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 Microsoft bond with a par value of $1,000 that pays 9.25 percent on its par value in​ interest, sells for 1,281.81​, and matures in 9 years.

Southwest Bancorp preferred stock paying a dividend of ​$2.17 and selling for ​$23.74.

Emerson Electric common stock selling for ​$63.97, with a par value of​ $5. The stock recently paid a ​$1.68 ​dividend, and the​ firm's earnings per share has increased from ​$2.36 to ​$3.78 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 4.00 percent for the​ bond,10.50 percent for the preferred​ stock, and 13.00 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 an earnings to grew 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). Value of the Microsoft bond: FV (par value) = 1,000; PMT (coupon payment) = coupon rate*par value = 9.25%*1,000 = 92.5; N = 9; rate (your required return from the bond) = 4%, CPT PV.

Value of the bond = 1,390.35

Value of Southwest Bancorp preferred stock = annual dividend/required return = 2.17/10.5% = 20.67

Value of Emerson Electric common stock = next dividend/(required return - growth rate)

growth rate over 5 years = [(3.78/2.36)-1] = 60.17%

growth rater per year (g) = [(1+60.17%)^(1/5)]-1 = 9.88%

Next dividend = last dividend*(1+g) = 1.68*(1+9.88%) = 1.85

Value of stock = 1.85/(13% - 9.88%) = 59.15

b).

	Current price	Calculated value
Microsoft bond	1,281.81	1,390.35
Southwest Bancorp preferred stock	23.74	20.67
Emerson Electric common stock	63.97	59.15

Only the Microsoft bond has a price lower than the calculated value so this investment should be selected as its return will be higher than the required return. Other two securities will have lower returns than the required returns.

c). If Emerson's earnings grow at 1% higher than the historical rate of 9.88% then the growth rate (g) = 9.88% + 1% = 10.88%

Value of Emerson stock = 1.68*(1+10.88%)/(13%-10.88%) = 87.84

This value is greater than the current price of 63.97 so funds can be invested in the stock now.

To choose between the bond and the common stock, we need to calculate the returns on both securities:

Bond YTM: FV = 1,000; PV = 1,281.81; PMT = 92.50; N = 9, CPT RATE.

YTM (or rate) = 5.24%

Common stock return = (D1/P0) + g = (1.68*(1+10.88%)/63.97) + 10.88% = 13.79%

Difference between calculated return and required return for the bond = 5.24% - 4% = 1.24%

Difference between calculated return and required return for the common stock = 13.79% - 13% = 0.79%

The bond will give a comparative higher return so that should be preferred over the common stock.

d). For the bond, if your required return is same as the YTM of the bond which is 5.24%, you would be willing to buy it.

For the preferred stock, return = annual dividend/current price = 2.17/23.74 = 9.14%

If your required return for the preferred stock is 9.14%, you would be willing to buy it.

For the common stock, return = (D1/P0) +g = (1.68*(1+9.88%)/63.97) + 9.88% = 12.77%

If your required return for the common stock is 12.77%, you would be willing to buy it.