# Calculating fair value of the given securities

1. A person is considering buying the stock of two home health companies that are similar in all respects except the proportion of earnings paid out as dividends. Both companies are expected to earn $6 per share in the coming year, but Company D (for dividends) is expected to pay out the entire amount as dividends, while Company G ( for growth) is expected to pay out only one-third of its earnings, or $2 per share. The companies are equally risky, and their required rate of return is 15%. D's constant growth rate is zero and G's is 8.33%. What are the intrinsic values of stocks D and G?

2. A broker offers to sell you shares of Bay Area Helthcare, which just paid a dividend of $2 per share. The dividend is expected to grow at a constant rate of 5% per year. The stock's required rate of return is 12%. What is the expected dollar dividend over the next three years? What is the current value of the stock and the expected stock price at the end of each of the next three years? What is the expected dividend yield and capital gains yield for each of the next three years? What is the expected total return for each of the next three years? How does the expected total return compare with the required rate of return on the stock? Does this make sense?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

1.

Company D

Dividend=D=$6

Required rate of return=r=15%

Intrinsic value of stock D=D/r=6/15%=$40

Company G

Current Dividend=Do=$2

Growth rate=g=8.33%

Required rate of return=r=15%

Intrinsic value of stock G=Do*(1+g)/(r-g)=2*(1+8.33%)/(15%-8.33%)=$32.48

2.

What is the expected dollar dividend over the next three years?

Current dividend=Do=$2

Growth rate=g=5%

Required rate of return=r=12%

Expected dividend at the end of Year 1=D1=Do*(1+g)=2*(1+5%)=$2.10

Expected dividend at the end of Year 2=D2=D1*(1+g)=2.10*(1+5%)=$2.205

Expected dividend at the end of Year 3=D3=D2*(1+g)=2.205*(1+5%)=$2.31525

What is the current value of the stock and the expected stock price at the end of each of the next three value of the stock and the expected stock price at the end of each of the next three years?

Current Price=Po=D1/(r-g)=2.10/(12%-5%)=$30.00

Expected price at the end of Year 1=P1=D2/(r-g)=2.205/(12%-5%)=$31.50

Expected price at the end of Year 2=P2=D3/(r-g)=2.31525/(12%-5%)=$33.075

Expected dividend at the of year 4=D4=D3*(1+g)=2.31525*(1+5%)=2.431013

Expected price at the end of Year 3=P3=D4/(r-g)=2.431013/(12%-5%)=$34.729

What is the expected dividend yield and capital gains yield for each of the next three years?

Dividend yield at the end of year 1=D1/Po=2.10/30=7.00%

Dividend yield at the end of year 2=D2/P1=2.205/31.5=7.00%

Dividend yield at the end of year 3=D3/P2=2.31525/33.075=7.00%

Capital Gain at the end of year 1=(P1-Po)/Po=(31.50-30.00)/30=5.00%

Capital Gain at the end of year 2=(P2-P1)/P1=(33.075-31.50)/31.50=5.00%

Capital Gain at the end of year 3=(P3-P2)/P2=(34.729-33.075)/33.075=5.00%

What is the expected total return for each of the next three years rate of return on the stock? How does the expected total return compare with the required rate of return on the stock? Does this make sense?

Expected total return at the end of Year 1=Dividend Yield+ Capital gain=7.00%+5.00%=12.00%

Expected total return at the end of Year 2=Dividend Yield+ Capital gain=7.00%+5.00%=12.00%

Expected total return at the end of Year 3=Dividend Yield+ Capital gain=7.00%+5.00%=12.00%

Expected total return is equal to required rate of return on the stock.

Yes it makes sense. Sum of capital gain and dividend yield is equal to the expected rate of return in each case.

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