Question

Equity valuation:

You are willing to make a 10 000 $ investment in equity. You have the three following alternatives for investing that money:

(i) Bank of America bonds with a par value of 1 000$, that pays 6,35% on its par value in interest, sells for 1 020 $ and matures in 5 years.

(ii) Southwest Bancorp preferred stock paying a dividend of 2,63$ and selling for 26,25$ on the market.

(iii) Emerson Electric common stock selling for 52$ on the market, with a par value of 5$. The stock recently paid a 1,6$ dividend and the firm's earnings per share has increased from 2,23$ to 3,30$ 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% for the bond, 8% for the preferred stock, and 12% for the common stock. Using this information, answer the following questions:

Ea: Calculate the value of each investment based on your required rate of return.

Eb: Which investment would you select, and why?

Ec: Assume Emerson Electric's managers expect earnings to grow at 1% above the historical growth rate. How does this affect your answers to parts Ea and Eb?

Ed: What required rates of return would make you indifferent to all three options?

Answer 1

Value of Bond
Face Value	1000
Coupont Payment(1000*6.35%)	63.5
Required Rate of return	0.05
Current Value of bond = C(1-(1+r)^-t)/r + face value/(1+r)^t			Calculation
where, r = required rate of return i.e, t = time period, C = coupon payment			1.05^5	1.276282
Current Value of bond = 63.5(1-(1+0.05)^-5)/0.05 + 1000/(1+0.05)^5			1000/(1+0.05)^5	783.5262
Current Value of Bond = 784.5262+274.9218	1058.447935		63.5(1-(1+0.05)^-5)	13.74609
			63.5(1-(1+0.05)^-5)/0.05	274.9218
Value of Preferred Stock
Present value of all the dividents(Since it is a perpetuity, we will use perpetuity formula i.e Dividend/required growth rate
Dividend	2.63
Required Growth Rate	0.08
Current value of stock	32.875
Value of Stock
First calculate growth rate and using that we will find the value of stock
Calculate growth rate from the following formula
Growth rate = (Ending eps/Initial eps)1/5 -1			Calculation
(3.30/2.23)1/5 -1	0.08153808		3.30/2.23	1.479821
	8.15%		(3.30/2.23)^1/5	1.081538
			(3.30/2.23)^1/5 - 1	0.081538
Now calculate value of stock from the following formula
Value of stock = (Current Dividend*(1+Growth Rate))/(Required rate - Growth rate)
(1.60*(1+ .0815))/(0.12-0.0815)	44.94545455

Let us compare all the value with given prices

Type	Value of Stock	Current Price
Bond	1058.447935	1020
Preferred	32.875	26.25
Stock	44.94545455	52

Clearly, I will buy either bond or preferred stock as current price of stock is higher than its value.

If growth rate increases by 1 percent then. New growth = 8.15 + 1 = 9.15%

Value of stock with new growth rate = (1.62*0.0915/0.12-0.015) = $ 61.277

Now, the value of stock is more favourable as it is priced low at $52. Hence, investment is worth it.

Ed.

Rate of return for bond

Present Value	1020
Face Value	1000
Coupont Payment(1000*6.35%)	63.5
Time Period	5.00
Required Rate of return for indifferent	5.88%		Using RATE function in excel

Rate of return for preferred stock

Price of preferred stock = Dividend/Requried Rate

26.25 = 2.63/r or r = 2.63/26.25 = 0.1002 = 10.02%

Rate of return for stock

Divident in future = 1.6*1.0815 = 1.7304

Price of stock = FutureDividend/(Requried Rate - Growth)

52 = 1.7304/(r-0.0815) or r-0.0815 = 1.7304/52

r = 0.114776 or 11.48%

If you have any doubt, ask me in the comment section. Cheers!