Question

Bond Price MovementsMiller Corporation has a premium bond making semiannual payments. The bond pays a coupon of 6.5 percent, has a YTM of 5.3 percent, and has 13 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond pays a coupon of 5.3 percent, has a YTM of 6.5 percent, and also has 13 years to maturity. Both bonds have a par value of $1,000. If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? In 3 years? In 8 years? In 12 years? In 13 years? What’s going on here? Illustrate your answers by graphing bond prices versus time to maturity

Answer 1

Miller company Bonds
Price of bond 1 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 5.3/2 = 2.65% nper =12*2 =24 pmt =1000*6.5%*1/2 =32.5 fv =1000 type =0	PV(2.65%,24,32.5,1000,0)	($1,105.55)
Price of bond 3 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 5.3/2 = 2.65% nper =10*2 =20 pmt =1000*6.5%*1/2 =32.5fv =1000 type =0	PV(2.65%,20,32.5,1000,0)	($1,092.22)
Price of bond 8 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 5.3/2 = 2.65% nper =5*2 =10 pmt =1000*6.5%*1/2 = 32.5fv =1000 type =0	PV(2.65%,10,32.5,1000,0)	($1,052.11)
Price of bond 12 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 5.3/2 = 2.65% nper =1*2 =2 pmt =1000*6.5%*1/2 = 32.5fv =1000 type =0	PV(2.65%,2,32.5,1000,0)	($1,011.54)
Price of bond 0 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 5.3/2 = 2.65% nper =0*2 =2 pmt =1000*6.5%*1/2 = 32.5fv =1000 type =0	PV(2.65%,0,32.5,1000,0)	($1,000.00)
Modigiliani Company Bonds
Price of bond 1 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 6.5/2 = 3.25% nper =12*2 =24 pmt =1000*5.3%*1/2 = 26.5 fv =1000 type =0	PV(3.25%,24,26.5,1000,0)	($901.07)
Price of bond 3 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 6.5/2 = 3.25% nper =10*2 =20 pmt =1000*5.3%*1/2 = 26.5 fv =1000 type =0	PV(3.25%,20,26.5,1000,0)	($912.76)
Price of bond 8 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 6.5/2 = 3.25% nper =1*2 =2 pmt =1000*5.3%*1/2 = 26.5 fv =1000 type =0	PV(3.25%,10,26.5,1000,0)	($949.47)
Price of bond 12 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 6.5/2 = 3.25% nper =12*2 =24 pmt =1000*5.3%*1/2 = 26.5 fv =1000 type =0	PV(3.25%,2,26.5,1000,0)	($988.56)
Price of bond 0 year from now	PRICE OF A PREMIUM BOND	Using present value function in MS excel	rate = 6.5/2 = 3.25% nper =0*2 =24 pmt =1000*5.3%*1/2 = 26.5 fv =1000 type =0	PV(3.25%,0,26.5,1000,0)	($1,000.00)

This can be concluded from the above analysis that as the bonds will approach to maturity, price of premium bond to start decreasing and price of discount bond will start increasing and on the date of maturity, price of both kind of bonds (Premium and discount) would be equal to face value of bonds.