Question

Miller Corporation has a premium bond making semiannual payments. The bond pays a coupon of 12 percent, has a YTM of 10 percent, and has 18 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond pays a coupon of 10 percent, has a YTM of 12 percent, and also has 18 years to maturity.

 

What is the price of each bond today? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

 

If interest rates remain unchanged, what do you expect the prices of these bonds to be 1 year from now? In 7 years? In 12 years? In 16 years? In 18 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Price of bond = C x [1-{1/ (1+r) ⁿ}/r] +M/ (1+r) ⁿ

C = Coupon amount = (Face Value x Coupon rate) / No. of coupon payments annually

r = Rate of interest, n = No of periods to maturity

M = Face Value = $ 1,000 (assumed)

Bond Price of Miller Corporation:

C = ($ 1,000 x 12 %)/2 = $ 120/2 = $ 60

r = 10 % p.a. or 0.1/2 = 0.05 semiannually

n = 18 yrs x 2 periods = 36 periods

Bond Price = $ 60 x [1-{1/ (1+0.05)³⁶}/0.05 ] + $ 1,000/ (1+0.05) ³⁶

                   = $ 60 x [1-{1/ (1.05) ³⁶}/0.05] + $ 1,000/ (1.05) ³⁶

                   = $ 60 x [1-(1/ 5.79181613597186)/0.05] + $ 1,000/ 5.79181613597186

                   = $ 60 x [(1- 0.172657414621502)/0.05] + $ 172.657414621502

                   = $ 60 x (0.827342585378498/0.05) + $ 172.657414621502

                  = $ 60 x 16.54685170757 + $ 172.657414621502

                 = $ 992.811102454197 + $ 172.657414621502

                  = $ 1,165.4685170757 or $ 1,165.47

Bond Price of Modigliani Company:

C = ($ 1,000 x 10 %)/2 = $ 100/2 = $ 50

r = 12 % p.a. or 0.1/2 = 0.06 semiannually

n = 18 yrs x 2 periods = 36 periods

Bond Price = $ 50 x [1-{1/ (1+0.06)³⁶}/0.06 ] + $ 1,000/ (1+0.06) ³⁶

                   = $ 50 x [1-{1/ (1.06) ³⁶}/0.06] + $ 1,000/ (1.06) ³⁶

                   = $ 50 x [1-(1/ 8.14725199985109)/0.06] + $ 1,000/ 8.14725199985109

                   = $ 50 x [(1- 0.122740771982784)/0.06] + $ 122.740771982784

                   = $ 50 x (0.877259228017216/0.06) + $ 122.740771982784

                  = $ 50 x 14.6209871336203 + $ 122.740771982784

                 = $ 731.049356681014 + $ 122.740771982784

                  = $ 853.790128663797 or $ 853.79

Current bond price of Miller Corporation is $ 1,165.47 and that of Modigliani Company is $ 853.79

Bond price can also be computed using PV factor table values as:

Bond price = C x PVIFA(r, n) + F x PVIF(r, n)

Bond Price change for Miller Corporation:

n = (18-1) x 2 = 17 x 2 = 34

Bond price = $ 60 x PVIFA (5 %, 34) + $ 1,000 x PVIF (5 %, 34)

                    = $ 60 x 16.192904 + $ 1,000 x 0.190355

                    = $ 971.57424 + $ 190.355 = $ 1,161.92904 or $ 1,161.93

n = (18 – 7) x 2 = 11 x 2 = 22

Bond price = $ 60 x PVIFA (5 %, 22) + $ 1,000 x PVIF (5 %, 22)

                    = $ 60 x 13.163003 + $ 1,000 x 0.34185

                    = $ 789.78018 + $ 341.85 = $ 1,131.63018 or $ 1,131.63

n = (18 – 12) x 2 = 6 x 2 = 12

Bond price = $ 60 x PVIFA (5 %, 12) + $ 1,000 x PVIF (5 %, 12)

                    = $ 60 x 8.86325 + $ 1,000 x 0.556837

                    = $ 531.795 + $ 556.873 = $ 1,088.63242 or $ 1,088.63

n = (18 – 16) x 2 = 2 x 2 = 4

Bond price = $ 60 x PVIFA (5 %, 4) + $ 1,000 x PVIF (5 %, 4)

                    = $ 60 x 3.5460 + $ 1,000 x 0.8227

                    = $ 212.76 + $ 822.7 = $ 1,035.46

n = (18 – 18) x 2 = 0

Bond price = $ 1,000

Bond Price change for Modigliani Company:

n = (18-1) x 2 = 17 x 2 = 34

Bond price = $ 50 x PVIFA (6 %, 34) + $ 1,000 x PVIF (6 %, 34)

                    = $ 50 x 14.3681 + $ 1,000 x 0.13791

                    = $ 718.405 + $ 137.91 = $ 856.315 or $ 856.32

n = (18 – 7) x 2 = 11 x 2 = 22

Bond price = $ 50 x PVIFA (6 %, 22) + $ 1,000 x PVIF (6 %, 22)

                    = $ 50 x 12.04158 + $ 1,000 x 0.2775

                    = $ 602.08 + $ 277.50 = $ 879.58

n = (18 – 12) x 2 = 6 x 2 = 12

Bond price = $ 50 x PVIFA (6 %, 12) + $ 1,000 x PVIF (6 %, 12)

                    = $ 50 x 8.38384 + $ 1,000 x 0.49697

                    = $ 419.192 + $ 496.97 = $ 916.162 or $ 916.16

n = (18 – 16) x 2 = 2 x 2 = 4

Bond price = $ 50 x PVIFA (6 %, 4) + $ 1,000 x PVIF (6 %, 4)

                    = $ 50 x 3.46511+ $ 1,000 x 0.792094

                    = $ 173.2555 + $ 792.094 = $ 965.3495 or $ 965.35

n = (18 – 18) x 2 = 0

Bond price = $ 1,000