Risk and Return + Diversification

a) Alpaca Company just paid a dividend of $0.70 a share. The current share price is $17.80    and the share price six months ago was $17.60. Calculate the holding period return on Alpaca Company over this six-month period.

R = (17.80- 17.60 + 0.70)/17.60 = 0.051136

R=5. 11% per six months

HPR= [(P1-P0)+CF]/P0

b) Bandicoot Company has the following probability distribution of returns:

(i)        Calculate the expected return of Bandicoot Company

E(R) = [0.2*(-0.05)] + (0.3*0) + (0.3*0.05) + (0.2*0.1) = 0.025 = 2.5%

(ii) Calculate the variance of Bandicoot Company

variance = 0.2(-0.05 – 0.025)2+ 0.3(0 – 0.025)2+ 0.3(0.05 – 0.025)2+ 0.2(0. 1 –0.025)2 = 0.002625

(recall: variance is movement away from the mean squared, applying probability to each        possible occurrence: there is a 20% chance that the return of -0.05 will vary from the mean of 0.025 squared, 30% chance that the return of 0 will vary from the mean of 0.025 squared and so on)

(iii) Calculate the coefficient of variation of Bandicoot Company

std dev = √(0.002625) = 0.051235

CV =std dev/mean return= 0.051235/0.025 = 2.05

(iv) If Alpaca Company has a CV of 1.75 which of the companies-Bandicoot or Alpaca would you choose as a risk averse investor?

Choose Alpaca as it has a lower CV which implies lower risk for each unit of return

(v) If the correlation coefficient between Bandicoot and Alpaca is 0.9787, would these two shares (Bandicoot and Alpaca) offer good diversification? Why or why not?

No, 0.9787 is very close to 1 which is perfect positive correlation, hence very little               diversification is possible. (However, recall that as long as correlation is less than 1, there is still possibility for diversification. In this case, it is just very little diversification being        possible, so not a good choice for diversification purposes).

Portfolio Theory

The table below presents the expected returns, betas and standard deviations for three assets A, B and C. The expected return on the market is 14% and the risk-free return is 3%.

a) What can you say about the systematic risk of each of the three assets relative to the systematic risk of the market?

A has less systematic risk than the market whereas B and C have more systematic risk than the market. (Recall: Beta of market=1)

b) What is the beta of a portfolio comprised of 20% in A, 30% in B, and 50% in C?

Beta = 0.2(0.8) + 0.3(1.2) + 0.5(1.6) = 1.32

c) Are the assets under- or over-priced according to the CAPM?

E(RA) = 0.03 + 0.8(0. 14 – 0.03) = 0.118 = 11.8%

E(RB) = 0.03 + 1.2(0. 14 – 0.03) = 0.162 = 16.2%

E(RC) = 0.03 + 1.6(0. 14 – 0.03) = 0.206 = 20.6%

A’s given expected return of 8% is less than that suggested by the CAPM (11.8%) meaning it is plotting below the SML (achieving a return lower than that its beta dictates according to

the CAPM)=so A is overpriced. (recall that the SML is the graphical representation of the CAPM formula and that the E(R) generated using the CAPM formula plot ON the SML).

B’s given expected return of 10.5% is less than that suggested by the CAPM (16.2%) meaning it is plotting below the SML so B is also overpriced.

C’s given expected return of 23% is more than that suggested by the CAPM (20.6%) meaning it is plotting above the SML so C is underpriced.

d) According to the Sharpe ratio, which asset is superior?

SharpeA = (0.08 –0.03)/0.06 = 0.83333

SharpeB = (0.105 – 0.03)/0.08 = 0.9375

SharpeC = (0.23 – 0.03)/0.12 = 1.66667

Asset C is superior as it has the highest Sharpe ratio

Cost of Capital

Comfyshoes is an all equity firm that has a current share price of $63, a beta of 1.1 and has just paid a dividend of $5.50 per share. Analysts expect Comfyshoes’ dividends to grow by 3% p.a. The market risk premium is 6.5% p.a. and the risk-free rate is 3.5% p.a.

a) Calculate the cost of equity of Comfyshoes using two different approaches.

re = 0.035 + 1.1(0.065) = 0. 1065=10.65%  (using CAPM-NOTE: market risk premium is E(Rm)-Rf so please don’t deduct 0.035 from 0.065! if they had given you E(Rm) then you would deduct Rf from it as per CAPM formula)

re = [5.5(1.03)/63] + 0.03 = 0. 11992=11.99% (using DGM; note $5.50 is D0 so D1=D0 *(1+g))

b) Explain why the cost of equity from the two approaches is different. In your answer, highlight the limitations of the two approaches for calculating cost of equity.

The cost of equity is different because there are limitations to both models and both rely on different inputs.

