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 $1,000, 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 your required rate of return.

b. Which investment would you select? Why?

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

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

Answer 1

a. Calculate the value of each investment based on your required rate of return.

Bond:

Par value, P = 1000

Coupon rate = 6.35 percent

Time = 5 years

Coupon amount = 6.35% * 1000 = 63.5

Assumption: annual payment of coupon

Required rate of return of bond = 5%

Value of the bond to you = PV of all future coupon payments + PV of par value at maturity

= 63.5/ (1+5%)^1 + 63.5/ (1+5%)^2 + 63.5/ (1+5%)^23+ 63.5/ (1+5%)^4 + 63.5/ (1+5%)^5 + 1000/ (1+5%)^5

= 1058.44

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Value of preffered stock

Dividend = $2.63

Required rate of return = 8%

current price = $26.25

Using gordon model without growth = Dividend / Req. rate of return

= 2.63/ 8% = 32.875

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Value of common stock:

Current market price = $52

par value = $5

dividend D =  $1.60

EPS increase = $2.23 to $3.30

So,Growth rate, g = CAGR between 3.30 and 2.23 over five years = (3.30 / 2.23)^(1/5) - 1 = 0.08153808 or 8.15%

EPS Payout ratio = 1.60 / 3.30 = 0.484848485 or 48.48% (Dividend /Latest EPS)

time of EPS change = 5 years

Required RoR, K = 12 percent

Using, D x (1 + g) / (K - g) = (1.6*(1+8.15%)) /(12% - 8.15%)

= 44.95

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b. Which investment would you select? Why?

Lets summarise:

Security	Valuation	Current Price($)	undervalued ?
Bond	1,058.44	1,020.00	Yes, Current price < Valuation
Preferred stock	32.875	$26.25.	Yes, Current price < Valuation
Common Stock	44.95	$52	No, Current price > Valuation

Based on the risk apetite of the investor, investment in preferred stock or bonds should be preferred because it's current market price is less than the value you find in it i.e. those are undervalued.

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

Revised growth rate in dividend, g = historical growth rate + 1% =   8.15%+ 1% = 9.15%

Value of the common stock = (1.6*(1+9.15%)) /(12% - 9.15%) = 61.28

Security	Valuation	Current Price($)	undervalued ?
Common Stock	61.28	$52	Yes, Current price < Valuation

So now you can invest in common stock.

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

To be indifferent - Your required rate of return should match with the expected rate of return .

For bond, your required rate of return should be the yield of the bond currently.

Yield = RATE(Period, payment, -PV, FV) = RATE(5,63.5,-1020,1000) = 5.88%

Hence, required rate of return on bond = Yield of the bond =5.88%

For preferred stock, required return = return expected by market = Dividend / Market price = $2.63 / $26.25.= 10.02%

For common stock, required return = return expected by shareholders = Dividend x (1 + growth) / Market price + g = 1.60 x (1 + 8.15%%) / 52+ 8.15%% = 11.48%

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