Question

Airnova Inc. has two types of bonds, Bond D and Bond F. Both have 8 percent coupons, make semiannual payments, and are priced at par value. Bond D has 2 years to maturity. Bond F has 15 years to maturity.

Airnova Inc. is considering four different types of stocks. They each have a required return of 20 percent and a dividend of $3.75 for share. Stocks, A, B, and C are expected to maintain constant growth rates in dividends for the near future of 10 percent, 0 percent, and -5 percent, respectively. Stock D is a growth stock and will increase its dividend by 30 percent for the next four years and then maintain a constant 12 percent growth rate after that.

• If interest rates suddenly rise by 2 percent, what is the percentage change in both bonds?

• If interest rates suddenly fall by 2 percent, what is the percentage change in both bonds?

• What does this tell you about the interest rate risk of longer-term bonds?

• What is the dividend yield for each of the four stocks?

• What is the expected capital gains yield?

• Discuss the relationship among the various returns that you find for each of the stocks.

I really only need the last 2-3 answered.

Answer 1

(As requested I am answering the last 3 parts)

Given: Details of four stocks

Stock	A	B	C	D
Dividend (Do)	$3.75	$3.75	$3.75	$3.75
Required rate of return	20%	20%	20%	20%
Growth rate	10%	0%	-5%	30% for 4 years & 12% thereafter

Stock A : Valuation of stock in case of constant growth

Po = 3.75(1+0.10)/(0.20-0.10)

Po = 4.125/.10

Po = $41.25

Current Price of Stock A =  $41.25

Stock B: Valuation of stock in case of no growth

Po = 3.75/0.20

Po = $18.75

Current Price of Stock B =  $18.75

Stock C: Valuation of stock in case of negative growth

Po = 3.75(1-0.05)/0.20+0.05

Po = 3.5625/0.25

Po = $14.25

Current Price of Stock C =  $14.25

Stock D: Valuation of stock in case of super normal growth

Year	Working	Dividend $	PVF@20%	Present value$
1	D1 = 3.75*(1.30^1)	4.8750	0.83333333	4.0625
2	D2 = 3.75*(1.30^2)	6.3375	0.69444444	4.4010
3	D3 = 3.75*(1.30^3)	8.2388	0.57870370	4.7678
4	D4 = 3.75*(1.30^4)	10.7104	0.48225309	5.1651
4	Price at the end of year 4 (note1)	149.9452	0.48225309	72.3116
			Total	90.7080

Current Price of Stock C =  $90.7080

Note

1. Price at the end of yr 4

P4 = D4(1+g)/Ke-g

P4 = 10.7104(1+0.12)/0.20-0.08

P4 = 11.995648/0.08

P4 = $ 149.9452

Part a): Calculation of Dividend yield of the four stocks

Dividend Yield = Dividend / Market Price of the share

Stock	A	B	C	D
Dividend (a)	$3.75	$3.75	$3.75	$3.75
Price of stock (b)	$41.25	$18.75	$14.25	$90.71
Dividend yield (a)/(b)	9.09%	20.00%	26.32%	4.13%

Part b): Calculation of Expected Capital Gain Yield

Expected Capital Gain Yield = Expected rate of return - Dividend Yield

Stock	A	B	C	D
Required rate of return (a)	20%	20%	20%	20%
Dividend yield (b)	9.09%	20.00%	26.32%	4.13%
Expected Capital Gain Yield (a) - (b)	10.91%	0.00%	-6.32%	15.87%

Part c) Relationship among the various returns for each of the stocks

The investor invest in stock with the aim of earning returns. The return can be in form of dividends or in form of capital gains.

In case of constant growth rate the dividend yield and capital gain yields are almost equivalent to each other.

In case of zero growth rate the dividend yield is equal to the required rate of return and capital gain yield is  zero as investor has no expectation of rise in stock price.

In case of negative growth rate the dividend yield is again high and the capital gain yield is negative as the investor has negative expectations in regard to change in stock price.

In case of super normal growth where dividend growth rates are higher in beginning year and later reduces to a constant growth rate. The dividend yield is lower and the capital gain yield is higher because in this case the investor has high expectation of appreciation in stock prices.