Answer:
YTM 7.02%
Explanation:
we will calcualte the YTM of the current bonds to know the market rate.
Issuing the bonds at this rate will put them at par value.
The YTM is the one which mades the future coupon payment and maturity equal to the market price.
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
Coupon payment: 1,000 x 8%/2 = 40
time 30 (15 years x 2 payment)
[tex]40 \times \frac{1-(1+r)^{-30} }{r} = PV\\[/tex]
PV coupon
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 30.00
[tex]\frac{1000}{(1 + r)^{30} } = PV[/tex]
PV maturity 355.24
PV coupon + PV maturity = 1,090
For maths reason the only way to solve for rate is with trial and error
we can, however use excel to do it more quickly than by hand:
we write on A1 cell 0.1
en on B1 cell: =PV(A1,30,40)
on C1 cell= 1,000/power(1+A1;1/30)
on D1 =B1+C1
What we are doing is expressing the formulas on excel
then we use goal seek on D1
w e want it on 1090 cahnging the cell A1 which is the rate
this give us the semiannual rate of :
0.035100422
we multiply by 2 to get the annual rate:
0.070200843
YTM = 7.02%
we need to issue the bond at this rate.
