Answer :
Answer:
A) YTM 7.06%
B) $847.8784
C) No I will not as it is overpriced.
Explanation:
A) the yield to maturity is calculate as the rate at which the present value of the coupon payment and maturity equals the market price.
It is done by approximation or using excel or financial calculator.
YTM using goal seek excel: 0.070630268 = 7.06%
Using this rate rounded:
Present value of the coupon payment.
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C: 1,000 x 8% = $ 80.00
time 15 years
YTM: 0.076
[tex]80 \times \frac{1-(1+0.0706)^{-15} }{0.0706} = PV\\[/tex]
PV $725.8798
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity: $1,000
time 15 years
YTM: 0.076
[tex]\frac{1000}{(1 + 0.0706)^{15} } = PV[/tex]
PV 359.41
PV coupon $725.8798 + PV maturity $359.4110 = $1,085.2909
B) Present value of the bond at comparable-risk YTM:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C: 1,000 x 8% = $ 80.00
time 15 years
comparable risk rate: 0.1
[tex]80 \times \frac{1-(1+0.1)^{-15} }{0.1} = PV\\[/tex]
PV $608.4864
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity $ 1,000.00
time 15 years
comparable risk rate: 0.1
[tex]\frac{1000}{(1 + 0.1)^{15} } = PV[/tex]
PV 239.39
PV coupon $608.4864 + PV market $239.3920 = $847.8784
I will not purchase as it is overvalued:
1,085 - 847.88= 237.12