You have finally saved $10,000 and are ready to make your first investment. You

Question

You have finally saved $10,000 and are ready to make your first investment. You have the three following alternatives for investing that money:

• Bank of America bonds with a par value of $1000, that pays a 6.35 percent on its par value in interest, sells for $1,020, and matures in 5 years.

• Southwest Bancorp preferred stock paying a dividend of $2.63 and selling for $26.25.

• Emerson Electric common stock selling for $52, with a par value of $5. The stock recently paid a $1.60 dividend and the firm’s earnings per share has increased from $2.23 to $3.30 in the past 5 years. The firm expects to grow at the same rate for the foreseeable future.

Your required rates of return for these investments are 5 percent for the bond, 8 percent for the preferred stock, and 12 percent for the common stock. Using this information, answer the following questions.

a. Calculate the value of each investment based on you required rates of return.

b. Which investment would you select? Why?

c. Assume Emmerson Electric’s managers expect earnings to grow at 1 percent above the historic growth rate. How does this affect your answers to (a) and (b)?

d. What required rates of return would make you indifferent to all three options?

Explanation / Answer

a) Let Fair value of Bond=P, c=coupon on Bond, y be required rate of return and FV= par value, T be time to maturity Bonds

P=(c/y)(1-1/(1+y)T)+FV/(1+y)T

Put values ,c=6.35%*1000=63.5,y=5%,FV=1000,T=5

P=(63.5/.05)(1-1/(1.05)5)+1000/(1.05)5

P=(1270)*(1-0.78353)+783.53=1058.45

preferred stock paying a dividend of $2.63 ,fair value=dividend/ required rate of return =2.63/.08=32.875

Let P=stock's current Fair Value=?

D0=just paid dividend= 1.60

Average growth of stock in past 5 years= (3.3/2.23)1/5-1 =0.0815 or 8.15%

g=dividend growth rate per year=8.15%

let r=expected rate of return=12%

According to constant growth model,

P=D0*(1+g)/(r-g)

P=1.60 *(1.0815)/(.12-.0815)=44.95

b) You should select Investment whose Fair Value>Current Price we see that value of bond 1058.45>1,020 ,fair value of preferred stock =32.875>26.25  we should buy and select these Investments of Bond and  preferred stock as for these investments Fair Value>Current Price but for stock its opposite Fair Value=44.95<Current Price=52 therefore we should not select this investment.

c)If  managers expect earnings to grow at 1 percent above the historic growth rate then revised growth rate for stocks=g= 8.15%+1%=9.15%

Stock fair value= P=D0*(1+g)/(r-g)

P=1.60 *(1.0915)/(.12-.0915)=61.28 Now Fair Value=61.28 >Current Price=52 therefore we should now select this investment also.

d) At this required rate of return fair value of instrument=Traded price of instrument.

For bond let y be required rate of return at which bond value equals the traded price.

1,020=(63.5/y)(1-1/(1+y)5)+1000/(1+y)5 ,

at 5.5% Value=(63.5/.055)*(1-.76513)+765.13 =1036

at 5.8% Value=(63.5/.058)*(1-.75435)+754.35 =1023

at 5.85% Value=(63.5/.0585)*(1-.75257)+752.57=1021.15

at 5.88% Value=(63.5/.0588)*(1-.7515)+751.5=1019.9 so approximate required rate of return for Bond is 5.88%.

For preferred stock, required rate of return=dividend /current Price=2.63/26.25=10.02%

For stock, Fair value=1.60 *(1.0915)/(r-.0915)=52

=> 1.7464/(r-.0915)=52 =>r-.0915=1.7464/52 =.0336=>r=.0915+.0336=0.1251 or 12.51% is required rate of return at which stock value equals the traded price and investor become indifferent to investing in stock.

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