BOND and STOCK PROBLEM SOLUTIONS

1. 1.      Six years ago, The Corzine Company sold a 20-year bond issue with a 14 percent annual coupon rate and a 9 percent call premium.  Today, Corzine called the bonds.  The bonds originally were sold at their face value of $1,000.  Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price.

 

PV = 1000; N = 6; PMT = 140; FV = 1090; CPT I/Y

I/Y = 15.02%

 

1. 2.      You just purchased a bond which matures in 5 years.  The bond has a face value of $1,000, and has an 8 percent annual coupon.  The bond has a current yield of 8.21 percent.  What is the bond’s yield to maturity?

 

CURRENT YIELD = ANNUAL COUPON ¸ PV

0.0821 = 80 ¸ PV

PV = 80 ¸ 0.0821 = 974.42

N = 5; PMT = 80; FV=1000; PV = 974.42 CPT I/Y

I/Y = 8.65%

 

1. 3.      The Dass Company’s bonds have 4 years remaining to maturity.  Interest is paid annually; the bonds have a $1,000 par value; and the coupon interest rate is 9 percent.  What is the yield to maturity at a current market price of $829?  Would you pay $829 for one of these bonds if you thought that the appropriate rate of return was 12 percent?

 

PV = 829; N = 4; FV = 1000; PMT =90; CPT I/Y

I/Y = 14.99%

YES, IF YOU THOUGHT THE APPROPRIATE RATE WAS 12%, YOUR PV WOULD ACTUALLY BE HIGHER MEANING YOU WOULD BE WILLING TO PAY MORE THAN $829.

 

1. 4.      Sitel Inc. has a bond which matures in 7 years and currently sells for $1,020.  The bond has a face value of $1,000 and a yield to maturity of 10.5883 percent.  The bond pays coupons semiannually.  What is the bond’s current yield?

 

CURRENT YIELD = ANNUAL COUPON ¸ PV

FV = 1000; PV = 1020; I/Y = 10.5583 ¸ 2 = 5.2942; N = 14; CPT PMT

PMT = $55

ANNUAL COUPON = 55x2 =110

CURRENT YIELD = 110 ¸ 1020 = 10.78%

 

1. 5.      Look up the prices of AT&T bonds in the Wall Street Journal.  If AT&T were to sell a new issue of $1,000 par value long-term bonds, approximately what coupon interest rate would it have to set on the bonds if it wanted to bring them out at par? 

 

STOCK PROBLEM SOLUTIONS

 

 1.    A stock is trading at $80 per share.  The stock is expected to have a year-end dividend of $4 per share which is expected to grow at some constant rate g throughout time.  The stock’s required rate of return is 14 percent.  If you are an analyst who believes in efficient markets, what would be your forecast of g?

 

P₀ = $80; d₁ =$4; k = 14%

k = (d₁ ¸ P_0­) + g

g = k - (d₁ ¸ P_0­) = 0.14 - (4 ¸ 80_­) = 0.14 - 0.05 = 0.09 = 9%

 

 2.    What will be the nominal rate of return on a preferred stock with a $100 par value, a stated dividend of 8 percent of par, and a current market price of $140?

 

P = D ¸ k

D = 8% X 100 = $8

k = D ¸ P = 8 ¸ 140 = 0.0571 = 5.71%

 

 3.    Microtech Corporation is expanding rapidly, and it currently needs to retain all of its earnings, hence it does not pay any dividends.  However, investors expect Microtech to begin paying dividends, with the first dividend of $1.00 coming 3 years from today.  The dividend should grow rapidly – at a rate of 50 percent per year – during Years 4 and 5.  After Year 5, the company should grow at a constant rate of 8 percent per year.  If the required return on the stock is 15 percent, what is the value of the stock today?

 

D₃ = 1.00

D₄ =1.00 (1.50) = 1.50

D₅ = 1.50 (1.50) = 2.25

Compute D₆ = 2.25 (1.08) = 2.43 just to use for constant growth model (DVM) for valuing dividends from year 6 to infinity.

P₅ = D₆  ¸ (k-g) = 2.43  ¸ (0.15 - 0.08) = 34.71

 

Using the cash flow worksheet:

CF0 = 0

CF1 = 0

F01 = 2

C02 = 1.00

C03 = 1.50

C04 = 2.25 + 34.71 = 36.96

NPV

I  = 15

NPV = $19.89

 

 4.    You buy a share of The Xu Corporation stock for $21.40.  You expect it to pay dividends of $1.07, $1.1449, and $1.2240 in Years 1, 2, and 3, respectively, and you expect to sell it at a price of $26.22 at the end of 3 years.  Calculate the growth rate in dividends.  Calculate the expected dividend yield.  What is this stock’s expected total rate of return?

 

P₀ = 21.40

D₁ = 1.07

D₂ =1.1449

D₃ = 1.2240

P₃ = 26.22

Growth rate in dividends:  PV= 1.07; FV = 1.2240; N = 2; CPT I/Y;    I/Y = 6.9544% Let's round to 7%.

Dividend yield = (d₁ ¸ P_0­) = 1.07 ¸ 21.40 = 0.05

Total return = 7% + 5% = 12%