The S&P 500 fell by 30% between February 20, 2020 and March 20, 2020. The objective

of this problem is to see how we can model this drop, and what it suggests for rms'

expected sales.

To x ideas, let's take the example of a single rm F with a of 1. We assume that

the value of the rm fell by 30% between February 20, 2020 and March 20, 2020, i.e.

(V Mar - V Feb)=V Feb = -30%.

The S&P 500 has generated a return of 10% on average over the last ve years. The risk

free rate has been constant and equal to 2% for the last ve years.

1. Based on the past values of the market return and the risk free rate, what is the

expected rate of return on rm F? Does the expected rate of return depend on the

risk-free rate? Why? (2 points)

2. Let's assume that F is an innite-lived rm that pays out a constant fraction of

earnings as dividends. Next year's dividend are expected to be equal to D = $50

(the unit is one billion dollar). Before February 20, the market was expecting that the

earnings of rm F would grow by 5% every year. What is the revised expected growth

rate of earnings on March 20? How would the results have changed if D = $80? (6

points)

3. An alternative way to model this drop is to keep g = 5%, but to assume that because

of the drop in earnings, rm F will not start paying out dividends before time t0. At

time t0, rm F starts paying out dividends equal to D = $50, and the earnings of

the rm grows at rate g from time t0 on. What is the t0 implied by the drop in the

S&P 500? The answer can be expressed in the following way: \t0 should be between

X and X + 1 years". (6 points)