Business, 29.10.2019 00:31 Danielyanez

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 $ 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 $ $

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Answer from: runninglovexoxo

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

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

C50.00 (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:

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

C1,000 x 8% / 2 payment per year : 40.00

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

rate10% annual rate /2 = 0.05

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

PVcoupon $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.

Answer from: Quest

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Answer from: Quest

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Miller corporation has a premium bond making semiannual payments. the bond pays a coupon of 10 perce...

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