Question

In: Finance

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

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 pays8.75 percent on its par value in​ interest, sells for ​$1,203.06​, and matures in 18 years.

Southwest Bancorp preferred stock paying a dividend of ​$3.253.25 and selling for $22.69.

Emerson Electric common stock selling for $55.55​, with a par value of​ $5. The stock recently paid a $1.04 ​dividend, and the​ firm's earnings per share has increased from $2.22 to $3.88 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 5.00 percent for the​ bond, 12.50 percent for the preferred​stock, and 14.00 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 22 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?

Solutions

Expert Solution

a.

Value of Bond (Microsoft) = Present Value of Coupon Payments + Present Value of Value at Redemption

Our required rate of return is 5% for the Bond, so we discount our inflows by this rate to find the present value today.

It sells for $1203.60, so we can buy $10,000/$1203.06 = 8.312137 units. We assume that it will be redeemed at PAR VALUE since no other redemption value is given.

Coupon Payment = 8.312137 x $1,000 x 0.0875 = $727.312

= $727.312 x 11.6896 + $10,000 x 0.4155

= $12,657.18

Value of Preferred stock (Southwest Bancorp) = Dividend / Required Rate of return

=$3.25 / 0.1250 = $26 per share

Our investment = ($10,000 / 22.69) x $26 = $11,458.79

Value of Common Stock (Emerson Electric)  

The​ firm's earnings per share has increased from $2.22 to $3.88 in the past 5 years. Therefore, we calculate the Compounded Annual Growth Rate (CAGR)

CAGR = ((End Value / Start Value)^(1/No. of Years)) - 1

= ((3.88/2.22)^(1/5)) - 1 = 11.81%

Value of Common Stock = (Dividend x (1+Growth Rate)) / (Required Rate of Return - Growth Rate)

= ($1.04 x (1+0.1181)) / (0.14 - 0.1181)

= $53.193 per share

Value of our Investment = $10,000/$55.55 x $53.193 = $9,575.75

b)

Based on our Calculations above, we should Select the Microsoft Bond. The Bond is also a relatively risk free debt instrument and we are assured of our coupon payments and redemption at a specified period, i.e. after 18 years. Considering low risk involved, we have used a low return rate requirement of only 5%.  The Bond gives us the maximum return based on our requirements as compared to our other investment options.  

c)

Emerson​ Electric's managers expect an earnings to grow at 22% above the historical growth rate.

Thus, the new growth rate is 14.413%

Now, Value of Emerson's stock = (Dividend x (1+Growth Rate)) / (Required Rate of Return - Growth Rate)

= ($1.04 x (1+0.14413)) / (0.14 - 0.14413)

A company's long-term growth rate generally would not surpass the amount of return required by the investors for the given stock. Expected return itself is function of variables like growth expected and dividend yield. Such a state would make the company virtually riskless.  

This is one of the drawbacks of the perpetuity growth formula for stock valuation. The formula itself will result in a negative value which is illogical.  

Therefore, we ignore this new growth rate and our answers remain uncganged for a) and b).

d)

To be indifferent, our value of investment should be the same, i.e. same absolute amount of return.  

Let us assume we want a value of $12,000 and work backwards.

For the Bond. Since we arrived at $12,657.18 with a required rate of 5%, let us try a rate of 5.5%

Value = $10,000 x 0.3814 + $727.312 x 11.246 = $11,994

For the Preferred Stock. Value per share = $12,000 x $22.69 / $10,000 = $27.228

Now, $3.25 /a = $27.228

Thus, the required rate (a) = 11.94%

For the Common Stock. Value per share = $12,000 x $55.55 / $10,000 = $66.66

Now, ($1.04 x (1+0.1181)) / (a - 0.1181) = $66.66

Thus, the required rate (a) = 13.56%


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