Question

1. Suppose that CRS Inc.’s stock currently pays a dividend of $1.50, which is growing annually at 8 percent. The risk-free rate of interest is 6.84 percent and investors anticipate that the market index will rise by 12.5 percent. To estimate the stock’s systematic risk, your research team found the following: the variance for CRS’ stock is 400 percent, the variance for the market index is 100 percent, and the correlation between CRS stock and the market is 0.67. Calculate the intrinsic value of CRS’ stock.

2. What is the return on CRS stock in (2) above if it is purchased for $38?

Answer 1

1.

Beta for CRS = correlation between market and CRS * SD of CRS / SD of market

Here,

correlation between market and CRS = 0.67

SD of CRS = 400% = 20%

SD of market = 100% = 10%

Beta for CRS = 0.67 * 0.2 / 0.1 = 1.34

As per CAPM,

required return on CRS stock = risk free rate + beta for CRS * (market index return - risk free rate)

here,

risk free rate = 6.84%

market index return = 12.5%

required return on CRS stock = 6.84% + 1.34 * (12.5% - 6.84%) = 14.4244%

As per the Gordon growth model,

intrinsic value = (current dividend * (1 + growth rate)) / (required return - growth rate)

current dividend = $1.5

growth rate = 8%

required return = 14.4244%

intrinsic value of CRS = (1.5 * (1 + 0.08)) / (0.144244 - 0.08)

= 1.62 / 0.064244

intrinsic value of CRS = $25.2164