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.

• 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.

Answer 1

1. Dividend yield for each of the four stocks

To find dividend yield (dividends/initial price),

We needed to find initial price.

a. Dividend yield of A

Here,

= 3.75 10% = $4.125

= 10%

Require Return = 20%

By calculating the above equation we get,

Initial cost (P0) = $41.25

dividend yield = (dividends/initial price)

= $4.125 / $41.25

= 10%

b. Dividend yield of B

Here,

= $3.75

= 0%

Require Return = 20%

By calculating the above equation we get,

Initial cost (P0) = $18.75

dividend yield = (dividends/initial price)

= $3.75 / $18.75

= 20%

c. Dividend yield of C

Here,

= 3.75- 5% = $3.5625

= -5%

Require Return = 20%

By calculating the above equation we get,

Initial cost (P0) = $14.25

dividend yield = (dividends/initial price)

=$3.5625 / $14.25

=25%

d. Dividend yield of D

Calculation of initial cost:-

where,

D4 = 3.75 (1.3)4

D4 = 10.71

Year	income	PVIF at 20%	PV of income
1	D1 = 4.875	.833	4.06
2	D2 =4.875 (1.3)= 6.34	.694	4.4
3	D3 =6.34 (1.3) = 8.238	.579	4.77
4	D4 =8.238 (1.3) = 10.71	.482	5.16
	P4 = 150	.482	72.3
	P0 =		$90.71

Initial cost (P0) = $90.71

dividend yield = (dividends/initial price)

=$3.75 / $90.71

=4.13%

2. Expected capital gains yield

Expected capital gains yield was calculated using (P1 - P0)/P0 for each stock.

a.Expected capital gains yield of Stocks A

Expected capital gains yield = (P1 - P0)/P0

Where,

P0 = 41.25

P1 = 49.916

Expected capital gains yield = 21.01%

b.Expected capital gains yield of Stocks B

Expected capital gains yield = (P1 - P0)/P0

Where,

P0 = 18.75

P1 = 18.75

Expected capital gains yield = 0%

c.Expected capital gains yield of Stocks C

Expected capital gains yield = (P1 - P0)/P0

Where,

P0 = 14.25

P1 = 12.863

Expected capital gains yield = -9.73%

a.Expected capital gains yield of Stocks A

Expected capital gains yield = (P1 - P0)/P0

Where,

P0 =  90.71

P1 = 103.98

Expected capital gains yield = 14.63%.

3.Relationship among the various returns that you find for each of the stocks

The dividend yield results I got didn't make a lot of sense in my head. I realize that a higher stock price means a lower yield result, and both the dividend price and stock price will change with time. One takeaway, if I did my calculations correctly, is that the dividend yield of stock D will continue to rise as the stock falls.  So for that first year, even though you lose almost 10% of the stock price, the dividend yield of 25% would still make it worth owning.  I have doubts about how this model would translate into true stock behavior however.

The capital gains yield made more sense to me, as it's just measuring the percent change in the stock price over a year. There's a positive correlation with dividend increase and stock price increase, and the stronger the dividend growth, the faster the stock will rise.