SEMIANNUAL SEMIANNUAL INTEREST AND INTEREST AND BOND VALUES BOND VALUES

Aileen V. Garrovillas |Ruth De Aileen V. Garrovillas |Ruth De Jesus SiaJesus Sia

BSA 3-14BSA 3-14

Value of the Bond at Time Zero Value of the Bond at Time Zero (B(B00))

Where:• I= annual interest paid in dollars.• M= par value in dollars.

d

dnkd

r

nrPVIFA

^11%,

)()( %,%,0 nkdnkd PVIFMPVIFAIB

nrPVIF dnkd ^1%,

Example:

Earl Washington wishes to Earl Washington wishes to find the value on Mills find the value on Mills Company’s bond. The bond Company’s bond. The bond has a 10% coupon interest has a 10% coupon interest rate and the required return rate and the required return on similar-risk bonds is 12% on similar-risk bonds is 12% annual interest and $1,000 annual interest and $1,000 par value, pays interest par value, pays interest semiannually, and has 10 semiannually, and has 10 years to maturity.years to maturity.

1.

Solution

1.

)()( %,%,0 nkdnkd PVIFMPVIFAIB

$50=I

x1/2$1,000x10%= I

Prt =I

2.

%6

20^%61120%,6

PVIFA

2.2.

d

dnkd

r

nrPVIFA

^11%,

%6

20^%61120%,6

PVIFA

46992122.1120%,6 PVIFA

3. nrPVIF dnkd ^1%,

20^%6120%,6 PVIF

311804726.020%,6 PVIF

2.

%6

20^%61120%,6

PVIFA

4. Then apply the resulted value of I, 4. Then apply the resulted value of I, PVIFAPVIFAkd%,n kd%,n and PVIFand PVIFkd%,n kd%,n to the Bto the B00 formula, which is;formula, which is;

oror

)()( %,%,0 nkdnkd PVIFMPVIFAIB

31180.0100046992.1150 oB

8.311496.573 oB

296.885oB30.885$oB

Exercises

1.1. Find the value of a bond Find the value of a bond maturing in 6 years, maturing in 6 years, semiannually, with a $1,000 semiannually, with a $1,000 par value and a coupon par value and a coupon interest rate of 10% (5% interest rate of 10% (5% paid semi- annually) if the paid semi- annually) if the required return on similar-required return on similar-risk bonds is 14% annual risk bonds is 14% annual interest (7% paid interest (7% paid semiannually).semiannually).

1.1.

Solution

1.

)()( %,%,0 nkdnkd PVIFMPVIFAIB

$50=I

x1/2$1,000x10%= I

Prt =I

2.

%6

20^%61120%,6

PVIFA

d

dnkd

r

nrPVIFA

^11%,

%7

12^%71112%,7

PVIFA

942686297.712%,7 PVIFA

3. nrPVIF dnkd ^1%,

12^%7112%,7 PVIF

444011959.012%,7 PVIF

2.

%6

20^%61120%,6

PVIFA

Then apply the resulted value of I, Then apply the resulted value of I, PVIFAPVIFAkd%,n kd%,n and PVIFand PVIFkd%,n kd%,n to the Bto the B00 formula, which is;formula, which is;

oror

)()( %,%,0 nkdnkd PVIFMPVIFAIB

44401.0100094269.750 oB

01.4441345.397 oB

1445.841oB14.841$oB

2. Calculate the value of each of the 2. Calculate the value of each of the bonds shown in the following table, all bonds shown in the following table, all of which pay interest semiannually.of which pay interest semiannually.

BondBond Par ValuePar Value Coupon Interest Coupon Interest raterate

Years to Years to MaturityMaturity

Required Required Stated Annual Stated Annual

ReturnReturn

AA $ 1,000$ 1,000 10%10% 1212 8%8%

BB 1,0001,000 12%12% 2020 12%12%

CC 500500 12%12% 55 14%14%

3. nrPVIF dnkd ^1%,

12^%7112%,7 PVIF

444011959.012%,7 PVIF

Solution:Solution:

2.2. )()( %,%,0 nkdnkd PVIFMPVIFAIB

Bond Solution Answer

AA BB00= $50 x (15.24696) + $1000 x (0.39012)== $50 x (15.24696) + $1000 x (0.39012)= $ 1152.47$ 1152.47

BB BB00= $60 x (15.04630) + $1000 x (0.09722)== $60 x (15.04630) + $1000 x (0.09722)= $ 1000$ 1000

CC BB00= $30 x (7.02358) + $500 x (0.50835)== $30 x (7.02358) + $500 x (0.50835)= $ 464.88$ 464.88

The Effective Annual Rate of The Effective Annual Rate of InterestInterest

(EAR) when Interest is Paid (EAR) when Interest is Paid Semiannually Semiannually

11

mr

m

EAR

For example, a bond with a 12% For example, a bond with a 12% required stated annual return, rrequired stated annual return, rdd, that , that pays semiannual interest would have pays semiannual interest would have an effective annual rate ofan effective annual rate of

1212.0

12

EAR

12

12

rEAR

106.12EAR

%36.12EAR

Exercise:Exercise:

Bella Valois wishes to Bella Valois wishes to find the effective annual find the effective annual rate associated with an rate associated with an 8% nominal annual rate 8% nominal annual rate when interest is when interest is semiannually.semiannually.

Solution:Solution:

%16.8

0816.0

10816.1

1

1

04.01

208.0

1

2

2

EAR

EAR

EAR

EAR

EAR