Question

Consider three bonds with 6.70% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years. a. What will be the price of the 4-year bond if its yield increases to 7.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. What will be the price of the 8-year bond if its yield increases to 7.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) c. What will be the price of the 30-year bond if its yield increases to 7.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.) d. What will be the price of the 4-year bond if its yield decreases to 5.70%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Bond Face Value(Assumed)	1,000	1,000	1,000	1,000
Bond Coupon Rate	6.70%	6.70%	6.70%	6.70%
Maturity(Years)	4	8	30	4
Yield to Maturity	7.70%	7.70%	7.70%	5.70%
We have to find out the present value of the inflows at yield to maturity rate to find out current price of the bond
					Assumed interest is payable half yearly.
Formula to calculate annuity of the present value is
PV of 1$=((1-(1+r)^(-n))/r) where r is the yield to maturity, n = period
So every six month interest will be paid=(1000*6.7%)/2				33.5
So we have calculate=Coupon*(PVIFA,r,n)+ Bond face value*(PVIF,r,n) where r is yield rate per period and n is period
					No we make our table to find out above
Bond Face Value(Assumed)	1,000	1,000	1,000	1,000
Maturity(Years)	8	16	60	8
Yield to Maturity	3.85%	3.85%	3.85%	2.85%
(a) Calculation of bond price with four year maturity & YTM 7.7%
So we have calculate=33.5*(PVIFA,3.85%,8)+ 1000*(PVIF,3.85%,8)
PVIFA=((1-(1+r)^(-n))/r) where r is the yield to maturity, n = period
PVIF=1/(1+r)^nwhere r is the yield to maturity, n = period
Let put the value into above
PVIFA=((1-(1+3.85%)^(-8))/3.85%)		6.77464
PVIF=1/(1+3.85%)^8		0.73918
put this value into above equation
Price of the Bond=33.5*(6.77464)+ 1000*(0.73918)			966.13
(b) Calculation of bond price with Eight year maturity & YTM 7.7%
So we have calculate=33.5*(PVIFA,3.85%,16)+ 1000*(PVIF,3.85%,16)
PVIFA=((1-(1+r)^(-n))/r) where r is the yield to maturity, n = period
PVIF=1/(1+r)^nwhere r is the yield to maturity, n = period
Let put the value into above
PVIFA=((1-(1+3.85%)^(-16))/3.85%)		11.78230
PVIF=1/(1+3.85%)^16		0.54638
put this value into above equation
Price of the Bond=33.5*(11.78230)+ 1000*(0.54638)			941.09
(c) Calculation of bond price with thirty year maturity & YTM 7.7%
So we have calculate=33.5*(PVIFA,3.85%,60)+ 1000*(PVIF,3.85%,60)
PVIFA=((1-(1+r)^(-n))/r) where r is the yield to maturity, n = period
PVIF=1/(1+r)^nwhere r is the yield to maturity, n = period
Let put the value into above
PVIFA=((1-(1+3.85%)^(-60))/3.85%)		23.28157
PVIF=1/(1+3.85%)^60		0.10366
put this value into above equation
Price of the Bond=33.5*(23.28157)+ 1000*(0.10366)			883.59
(d) Calculation of bond price with four year maturity & YTM 5.7%
So we have calculate=33.5*(PVIFA,2.85%,8)+ 1000*(PVIF,2.85%,8)
PVIFA=((1-(1+r)^(-n))/r) where r is the yield to maturity, n = period
PVIF=1/(1+r)^nwhere r is the yield to maturity, n = period
Let put the value into above
PVIFA=((1-(1+2.85%)^(-8))/2.85%)		7.06432
PVIF=1/(1+2.85%)^8		0.79867
put this value into above equation
Price of the Bond=33.5*(7.06432)+ 1000*(0.79867)			1,035.32
So is shows as interest rate decreases price of the bond increases