Question

QUESTION 1: (a) If a coupon bond of 15 years pays an 10.7% coupon and the prevailing discount rate is 9.6%, compute its current price. Is this a discount or premium bond? b) Assume the bond in (a) is a semi-annual coupon bond. Using the other information in (a), compute its price. c) Common shares of Linux Ltd. will grow at 13.21% for three years and 9.3% for another two years. The growth rate will eventually drop to 7.5% and remain constant thereafter. The company just paid a dividend of GH¢ 1.01. If the cost of equity is 11.1%, compute its price. d) What is the market value of a $1,000 face-value bond with a 12 percent coupon rate when the market's rate of return is 8 percent?

Answer 1

1. a. The price of a bonds needs to be calculated by using PV function in EXCEL

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

rate=9.6%

nper=15

pmt=coupon payment*face value=10.7%*1000=107

fv=1000

=PV(9.6%,15,107,1000,0)

PV=$1085.61

The market price is higher than the face value, hence it is a premium bond

b. If the payments are semi-annual

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

rate=9.6%/2=4.8%

nper=15*2=30

pmt=semi- annual coupon payment=(coupon rate*face value)/2=(10.7%*1000)/2=107/2=53.5

fv=1000

=PV(4.8%,30,53.5,1000,0)

PV=$1086.51

2. Dividends paid D0=1.01

For next three years, dividends grow at 13.21% and 9.3% for another 2 years

D1=1.01*1.1321=1.143

D2=1.143*1.1321=1.294

D3=1.294*1.1321=1.465

D4=1.465*1.093=1.602

D5=1.602*1.093=1.751

Then eventually drops to 7.5% and continues forever

D6=1.751*1.075=1.882

Terminal value at Year5=D6/(cost of equity-growth rate)=1.882/(11.1%-7.5%)=52.28

Value of the Stock=(D1/(1+11.1%))+(D2/(1+11.1%)^2)+(D3/(1+11.1%)^3)+(D4/(1+11.1%)^4)+((D5+Terminal value at Year5)/(1+11.1%)^5)

=(1.143/1.111)+(1.294/1.111^2)+(1.465/1.111^3)+(1.602/1.111^4)+(54.029/1.111^5)

=1.029+1.049+1.069+1.051+31.920

=36.12

Value of the Share=36.12

3. The price of a bond needs to be found by using PV function in EXCEL

In this case, the maturity time has not provided like they provided in 1st case. If maturity=nper=0,Then the bond price will be same as face value. If you have maturity period, just input the number in nper

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

rate=8%

nper=0

pmt=coupon payment=12%*1000=120

fv=1000

=PV(8%,0,120,1000,0)

PV=1000

The price of the bond=1000

If the maturity period is 15 just like in the 1st problem,

=PV(8%,15,120,1000,0)

PV=1342.38

The price of the bond=1342.38