Review

Stocks and Bonds

Valuation

Callaghan Motors’ bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8 percent. The bonds have a yield to maturity (market rate) of 8 percent. 1- What is the current market price of these bonds?

2- If The bonds have a yield to maturity (market rate) of 9 percentWhat is the current market price of these bonds?

Bond Value

CURRENT YIELD

Heath Foods’ bonds have 7 years remaining to maturity. The bonds have a face value of $1,000 and a yield to maturity of 8 percent. They pay interest annually and have a 9 percent coupon rate.

What is their current yield?

Annual coupon pmtCurrent price

Solution

( )V

.08 B = $1,000

17

+= $1,052.08+

0.08)0(1

11- 708.

90+

Current yield=

= 901052.8

=8.55%

BOND VALUATIONSemiannually PMT Nungesser Corporation has issued bonds that

have a 9 percent coupon rate, payable semiannually.

The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 8.5 percent.

What is the price of the bonds?

Solution

( )V

.085 B = $1,000

17

+ = $1028.6

+2

0.085/2)0(1

11- 162/085.

45+

CONSTANT GROWTHSTOCK VALUATION

Ewald Company’s current stock price is $36, and its last dividend was $2.40. In view of Ewald’s strong financial position and its consequent low risk, its required rate of return is only 12 percent.

If dividends are expected to grow at a constant

rate, g, in the future, and if rs is expected to

remain at 12 percent, what is Ewald’s expected stock price 5 years from now?

Solution

g

g

gr

gDP

s

−+=

−+=

12.

4.24.236

)1(ˆ 0

0

g = 5%

)1(ˆ

6

0

5 gr

gDP

s −+

= 45.95 07.0

)05.1(4.26

==

SUPERNORMAL GROWTHSTOCK VALUATION Snyder Computer Chips Inc. is experiencing a period

of rapid growth. Earnings and dividends are expected to grow at a rate of 15 percent during the next 2 years, at 13 percent in the third year, and at a constant rate of 6 percent thereafter. Snyder’s last dividend was $1.15, and the required rate of return on the stock is 12 percent.a. Calculate the value of the stock today.b. Calculate P1 and P2.c. Calculate the dividend yield and capital gains yield for

Years 1, 2, and 3.

ˆ ˆ

Important

Solution

a. Calculate the value of the stock today.Steps1. Find the PV of the dividends during the

period of nonconstant growth.2. Find the price of the stock at the end of the

nonconstant growth period, at which point it has become a constant growth stock, and discount this price back to the present.

3. Add these two components to find the intrinsic value of the stock, P0.̂

Solution a:

0

1.1809

1.2125

1.2233

21.61

1 2 3 4rs=12%

25.23 = P0

g = 15% g =15% g = 13% g = 6%

D0 = 1.15 1.3225 1.5209 1.7186 1.8217

^

0803.32060120

8217.13̂ $

..

$P =

−=

a -

Solution b (with the same way of Solution a)

0

1.3579

1.370124.2030

1 2 3 4rs=12%

26.93 = P1

g = 15% g =15% g = 13% g = 6%

D0 = 1.15 1.3225 1.5209 1.7186 1.8217

^

b -

P1= 1.3579 + 1.3701 + 24.2030 = 26.93^

0803.32060120

8217.13̂ $

..

$P =

−=

Solution b

0

1.5342

1 2 3 4rs=12%

g = 15% g =15% g = 13% g = 6%D0 = 1.15 1.3225 1.5209 1.7189 1.822

3617.30060120

822.13̂

$..

$P

=−

=

b -

P2= 1.5342 + 27.1084 = 28.64^

27.1084

Solution c

c-

Year 1

Year 2

Dividend yield = = = 5.24%.$1.3225

$25.23

D1

P0

CG Yield = 12% - 5.24% = 6.74%.

Dividend yield = = = 5.65%.$1.5209

$26.93

D2

P1

CG Yield = 12% - 5.65% = 6.35%.

Solution

Year 3

Dividend yield = = = 6%.$1.786

$28.64

D3

P2

CG Yield = 12% - 6% = 6%.

Remember that : Total yield (rs) = Dividend yield + (CG)Capital Gains Yield

PREFERRED STOCK VALUATION

Fee Founders has preferred stock outstanding which pays a dividend of $5 at the end of each year. The preferred stock sells for $60 a share. What is the preferred stock’s required rate of return?

Vp =

60=

Dp

rp

5rp

rp = 8.33%