolio consisting of stocks A and B has 20% more systematic risk than the market. Calculate the total risk of this portfolio.

c. Julia invests 20% of her wealth in the risk free asset and the rest in FB shares and BHC shares. The risk premium on FB shares is 10%, the risk premium on BHC is 7% and the market risk premium is 8%. Julia’s total portfolio of the three assets is 10% less risky than the market portfolio. Calculate the weight of FB in her portfolio. Assume that the Capital Asset Pricing Model holds.

2022-11-25