Question

Assume a par value of $1,000. Caspian Sea plans to issue a 16.00 year, semi-annual pay bond that has a coupon rate of 8.18%. If the yield to maturity for the bond is 7.62%, what will the price of the bond be?

Assume a par value of $1,000. Caspian Sea plans to issue a 7.00 year, annual pay bond that has a coupon rate of 8.20%. If the yield to maturity for the bond is 7.84%, what will the price of the bond be?

Assume a par value of $1,000. Caspian Sea plans to issue a 10.00 year, semi-annual pay bond that has a coupon rate of 7.80%. If the yield to maturity for the bond is 8.46%, what will the price of the bond be?

Caspian Sea Drinks needs to raise $34.00 million by issuing bonds. It plans to issue a 17.00 year semi-annual pay bond that has a coupon rate of 5.05%. The yield to maturity on the bond is expected to be 4.77%. How many bonds must Caspian Sea issue? (Note: Your answer may not be a whole number. In reality, a company would not issue part of a bond.)

The market price of a semi-annual pay bond is $983.20. It has 11.00 years to maturity and a coupon rate of 5.00%. Par value is $1,000. What is the yield to maturity?

A firm issues preferred stock with a dividend of $3.13. If the appropriate discount rate is 11.56% what is the value of the preferred stock?

The risk-free rate is 3.12% and the market risk premium is 5.32%. A stock with a β of 1.75 just paid a dividend of $1.41. The dividend is expected to grow at 23.87% for three years and then grow at 3.71% forever. What is the value of the stock?

Answer 1

1. current price of the bond can be found using PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

Here the payments are semi-annual

rate=YTM/2=7.62%/2=3.81%

nper=2*16=32

pmt=annual coupon payment/2=81.8/2=40.9

fv=face value=1000

=PV(3.81%,32,40.9,1000,0)

PV=$1051.28

The price of the bond=$1051.28

2.In this case, the payments are annual

=PV(rate,nper,pmt,fv,type)

=PV(7.84%,7,82,1000,0)

PV=$1018.85

The price of the bond=$1018.85

3. Again, in this the payments are semi annual

=PV(rate,nper,pmt,fv,type)

rate=YTM/2=8.46%/2=4.23%

nper=2*10=20

pmt=annual coupon payment/2=78.0/2=39

fv=face value=1000

=PV(4.23%,20,39,1000,0)

PV=$956.05

4. The number of he need to issue is,

rate=YTM/2=4.77%/2=2.385%

nper=2*17=34

pmt=annual coupon payment/2=50.5/2=25.25

fv=face value=1000

=PV(2.385%,34,25.25,1000,0)

PV=$1032.36

The current bond value=$1032.36

The number of bonds need to issue=$34,000,000/$1032.36=32,934

5. YTM can be calculated using RATE function in EXCEL

=RATE(nper,pmt,pv,fv,type)

nper=2*11=22

pmt=50/2=25

=RATE(22,25,-983.2,1000,0)

RATE=2.60%

Semi annual yield=2.60%

Annual yield=2*2.60%=5.20%

6. Value of the preferred stock=Dividend/discount rate=3.13/11.56%=$27.08

7. Cost of equity (r)=risk free rate+(beta*market risk premium)

r=3.12%+(1.75*5.32%)=12.43%

D0=$1.41

D1=D0*(1+23.87%)=($1.41*1.2387)=$1.74657

D2=D1*(1+23.87%)=$1.74657*1.2387=$2.16347

D3=D2*1.2387=$2.67989

From 4th year onwards dividends grows at g=3.71% forever.

Terminal value at year 3= D4/(r-g)=(D3*(1+3.71%))/(12.43%-3.71%)

Terminal value=$31.87

Value of the stock=(D1/(1+r))+(D2/(1+r)^2)+((D3+Terminal value)/(1+r)^3)

=(1.74657/1.1243)+(2.16347/(1.1243)^2)+(34.5528)/(1.1243)^3

=$27.58

Value of the stock=$27.58