Question

Miller Corporation has a premium bond making semiannual payments. The bond pays a coupon of 10 percent, has a YTM of 8 percent, and has 14 years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond pays a coupon of 8 percent, has a YTM of 10 percent, and also has 14 years to maturity.What is the price of each bond today? Price of Miller Corporation bond $ ____ Price of Modigliani Company bond $ ____If interest rates remain unchanged, what do you expect the prices of these bonds to be 1 year from now? In 4 years? In 9 years? In 13 years? In 14 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)Price of bond Miller Corporation Bond Modigliani Company Bond 1 year $ _________ $ _________ 4 years $ _________ $_________ 9 years $ _________ $_________ 13 years $ _________ $ _________ 14 years $_________ $_________

Answer 1

Answer:

          Miller Bond:                    

Today:      1,166.63

1-year       1,159.83

4-years     1,135.90

9-years     1,081.11

13-years   1,018.86

14-years  1,000 (maturity)

Modigliani Bond

Today:     851.01

1-year      856.25

4-years    875.38

9-years     922.78

13-years   981.41

14-years  1,000 (maturity)

Explanation:

The present value will be the discount coupon payment and maturirty at the YTM rate:

Miller Bond:

The coupon payment are calcualte as ordinary annuity

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 50.00 (1,000 x 10% / 2)

time      28 (14 years x 2 payment per year)

rate   0.04 (8% YTM / 2 payment per year)

$50 \times \frac{1-(1+0.04)^{-28} }{0.04} = PV$

PV $833.1532

While Maturity, using the lump sum formula

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  $1,000.00

time   28 semesters

rate  0.04

$\frac{1000}{(1 + 0.04)^{28} } = PV$  

PV   333.48

PV coupon $833.1532  +PV maturity  $333.4775  = Total $1,166.6306

For the subsequent time we must adjust t

in one year, there will be 26 payment until maturity

$50 \times \frac{1-(1+0.04)^{-26} }{0.04} = PV$

PVcoupon $799.1385

$\frac{1000}{(1 + 0.04)^{26} } = PV$  

PVmaturity   360.69

Total $1,159.8277

As the bond get closer to maturity it will get closer to face value until maturity when it will equalize it.

We recalculate the same formula with values of:

in 4-year : then 10 years to maturity t = 20

in 9-years: then 5 years to maturity t= 10

in 13-years: 1 year to maturity t = 2

at 14 years: is maturity date so equals the face value of 1,000

Remember: there are two payment per year.

Same process will be done with Modigliani bond:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 1,000 x 8% / 2 payment per year : 40.00

time: 14 years x 2 payment per year = 28 payment

rate 10% annual rate /2 = 0.05

$40 \times \frac{1-(1+0.05)^{-28} }{0.05} = PV$

PV coupon $595.9251

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity $ 1,000.00

time   28 semester

rate  0.05

$\frac{1000}{(1 + 0.05)^{28} } = PV$  

PV  maturity 255.09

PV coupon $595.9251  + PV maturity  $255.0936 = Total $851.0187

and then we calcualte for the same values of t we are asked for the Miller bond.