Question

A bond has a face value of $1,000, a coupon rate of 8%, and a maturity of 10 years.  The bond makes semi-annual coupon payments.  The bond’s yield to maturity is 9%.  In Excel, the =PV formula can be used to find the price of the bond.  Fill in the table with the appropriate values:

RATE
NPER
PMT
FV
TYPE

Repeat problem , but with annual coupon payments.

RATE
NPER
PMT
FV
TYPE

Answer 1

Face value of the bond = 1000

Annual coupon rate = 8%

Annual coupon payment = Annual coupon rate*Face Value = 8%*1000 = 80

Time to maturity =10 years

Yield to maturity = 9%

Semi-annual coupon payments

For semi-annual coupon payments, we will consider semi-annual coupons, semi-annual YTM, and semi-annual periods to maturity

Semi-annual coupon payments = PMT = Annual coupon payments/2 = 80/2 = 40

semi-annual YTM = RATE = 9%/2 = 4.5%

No. of semiannual periods = NPER = 10*2 = 20

Face Value = FV = 1000

RATE = 4.5%

NPER = 20

PMT = 40

FV = 1000

TYPE = 0

=PV(4.5%,20,40,1000) = -934.96

Price of the bond with semiannual coupons = $934.96

Annual coupon payments

Yield to maturity = RATE = 9%

Time to maturity = NPER = 10 years

Annual coupon payments = PMT = 80

Face value = FV = 1000

RATE = 9%

NPER = 10

PMT = 80

FV = 1000

TYPE = 0

=PV(9%,10,80,1000) = -935.82

Price of the bond with annual coupons = $935.82