Question

Suppose the risk-free rate is 3.61% and an analyst assumes a market risk premium of 7.61%. Firm A just paid a dividend of $1.41 per share. The analyst estimates the β of Firm A to be 1.49 and estimates the dividend growth rate to be 4.35% forever. Firm A has 250.00 million shares outstanding. Firm B just paid a dividend of $1.97 per share. The analyst estimates the β of Firm B to be 0.73 and believes that dividends will grow at 2.16% forever. Firm B has 186.00 million shares outstanding. What is the value of Firm A?

Answer format: Currency: Round to: 2 decimal places.

not sure if I'm doing the process right. thanks

Answer 1

We need to find the required return on equity or cost of equity as per CAPM & then apply it on the dividend discount model , to find the share price of Firm A --with which we will multiply the total no.of its shares o/s to find the total value of firm A

So,

As per CAPM, Cost of Equity,

ke=RFR+(Beta*Market risk premium)

ie. Cost of Equity=Risk-free rate+(Beta*Mkt.risk premium)

For firm A-- with the given values,

RFR=3.61% ,beta=1.49 & MRP=7.61%

ke=3.61%+(1.49*7.61%)=

14.95%

Now with this cost of equity, & dividend growth rate

we can find the current price /share of Firm A

Using the dividend discount model formula , for constant growth rate of dividends

ie.P0=D1/(r-g)

where D1= Current dividend*(1+growth Rate)

A's dividend growth rate =4.35% & its cost of equity , as found out above=14.95%

P0 for Firm A=(1.41*(1+4.35%))/(14.95%-4.35%)=

13.88

Now, given that

Firm A has 250.00 million shares outstanding.

Value of Firm A= No.of shares o/s *Price/share

ie. 250*13.88=

$ 3470 millions

Similarly, for Firm B

As per CAPM, Cost of Equity,

ke=RFR+(Beta*Market risk premium)

ie. Cost of Equity=Risk-free rate+(Beta*Mkt.risk premium)

For firm B - with its given values for beta= 0.73

RFR=3.61% ,beta=0.73 & MRP=7.61%

ke=3.61%+(0.73*7.61%)=

9.17%

Now with this cost of equity, & dividend growth rate

we can find the current price /share of Firm B

Using the dividend discount model formula , for constant growth rate of dividends

ie.P0=D1/(r-g)

where D1= Current dividend*(1+growth Rate)

B's dividend growth rate =2.16% & its cost of equity , as found out above=9.17%

P0 for Firm B=(1.97*(1+2.16%))/(9.17%-2.16%)=

28.71

Now, given that

Firm B has 186.00 million shares outstanding.

Value of Firm B= No.of shares o/s *Price/share

ie. 186*28.71=

$ 5340.06 millions