MGCR 341: Finance 1
Summer 2010
Vadim di Pietro
Assignment 3 Solutions
1)
Topic: Equity Valuation
True or False, no explanation required.
For the questions below, assume that a fraction
p
of earnings are paid out as dividends,
and thus the value of the S&P 500 is given by P =
p
(EPS
1
)/(r
E
-g), where r
E
, the required
rate of return on the market is given by the CAPM: r
E
= r
f
+ (1)(E[r
m
]-r
f
). (Note, the beta
of the market is 1.) In each case below, assume
p
remains unchanged
.
The answers to parts a) through e) are all TRUE. This follows simply from applying the
above formula. If the math/intuition is not clear to you, then ask me to explain during
office hours.
a) If 1) the risk free rate increases, 2) the market risk premium E[r
m
]-r
f
remains unchanged, and 3) g remains unchanged, then the S&P 500’s PE
ratio will fall (i.e., earnings yields will rise).
b) If g increases, and everything else remains unchanged, the S&P 500’s PE
ratio will rise (i.e., earnings yields will fall).
c)
Assume inflation expectations increase by 2%. Assume this causes the risk
free rate to increase by 2%. Also, assume this causes growth expectations
to increase by 2% (since equity earnings are derived from
real
assets).
Under these assumptions, and holding the market risk premium constant,
the S&P 500’s PE ratio and earnings yield will remain unchanged when
inflation expectations increase.
d) Holding all else equal, if the market risk premium increases, the S&P
500’s PE ratio will fall (i.e., earnings yields will rise).
e)
Same assumptions as in part c, except assume the market risk premium
increases when inflation increases. Under this new assumption, the S&P
500’s PE ratio will fall (i.e., earnings yields will rise) when inflation
expectations increase.