Question

18. Bond Price Movements Bond X is a premium bond making semiannual

payments. The bond has a coupon rate of 7.5 percent, a YTM of 6 percent,

and 13 years to maturity. Bond Y is a discount bond making semiannual

payments. This bond has a coupon rate of 6 percent, a YTM of 7.5 percent,

and also 13 years to maturity. What are the prices of these bonds today

assuming both bonds have a $1,000 par value? If interest rates remain

unchanged, what do you expect the prices of these bonds to be in 1 year?

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. Need steps in Exel

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

B Bond X $1,000.00 7.50% $1,000.00 6.00% Face value Coupon rate Coupon frequency Years to maturity Yield to maturity Bond Y Face value Coupon rate Coupon frequency Years to maturity Yield to maturity 2 13 6% 13 7.50% Current Price of Bond-X $1,134.08 Current Price of Bond-Y $876.80 Year 1 13 14 Price Bond X $1,127.02 $1,111.58 $1,063.98 $1,014.35 $1,000.00 Bond Y $882.66 $895.78 $938.40 $985.80 $1,000.00 15 8 16 12 13 Bond Price vs. Time to maturity $1,200.00 $1,100.00 $1,000.00 Price $900.00 $800.00 32 $700.00 + 1 3 5 7 9 11 13 15 33 34 35 36 37 Years Bond X Bond Y 38

Cell reference -

А В Bond X Bond Y 1000 1000 0.075 0.06 Face value Coupon rate Coupon frequency Years to maturity Yield to maturity Face value Coupon rate Coupon frequency Years to maturity Yield to maturity 13 13 0.06 0.075 Current Price of Bond-X =PV(C7/2,C6*2,-C4/2*C3,-C3,0) Current Price of Bond-Y =PV(F7/2,F6*2,-F4/2*F3,-F3,0) Year Price Bond X Bond Y =PV($C$ 7/2,(13-B13)*2,-$C$4/2*$C$3,-$C$3,0) =PV($F$ 7/2,(13-B13)* 2,-$F$4/2*$F$3,-$F$3,0) =PV($C$7/2,(13-B14)*2,-$C$4/2*$C$3,-$C$3,0) =PV($F$7/2,(13-B14)*2,-$F$4/2*$F$3,-$F$3,0) =PV($C$7/2,(13-B15)*2,-$C$4/2*$C$3,-$C$3,0) =PV($F$7/2,(13-B15)*2,-$F$4/2*$F$3,-$F$3,0) =PV($C$7/2,(13-B16)*2,-$C$4/2*$C$3,-$C$3,0) =PV($F$7/2,(13-B16)*2,-$F$4/2*$F$3,-$F$3,0) =PV($C$7/2,(13-B17)*2,-$C$4/2*$C$3,-$C$3,0) =PV($F$7/2,(13-B17)*2,-$F$4/2*$F$3,-$F$3,0) Bond Price vs. Time to maturity $1,200.00 $1,100.00 $1,000.00 Price $900.00 $800.00 $700.00 11 13 Years Bond X Bond Y

Both bonds, premium and discount, are reaching to its maturity value (face value) as time to maturity reducing.

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.