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 8.50 percent on its par value in interest, sells for $1,284.92, and matures in 11 years Southwest Bancorp preferred stock paying a dividend of $2.21 and selling for $24.69 Emerson Electric common stock selling for $62.49, with a par value of $5. The stock recently paid a $1.21 dividend, and the firm's earnings per share has increased from $2.38 to $3.85 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 6.00 percent for the bond, 8.50 percent for the preferred stock, and 14.50 percent for the common stock. Using this information, answer the following questions on your required rate of return. a. Calculate the value of each investment based b. Which investment would you select? Why? c. Assume Emerson Electric's managers expect an earnings to grew at 3 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

Part (a)

Value of the bond:

Par value, P = 1000

Coupon rate = 8.5%

Hence coupon amount, C= 8.5% x 1000 = 85

Assume annual payment of coupon

Time to maturity, N = 11 years

Required rate of return, R = 6%

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

The same can also be calculated using the PV function of excel

Value of the bond to you = PV(rate, period, payment, Future value) = PV(6%,11, 85, 1000) = 1,197.17

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Value of preferred stock:

Dividend, D_p = 2.21

Required rate of return, K_p = 8.50%

Recall Gordan model without growth.

Hence, value of the preferred stock to you = D_p / K_p = 2.21 / 8.5% = 26

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Value of common stock:

Last dividend, D₀ = 1.21

Growth rate, g = CAGR between 3.85 and 2.38 over five years = (3.85 / 2.38)^(1/5) - 1 = 10.10%

Required rate of return, K_e = 14.50%

Recall Gordan Growth Model

Value of the common stock to you = D₀ x (1 + g) / (K_e - g) = 1.21 x (1 + 10.10%) / (14.50% - 10.10%) = 30.26

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Part (b)

Let summarize the current price against the value to you for each of the security:

Sl. No	Security	Value to you ($)	Current Price($)	Undervalued for you
1	Bond	1,197.87	1,284.92	No, Current price > Value to me
2	Preferred stock	26.00	24.69	Yes, Current price < Value to me
3	Common Stock	30.26	62.49	No, Current price > Value to me

You should select investment in preferred stock because it's current market price is less than the value you find in it.

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Part (c)

Revised growth rate in dividend, g = historical growth rate + 3% = 10.10% + 3% = 13.10%

Value of the common stock to you = D₀ x (1 + g) / (K_e - g) = 1.21 x (1 + 13.10%) / (14.50% - 13.10%) = 97.56

Sl. No	Security	Value to you ($)	Current Price($)	Undervalued for you
1	Bond	1,197.87	1,284.92	No, Current price > Value to me
2	Preferred stock	26.00	24.69	Yes, Current price < Value to me
3	Common Stock	97.56	62.49	Yes, Current price > Value to me

Now the value to you > Current price of the stock = 62.49

Hence, you should select investment in common stock

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Part (d)

You will be indifferent to the options, if your required rate of return matches with the expected rate of return by the current holders of each of the three securities.

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

Yield can be calculated using the RATE function of excel.

Yield = RATE(Period, payment, -PV, FV) = RATE(11,85,-1284.92,1000) = 5.06%

Hence, required rate of return on bond = Yield of the bond =5.06%

For preferred stock, required return = return expected by market = D_S / P_S = 2.21 / 24.69 = 8.95%

For common stock, required return = return expected by shareholders = D₀ x (1 + g) / P_e + g = 1.21 x (1 + 10.10%) / 62.49 + 10.10% = 12.23%