Question

 The 9​-year ​$1 comma 1000 par bonds of Vail Inc. pay 14 percent interest. The​ market's required yield to maturity on a​ comparable-risk bond is 10 percent. The current market price for the bond is $ 1110. a.  Determine the yield to maturity. b.  What is the value of the bonds to you given the yield to maturity on a​ comparable-risk bond? c.  Should you purchase the bond at the current market​ price?

Answer 1

a) Here face value = $1000 ,
Interest = face value x coupon rate
= 1000 x 14%
= 140$
n = no of coupon payments= 9
Current market price = $1110
YTM = Interest + (Face value - selling price)/n / (Face value + selling price)/2
=140 + (1000-1110)/9 / (1000+1110)/2
=140 + (-110/9) / (2110/2)
=140 + (-12.2222) / 1055
= 127.78 / 1055
= 0.12112
= i.e 12.11%

b) Here face value = $1000 ,
Interest = face value x coupon rate
= 1000 x 14%
= 140$
n = no of coupon payments= 9
YTM = 10%
Value of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(10%,9) = [1-(1/(1+10%)^9 / 10%]
=[1-(1/(1+0.10)^9 / 0.10]
=[1-(1/(1.10)^9 / 0.10]
=[1-0.4241 / 0.10]
=0.5759/0.10
=5.7590
PVIF(10%,9) = 1/(1+10%)^9
=1/(1.10)^9
= 0.4241
Value of bond = 140 x 5.7590 + 1000 x 0.4241
=806.26 + 424.097
= 1230.36 $

c) yes bond should be purchased as derieved market price is more than actual market price