With the CAPM, you have to estimate the market risk premium and the beta of the stock, and both of these can never be estimated precisely.

With the DGM, you have to estimate the growth rate in dividends and this cannot be          estimated precisely. Also note that DGM is very sensitive to the growth rate being used.    (Further review the advantages and disadvantages of each approach as per Tutorial 11 Q5)

c) Comfyshoes is considering investing in two new projects that are of similar risk to the overall firm. Project A is expected to generate a return of 12.5% and project B is expected to

generate a return of 15%. Which project(s), if any, should Comfyshoes invest in? Explain your answer.

Comfyshoes should invest in both projects A and B, because both offer a higher return than the cost of equity estimates calculated.

d) Comfyshoes has uncovered a new potential project, project C. This project is expected to return 12% but is considered 50% more risky than the average project that firms in the stock market invest in. Should Comfyshoes invest in project C? Explain your answer.

re = 0.035 + [1.5(0.065) ]= 0. 1325=13.25%

Comfyshoes should not invest in project C, as it has a lower return (12%) than the cost of capital of project C (13.25%).

g) Firm Helix has an unlevered cost of equity of 10% and a pre-tax cost of debt of 6%. The value of Helix’s debt is $1.5 billion and the value of levered equity is $7 billion. The          corporate tax rate is 30%.

(i) According to MM 1958 and 1963, what is the levered cost of equity of Helix?

MM58 r = r + (D / E) (r - r )

E U U d

re= 0.10 + [(1.5/7)(0.10 – 0.06)] = 0. 10857=10.86%

MM63 r = r + (D / E) (r - r )(1-T)

E U U d

re = 0.10 + [(1.5/7)(0.10-0.06)(1-0.3)] = 0. 106=10.6%

(ii) Explain the difference in the levered cost of equity obtained in (i) from using MM1958 and MM1963.

The levered cost of equity is lower under MM63 because of the tax shield on debt. Extra:

What is this tax shield of debt? T*D=0.3*$1.5 billion=$0.45 billion.

What is the value of the levered firm under MM1963: VL=D+E=1.5+7=$8.5 billion

What is the value of the unlevered firm under MM1963: VL=VU+TD so VU=VL-TD=8.5- (0.3*1.5)=8.5-0.45=$8.05 billion

Market Efficiency + Dividend Policy

(a) Bizzy is a $53 stock about to pay a $3 dividend. An investor in Bizzy owns 1,000 shares and prefers a $5 dividend.

(i) Explain how the investor can create a $5 dividend using the homemade dividend policy.

Cash from selling stock: how to find how many shares need to be sold to replicate a $5 dividend payout?

As payment from dividends will be $3000, need to get $2000 additional cash to replicate investment in a company that would pay a $5 dividend.

As share price will now be $50 (since a $3 dividend has been paid, the share price falls by the amount of the dividend from $53 to $50, ignoring transaction costs, taxes etc..), so:

$2000=50*number of shares to be sold

Number of shares to be sold=$2000/$50=40 shares

So, getting a $3 dividend on 1000 shares owned and then selling 40 shares at $50 (total $2000) is the same as owning 1000 shares in a company paying a $5 dividend.

(ii) In practice, it is not possible to implement a costless homemade dividend policy for          reasons such as transaction costs and tax. Briefly explain, using either transaction costs or tax as an example, why it is not possible in practice to implement a costless homemade dividend policy.

In practice, due to transaction costs you will have to pay fees to sell 40 shares. Therefore, your homemade dividend policy will net you less than $5000 from selling 40 shares.

Alternately:

The tax implications of selling shares will be different to receiving dividends, particularly in Australia, which has a dividend imputation tax system. Capital gains in Australia are            generally taxed differently to dividends. Thus, after considering tax, selling 40 shares will    most likely not net you the same amount as receiving a $5 dividend.

Answer the following multi-part question demonstrating your understanding with respect to market efficiency.

(i) When new information is released to the market, the adjustment of prices to that      information in an efficient market will be both _______________ and _____________

When new information is released to the market, the adjustment of prices to that information in an efficient market will be both instantaneous and unbiased

(ii) If price sensitive new information about record earnings for Kathmandu company is      received at 9am on 30th May and the price slowly adjusts upwards to reach the correct new level by 5pm that day, what type of reaction has occurred?

Underreaction: A biased response in the share price to information in which the initial price movement can be expected to continue (delayed response).

(iii) Kathmandu releases subsequent information on 31st May to advise shareholders that

their annual meeting will be held at 5pm instead of 6pm. There is no price adjustment to this information. Is this behaviour consistent with that in an efficient market? Explain your         answer.

Yes, this behaviour is consistent with an efficient market. Under the EMH, prices should only react to new (unexpected) information that is price sensitive. The change of meeting time has no price implication and so no price reaction would be expected.

