Bond valuation—Quarterly interest: Calculate the value of a ?$5,000?-par-value bond paying quarterly interest at an annual coupon interest rate of 12?% and having 6 years until maturity if the required return on? similar-risk bonds is currently a 11?% annual rate paid quarterly

1) Computation of Present Value of Bond using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Present Value = ?

Rate = 11%/4 = 2.75% compounded quarterly 

Nper = 6 Years*4 quarters = 24 quarters

PMT = $5,000*12%/4 = $150

FV = $5,000

Substituting the values in formula:

=-pv(2.75%,24,150,5000)

PV or Present Value of Bond = $5,217.51

2)

Computation of Present Value of Bond A using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Present Value = ?

Rate = 11%/2 = 5.50% compounded periods

Nper = 9 Years*2 periods = 18 periods 

PMT = $1,000*7%/2 = $35

FV = $1,000

Substituting the values in formula:

=-pv(5.50%,18,35,1000)

PV or Present Value of Bond = $775.08

Computation of Present Value of Bond B using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Present Value = ?

Rate = 12%/2 = 6% compounded periods

Nper = 20 Years*2 periods = 40 periods 

PMT = $500*13%/2 = $32.5

FV = $500

Substituting the values in formula:

=-pv(6%,40,32.50,500)

PV or Present Value of Bond = $537.62

Computation of Present Value of Bond C using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,

PV = Present Value = ?

Rate = 12%/2 = 6% compounded periods

Nper = 4 Years*2 periods = 8 periods 

PMT = $500*15%/2 = $37.50

FV = $500

Substituting the values in formula:

=-pv(6%,8,37.50,500)

PV or Present Value of Bond = $546.57