Question

 The 10​-year $1,000 par bonds of Vail Inc. pay 11 percent interest. The​ market's required yield to maturity on a​ comparable-risk bond is 8 percent. The current market price for the bond is $1,090.

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?

(round to two decimal places).

Answer 1

(a)

Computation of YTM(r):

Price of Bond = Present Value of all future expected Cashflows

Price of Bond = Present Value of Coupon Payments and Redemption Amount

$1090 = [($1000*11%) * PVAF(r%, 10 Years)] + [$ 1000 * PV(r%, 10 Years)]

Let us discount at 8%,

Price of Bond = [$110 * PVAF(8%, 10 Years)] + [$ 1000 * PV(8%, 10 Years)]

Price of Bond = [$110 * 6.7100] + [$ 1000 * 0.4632]

Price of Bond = $ 1,201.30 (If YTM is 8%, Price should be $ 1,201.3)

As at 8% the PV of Future expected payments is morethan the Current Market price, the YTM will be lessthan 8%

Let us assume YTM = 7.88%

Then, Price of Bond = [$110 * PVAF(7.88%, 10 Years)] + [$ 1000 * PV(7.88%, 10 Years)]

Price of Bond = [$110 * 6.7462] + [$ 1000 * 0.4684]

Price of Bond = $ 1,090

At 7.88%, PV of Future expected payments is same sa current market price, the YTM is 7.88%

(b)

Price of Bond = [$110 * PVAF(8%, 10 Years)] + [$ 1000 * PV(8%, 10 Years)]

Price of Bond = [$110 * 6.7100] + [$ 1000 * 0.4632]

Price of Bond = $ 1,201.30

(c) No, It is not advisable to buy the bond at current price as the YTM of the bond is less than the YTM of Comparable bond.

r	1+r	(1+r)^-n	1- [(1+r)^-n]	[1- [(1+r)^-n]] /r
8.00%	1.0800	0.4632	0.5368	6.7100
7.88%	1.0788	0.4684	0.5316	6.7462