(iv) Technical analysis, which is defined as the analysis of historical trends of prices, is an important field in finance. Which form of efficiency is this field based on?

a.    Strong form inefficiency. *b.  Weak form inefficiency.

c.    Semi-strong form inefficiency.

d.    It has nothing to do with efficiency.

(explanation: if markets are weak-form efficient, then an analysis of historical trends of       prices will not generate abnormal returns since past prices are already reflected in current market prices).

(v) A stock’s price rises 8 percent two days before the announcement of a large long-term project takes place. Which form of efficiency is contradicted?

*a.  Strong form.

b.    Weak form.

c.    Semi-strong form.

d.    No form of efficiency is contradicted.

(explanation: private information seems  to  have  been  traded  upon,  with potential for abnormal returns being achieved by those who traded using this private information, hence market does not seem to be strong form efficient).

Capital Budgeting-Comprehensive Problem (note this is slightly different to the tutorial problem given as Question 2 in Tutorial 6; note also that in a two-hour and 10 mns exam it is unlikely that the problem would be as extensive as the one below-this was adapted from a past 3-hour and 10 mins exam. In a 2-hour and 10 mns exam-our current case-it is more likely that calculation of WACC and identification of capital structure would be separate problems; however, the problem below provides good practice across three topics: capital budgeting, cost of capital and capital structure, and provides an understanding of the links between the three topics)

International Foods (IFC) currently processes seafood with a unit it purchased several years ago.  The unit, which originally cost $500,000, currently has a book value of $250,000.  IFC is considering replacing the existing unit with a newer, more efficient one.  The new unit will cost $750,000 and will also require an initial increase in net working capital of $40,000.  The new unit will be depreciated on a straight-line basis over 5 years to a zero balance. The existing unit is being depreciated at a rate of $50,000 per year. IFC expects to sell the existing machine for $275,000. IFC’s tax rate is 40 percent.

If IFC purchases the new unit, annual revenues are expected to increase by $100,000 (due to increased capacity), and annual operating costs (exclusive of depreciation) are expected to decrease by $20,000.  Annual revenues and operating costs are expected to remain constant at this new level over the 5-year life of the project.  IFC estimates that its net working capital investment will increase by $10,000 per year over the life of the project. Accumulated net working capital will be recovered at the end of 5 years.

IFC’s Balance sheet is given below:

IFC’s equity beta is 1.3, pre-tax cost of debt is 10% and the risk-free rate and market return are 8% and 14% respectively.

Answer the following:

a)   Calculate the project’s initial net investment.

b)  If IFC considers its current capital structure to be optimal how should it fund the project? That is, determine how much of the investment should be funded through debt and how much through equity)

c)   Calculate the annual net operating cash flows for the project.

d)  Calculate the terminal cash flows for the project.

e)   Calculate IFC’s cost of equity and weighted average cost of capital.

f)   Should IFC proceed with the project? Why?

SOLUTION

a)   Initial Investment (CF0)

Cost New unit

Sale Old unit

Less tax                   (10,000*)

NWC                    (40,000)

(525,000)

*tax payable as a profit is made on the sale of the old machine as a profit is made on this sale. When you sell the machine (old or new), identify if a loss or profit is made as follows: SV- BV.

Note: if BV not given, one way of identifying it is to find out how much depreciation is left to claim on the machine. Here SV(old) is given to us as $275,000 and BV(old) is given to us as $250,000 so the profit made on sale=$25000. Tax needs to be paid on profit made so 40% times $25000=$10,000 tax payable.

b) Operational cash flows year 1 to 5 (check if operational CFs are always the same-they may differ if there are cost/revenue/NWC capital changes that don’t apply to each year through the life of the project-in the example here, all operational cash flows from year 1 to 5 are the same)

*Depreciation(new)=$750,000/5=$150,000   and   Depreciation(old)   given   as   $50,000   so depreciation (new-old)=$100,000

c) Terminal cash flows (CF at time 5)

Recovery of NWC=+90,000 (recover all incurred NWC from time 0 to time 5)

Note: there is no mention of selling the new machine at the end of the project.

Note: when you will discount the cash flows to calculate the NPV of the project you will have two cash flows at the end of the project (here at time 5): the last operating cash flow and the terminal cash flows. Be mindful of this! Meaning CF at time 5 will be $102,000+90,000= $192,000

d)  If IFC undertakes this project, it will require funding of $525,000 (initial investment).

Note: you can use CFj to find NPV as follows:

+/- 525000 CFj

102000 CFj (press 4 times)

192000 CFj (recall this is (102000+90000)

11.88 i/Y

Arrow down PRC

Gives NPV=- 104874.26