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:

- A CBS bond with a par value of $1000, an interest rate of 7.625%, and a maturity of 10 years. The bond is selling for $986.

- Alabama Power Company preferred stock with a $50 par value and a dividend of $2.8125 per year. The stock is currently trading at $39 per share.

- Emerson Electric common stock that is selling for $80 with a par value of $5. This stock recently paid a $2.10 dividend, and the form’s earnings per share have increased from $2.40 to $4.48 in the past 5 years. An equivalent amount of growth in the dividend is expected.
Your required rates of return for these investments are 6% for the bond, 7% for the preferred stock, and 15% 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 an earnings downturn and a resulting decrease in growth of 3%. How does this affect your answers to parts 1 and 2?

d. What required rates of return would make you indifferent to all 3 options?

Explanation / Answer

1. A CBS bond with a par value of $1,000, an interest rate of 7.625 percent, and a maturity of 10 years. The bond is selling for $986.

Rate of Return Kd = Rate(nper,PMT,PV,FV)
nper = Bond Term = 10Yrs, PMT = Coupon rate*FV = 7.625%*1000 = $76.25, PV = -986, FV = 1000
So Kd = Rate(10,76.25, -986, 1000) = 7.83%

2. Alabama Power Company preferred stock with a $50 par value and a dividend of $2.8125 per year. The stock is currently trading at $39 per share.

Return on Prefered Stock Kp = Dividend/Current Price = 2.8125/39 = 0.0721 = 7.21%

3. Emerson Electric common stock that is selling for $80 with a par value of $5. This stock recently paid a $2.10 dividend, and the firm's earnings per share have increased from $2.40 to $4.48 in the past 5 years. An equivalent amount of growth in
the dividend is expected.

Return on Common stock is Ks.
In case of Constant Growth stock, Dividiend at time t is Dt = D0*(1+g)^t
Here t= 5 yrs, Do= 2.40 & D5 = 4.48.
Putting values, we get 4.48 = 2.40*(1+g)^5
ie (1+g)^5 = 4.48/2.40 = 1.8667
Taking log, we get 5*Log(1+g) = Log(1.8667) = 0.2711
ie Log(1+g) = 0.2711/5 = 0.0542
Taking ANtilog, we get (1+g) = 10^0.0542 = 1.1330
ie g = 1.133-1 = 0.133 = 13.3%

In case on Cosntant Growth stock, Price of Stock P0 = D0*(1+g)/(Ks - g)
We have P0 = 80, Do=2.40, g = 13.3%. Putting values, we get
80 = 2.40*(1+0.133)/(Ks-0.133)
ie Ks-0.133 = 2.40*1.133/80 = 0.03399
ie Ks = 0.03399 + 0.133 = 0.16699 = 16.7%

Your required rates of return for these investments are 6 percent for the bond, 7 percent for the preferred stock, and 15 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.
1. Value of Bond when Kd = 6%, N= Bond Term = 10Yrs, PMT = Coupon rate*FV = 7.625%*1000 = $76.25, M = 1000
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N)
Putting values we get
Vb=76.25(PVIFA 6%,10) + 1000(PVIF 6%,10)
ie Vb = 76.25*[1/(Kd) - 1/{(Kd)(1+Kd)^N}] + 1000*(1/(1+Kd)^N
ie Vb = 76.25*[1/6% - 1/{6%*(1+6%)^10}] + 1000*(1/(1+6%)^10)
ie Vb = 76.25*(1/6% - 9.3066) + 558.39
ie Vb = 76.25*7.36 + 558.39
ie Vb= 1119.59
So value of Bond is 1119.59 when Kd = 6%

2. Return on Prefered Stock Kp = Dividend/Current Price
So Current Price of Pref Stock = Div/Kp = 2.8125/7% = $40.18

3. Ks=15%
Price of Stock P0 = D0*(1+g)/(Ks - g) = 2.40*(1+13.3%)/(15%-13.33%) = $162.83

b. Which investment would you select? Why?
If I am risk averse, I will invest in Bond as I am assured of 7.825% pa return for 10 Yrs & also the return on Bond is greater than my expected rate of return.
If I have risk appetite, I will invest in Common stock.
However the best investment will be a judicious mix of Bond & Common stock.

c. Assume Emerson Electric's managers expect an earrings downturn and a resulting decrease in growth of 3 percent. How does this affect your answers to parts 1 and 2?
If g = -3%, Price of Stock P0 = D0*(1+g)/(Ks - g)
We have P0 = 80, Do=2.40, g = -3%. Putting values, we get
80 = 2.40*(1-0.03)/(Ks+0.03)
ie Ks+0.03 = 2.40*0.97/80 = 0.0291
ie Ks = 0.0291 -0.03 = -0.0009 = -0.09%
Thus due to negative return, I will invest only in Bond & Prefered stock.

d. What required rates of return would make you indifferent to all three options?
Please show how you got your answers.
As calcultaed above, If my reqd rate of Return on Bond is 7.83%, On Common stock is 16.7% & on Pref Stock is 7.21%, I will be indifferent to 3 options.

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