Question

Bond j has a coupon rate of 5 percent and bond k has a coupon rate of 11 percent. both bonds have 13 years to maturity, make semiannual payments, and have a ytm of 8 percent. if interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? (negative amounts should be indicated by a minus sign. do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places,
e.g., 32.16.) percentage change in price of bond j % percentage change in price of bond k % what if rates suddenly fall by 2 percent instead? (do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places,
e.g., 32.16.) percentage change in price of bond j % percentage change in price of bond k %

Answer 1

To find the change in the price of the bonds, first need to find the price of individual Bond.

Bond Price is directly related to the change in the YTM of the bond. If the YTM rises by 2%, the price of the bond will fall.

Bond J :

(WHEN YTM IS 8%)

Coupon Rate: 5%

Coupon Amount (PMT): $1,000 * 5% = $50/2 = $25 (Semi annual coupon amounts)

Number of years (NPER) = 13*2 = 26

YTM (rate) = 8%/2 = 4%

Face Value: $1000

Price (PV0) : ?

To find the price of the bond, can either use excel or with formula.

When input the below formula in excel,

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

P0 =pv(4%,26,-25,-1000)

When input the formula in excel, we get PV as $760.26

(WHEN YTM RISES BY 2%, NEW YTM IS 10%)

Coupon Amount (PMT): $25 (Semi annual coupon amounts)

Number of years (NPER) = 26

YTM (rate) = 10%/2 = 5%

Face Value: $1000

Price (PV1) : ?

To find the price of the bond, can either use excel or with formula.

When input the below formula in excel,

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

P1 =pv(5%,26,-25,-1000)

When input the formula in excel, we get PV as $640.62

CHANGE IN THE BOND PRICE OF BOND J DUE TO THE CHANGE IN THE YTM

%change = (P1 – P0)/P0

%change = ($640.62 - $760.26)/$760.26

%change = -18.68%

Therefore, with the increase in 2% YTM of BOND J, the price falls by 18.68%

Bond K :

(WHEN YTM IS 8%)

Coupon Rate: 11%

Coupon Amount (PMT): $1,000 * 11% = $110/2 = $55 (Semi annual coupon amounts)

Number of years (NPER) = 13*2 = 26

YTM (rate) = 8%/2 = 4%

Face Value: $1000

Price (PV0) : ?

To find the price of the bond, can either use excel or with formula.

When input the below formula in excel,

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

P0 =pv(4%,26,-55,-1000)

When input the formula in excel, we get PV as $1,239.74

(WHEN YTM RISES BY 2%, NEW YTM IS 10%)

Coupon Amount (PMT): $55 (Semi annual coupon amounts)

Number of years (NPER) = 26

YTM (rate) = 10%/2 = 5%

Face Value: $1000

Price (PV1) : ?

To find the price of the bond, can either use excel or with formula.

When input the below formula in excel,

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

P1 =pv(5%,26,-55,-1000)

When input the formula in excel, we get PV as $1,071.88

CHANGE IN THE BOND PRICE OF BOND K DUE TO THE CHANGE IN THE YTM

%change = (P1 – P0)/P0

%change = ($1071.88 - $1239.74)/$1239.74

%change = -13.54%

Therefore, with the increase in 2% YTM of BOND k, the price falls by 13.54%

SIMILALRY IF THE BOND PRICES FALLS BY 2%, the YTM WILL BE 6%/2 = 3% **(REFER THE IMAGE ATTACHED)