Question

kwesa corporation has a premium bond making semiannual payments . the bond pays a 9% coupon, has a YTM of 7%, and has 13 years to maturity. the modigliani company has a discount bond making semiannual payments. This bond pays 7%coupon, has YTM of 9%, and also has 13 years to maturity. if interest rate remain unchanged, what do you expect the price of these bonds to be?

i) a year from now

ii) in 3 years

iii) in 8 years

iv) in 12 years

whats going on here

Answer 1

i]

Price of Kwesa bond is calculated using PV function in Excel :

rate = 7% / 2 (converting annual YTM into semiannual YTM)

nper = 12 * 2 (12 years left to maturity with 2 semiannual coupon payments each year)

pmt = 4.5 (semiannual coupon payment = face value * coupon rate / 2 = 100 * 9% / 2)

fv = 100 (face value receivable on maturity)

PV is calculated to be $116.06

Price of Modigliani bond is calculated using PV function in Excel :

rate = 9% / 2 (converting annual YTM into semiannual YTM)

nper = 12 * 2 (12 years left to maturity with 2 semiannual coupon payments each year)

pmt = 3.5 (semiannual coupon payment = face value * coupon rate / 2 = 100 * 7% / 2)

fv = 100 (face value receivable on maturity)

PV is calculated to be $85.50

ii]

Price of Kwesa bond is calculated using PV function in Excel :

rate = 7% / 2 (converting annual YTM into semiannual YTM)

nper = 10 * 2 (10 years left to maturity with 2 semiannual coupon payments each year)

pmt = 4.5 (semiannual coupon payment = face value * coupon rate / 2 = 100 * 9% / 2)

fv = 100 (face value receivable on maturity)

PV is calculated to be $114.21

Price of Modigliani bond is calculated using PV function in Excel :

rate = 9% / 2 (converting annual YTM into semiannual YTM)

nper = 10 * 2 (10 years left to maturity with 2 semiannual coupon payments each year)

pmt = 3.5 (semiannual coupon payment = face value * coupon rate / 2 = 100 * 7% / 2)

fv = 100 (face value receivable on maturity)

PV is calculated to be $86.99

iii]

Price of Kwesa bond is calculated using PV function in Excel :

rate = 7% / 2 (converting annual YTM into semiannual YTM)

nper = 5 * 2 (5 years left to maturity with 2 semiannual coupon payments each year)

pmt = 4.5 (semiannual coupon payment = face value * coupon rate / 2 = 100 * 9% / 2)

fv = 100 (face value receivable on maturity)

PV is calculated to be $108.32

Price of Modigliani bond is calculated using PV function in Excel :

rate = 9% / 2 (converting annual YTM into semiannual YTM)

nper = 5 * 2 (5 years left to maturity with 2 semiannual coupon payments each year)

pmt = 3.5 (semiannual coupon payment = face value * coupon rate / 2 = 100 * 7% / 2)

fv = 100 (face value receivable on maturity)

PV is calculated to be $92.09

iv]

Price of Kwesa bond is calculated using PV function in Excel :

rate = 7% / 2 (converting annual YTM into semiannual YTM)

nper = 1 * 2 (1 years left to maturity with 2 semiannual coupon payments each year)

pmt = 4.5 (semiannual coupon payment = face value * coupon rate / 2 = 100 * 9% / 2)

fv = 100 (face value receivable on maturity)

PV is calculated to be $101.90

Price of Modigliani bond is calculated using PV function in Excel :

rate = 9% / 2 (converting annual YTM into semiannual YTM)

nper = 1 * 2 (1 years left to maturity with 2 semiannual coupon payments each year)

pmt = 3.5 (semiannual coupon payment = face value * coupon rate / 2 = 100 * 7% / 2)

fv = 100 (face value receivable on maturity)

PV is calculated to be $98.13

As the bonds near their maturity, their price converges to their face value. The discount bond increases in price, and the premium bond decreases in price, until, at maturity, the prices of both bonds equal their face value