Question

1. I am considering one of two investments Growth, Inc and Value, Inc. The Treasury bill rate is 3% (risk-free rate) and the market or equity risk premium is 8%. Growth, Inc. costs $1,000 per share, has a P/E ratio of 75 and a beta of 3. Value, Inc. costs $100 per share, has a P/E ratio of 18 and a beta of 1. What are the implied growth rates for each of the firms? What are the PVGO (present value of growth opportunities) for each firm? If I form a portfolio with 100 shares of each, what is the beta and what is the P/E ratio of the portfolio?

Answer 1

First let us put the given information in tabular format:

RF	3.0%
RM-RF	8.0%

• Here RF = risk free rate,
• RM-RF = equity risk premium

Particulars	growth	value
Price	1000	100
p/e	75	18
beta	3	1
Er = RF + beta x (RM-RF)	3%+ 3 x (8%) = 27.00%	3% - 1x (8%) = 11.00%
eps= Price / (p/e)	1000/75 = 13.33	100/18 = 5.56

here g is the growth rate and Er is the expected return calculated above using the CAPM equation

Particulars	growth	value
g

Particulars	growth	value
PVGO

	growth	value	Total
Price	1000	100
beta	3	1
eps	13.33	5.56
no. of shares	100	100	200
Portfolio value = price x no. of shares	1000 x 100 = 100000	100 x 100 = 10000	100000 + 10000 = 110000
Earnings = eps x no. of shares	13.33 x 100 = 1,333.33	5.56 x 100 = 555.56	1333.33 + 555.56 = 1888.89
p/e = Portfolio value /Earnings			110000 / 1888.89 = 58.24
beta = Weighted portfolio value x beta of stock			100000/110000 x 3 + 10000/110000 x 1 = 2.82