Memories of the 2007-2009 financial crisis have made you more risk averse, doubling the risk premium you require to purchase a stock. Suppose that your risk premium before the crisis was 4 percent and that you had been willing to pay $412 for a stock with a dividend payment of $10 and expected dividend growth of 3 percent.

Using the dividend discount model, with unchanged risk-free rate, dividend payment and expected dividend growth, what price would you now be willing to pay for this stock?

Price=D (1+g) / r-g

Dividend = $10

g=3%

risk premium=4%

Price=$412

Solution:

In order to find the r=cost of equity we undertake the following steps

Price=D (1+g) / r-g

412=10 (1+0.03) / r-0.03

r-0.03=10.3/412

r-0.03=0.025

r=0.025+0.03

r=0.055 or 5.5%

risk premium = (market risk - risk free rate)

0.04 = (0.055 - risk free rate)

risk free rate = 0.015 or 1.5%

as we double the risk premium rate from 4% to 8%

then

market risk will be

risk premium = market risk - risk free rate (unchanged)

8%=market risk - 1.5%

market risk = 9.5%

Using dividend discount model

Price=D (1+g) / r-g

price = 10 (1+0.03) / 0.095-0.03

Price = $158