Answered

The 15​-year, ​$1,000 par value bonds of Waco Industries pay 8 percent interest annually. The market price of the bond is ​$1,085​, and the​ market's required yield to maturity on a​ comparable-risk bond is 10 percent.
a. Compute the​ bond's yield to maturity.
b. Determine the value of the bond to you given the​ market's required yield to maturity on a​ comparable-risk bond.
c. Should you purchase the​ bond?

Answer :

TomShelby

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

Other Questions