John is interested in joining with a large corporation in a cooperative venture to share risks and pool resources for his small
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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:
<u>Miller Bond:</u>
The coupon payment are calcualte as ordinary annuity
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)
PV $833.1532
While Maturity, using the lump sum formula
Maturity $1,000.00
time 28 semesters
rate 0.04
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
PVcoupon $799.1385
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.
<u>We recalculate the same formula with values of:</u>
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
<em>Remember:</em> there are two payment per year.
Same process will be done with Modigliani bond:
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
PV coupon $595.9251
Maturity $ 1,000.00
time 28 semester
rate 0.05
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.