Question

You have finally saved​ $10,000 and are ready to make your first investment. You have the three following alternatives for investing that​ money: bullet • A Microsoft bond with a par value of ​$ 1 comma 000 1,000 that pays 9.25 9.25 percent on its par value in​ interest, sells for ​$ 1 comma 218.53 1,218.53​, and matures in 7 7 years. bullet • Southwest Bancorp preferred stock paying a dividend of ​$ 2.11 2.11 and selling for ​$ 28.27 28.27. bullet • Emerson Electric common stock selling for ​$ 56.23 56.23​, with a par value of​ $5. The stock recently paid a ​$ 1.76 1.76 ​dividend, and the​ firm's earnings per share has increased from ​$ 2.37 2.37 to ​$ 3.81 3.81 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 6.50 6.50 percent for the​ bond, 8.00 8.00 percent for the preferred​ stock, and 13.00 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 2 2 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? a. If your required rate of return on the bonds is 6.50 6.50​%, what is the value of Microsoft​ bond? ​$ nothing   ​(Round to the nearest​ cent.)

Answer 1

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

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Value of the bond:

Par value, P = 1000

Coupon rate = 9.25%

Hence coupon amount, C= 9.25% x 1000 = 92.5

Assume annual payment of coupon

Time to maturity, N = 7 years

Required rate of return, R = 6.50%

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

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PV of all future coupon payments = coupon interest * PVIFA,6.50%,7

PVIFA,6.50%,7 = resent value of interest factor annuity, 6.50%, n-7 = 5.48452

PV of all future coupon payments = 92.5 * 5.48452 = 507.32

PV of par value at maturity = Par * PVIF

PVIF,6.5%,7n = Present value of interest, @6.50%, n= 7 = 0.643506

PV of par value at maturity = 1000 * 0.643506 = 643.51

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Value of the bond to you = 507.32 + 643.51 = $1150.83

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Value of preferred stock:

Dividend, Dp = 2.11

Required rate of return, Kp = 8%

Recall Gordan model without growth.

Hence, value of the preferred stock to you = Dp / Kp

Value of preferred stock = 2.11 / 8% = $26.38

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Value of common stock:

Last dividend, D0 = 1.76

Growth rate, g = CAGR between 3.81 and 2.37 over five years = ( (3.81 / 2.37) - 1 ) / 5 = 12.15%

Required rate of return, Ke = 13%

Recall Gordan Growth Model

Value of the common stock to you = D0 x (1 + g) / (Ke - g)

Value of the common stock = 1.76 x (1 + 12.15%) / (13% - 12.15%)

Value of the common stock = 1.97384 / 0.85%

Value of the common stock = $232.22

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Part b. Which investment would you​ select? Why?

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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	1150.83	1,218.53	No, Current price > Value to me
2	Preferred stock	26.38	28.27	Yes, Current price < Value to me
3	Common Stock	232.22	56.23	No, Current price > Value to me

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

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Part c.. Assume Emerson​ Electric's managers expect an earnings to grew at 2 2 percent above the historical growth rate. How does this affect your answers to parts a and​ b?

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Revised growth rate in dividend, g = historical growth rate + 2.2% = 12.15% + 2.2% = 14.35%

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Value of the common stock to you = D0 x (1 + g) / (Ke - g) = 1.76 x (1 + 14.35%) / (13% - 14.35%)

Here the denominator will become minus value, which is the growth rate are higher than required rate of return, the stock price are are negative.

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If the required rate of return is less than the growth rate of dividends per share, the result is a negative value, rendering the model worthless

.

Cannot calculate value

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

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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 to maturity of the bond currently.

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Yield can be calculated using the RATE function of excel.

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Yield = RATE(Period, payment, -PV, FV) = RATE(7,92.5,-1218.53,1000) = 5%

.

Or manually

YTM = ( C + ( P - M ) / N ) / ( ( P + M ) / 2 )

Where,

C = coupon = 92.5

P = par = 1000

M = Current price = 1218.53

N = 7

YTM = ( 92.5 + ( 1000 - 1218.53 ) / 7 ) / (( 1000 + 1218.53 ) / 2 )

YTM = 92.5 + - 31.21857 )

YTM = 61.28142858 / 1109.265

YTM = 0.0552 = 5.52%

*There is different in manually and excel

..

Hence, required rate of return on bond = Yield of the bond =5%

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** For preferred stock, required return =

return expected by market = DS / PS = 2.11 / 28.27 = 0.0746 = 7.46%

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**For common stock, required return =

return expected by shareholders = D0 x (1 + g) / Pe + g

required return = 1.76 x (1 + 12.15%) / 56.23 + 0.1215

required return = 1.97384 / 56.23 + 0.1215

required return = 0.0351029 + 0.1215

required return = 0.1566 = 15.66%