Question

1. You are considering Pure Image Inc (PII) and South Vacation Tours (SVT) as potential investments. Currently, PII shares are selling at $45 per share while the shares of SVT are selling at $50 per share. Your analysis suggests that in a year from today PII shares are expected to reach $50.45 while the shares of SVT are expected to rise to $57. You estimate the betas to be respectively 1.25 for PII and 1.30 for SVT. In addition, you learn that the consensus of financial analysts suggests that over the next year, the risk-free rate is expected to be 6% while the expected return on the TSX index is 10%.

a) What is the required rate of return on each of PII and SVT?

b) If you want to invest in PII or in SVT but not both, which one would you choose and why? Hint: Calculate the reward per unit of risk for each security.

c) You decided to purchase 400 shares of PII and 300 shares of SVT. What will be the beta of your portfolio?

Steps please

Answer 1

Soln : Expected return on TSX index or market return, m = 10%, risk free rate, R = 6%

a) Required rate of return(r) can be calculated by using the CAPM model here with the help of given factors.

CAPM Model , r = R + market risk premium * beta of stock

r_PII = 6 + (10-6)*1.25 = 6 + 4*1.25 = 11% = Required rate of return for PII

Similarly, r_SVT = 6 + (10-6) *1.30 = 6 + 5.2 = 11.2% = Required rate of return for SVT

(b) Now, need to calculate the better option to invest, to compare the 2 stocks we can use the Treynor ratio for both stock

For PII, treynor ratio = (Stock return - risk free rate)/beta of stock

Stock return = (50.45-45)/45 = 12.11%

Treynor ratio = (12.11- 6)/1.25 = 4.89

Similarly in case of SVT,

Treynor ratio = (14-6)/1.30 = 6.15

So, Treynor ratio is more for SVT , hence it is better option to choose for investment.

c) Total amount invested in PII = 400*45 = $18000

Amount invested in SVT = 300*50 = $15000

Total amount of portfolio = $33000

Now, beta of portfolio = (18000/33000) *1.25 + (15000/33000)*1.30 = 0.682 +0.591 = 1.273

Portfolio beta = 1.273