Question

The 10​-year ​$1,000 par bonds of Vail Inc. pay 14 percent interest. The​ market's required yield to maturity on a​ comparable-risk bond is 17 percent. The current market price for the bond is $ 940.

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)- The​ bond's yield to maturity.

The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Face Value [$1,000]	FV	1,000
Coupon Amount [$1,000 x 14%]	PMT	140
Yield to Maturity [YTM]	1/Y	?
Time to Maturity [10 Years]	N	10
Bond Price [-$940]	PV	-940

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the yield to maturity (YTM) on the bond = 15.20%

“Hence, the yield-to-maturity of the Bond will be 15.20%”

(b)-The value of the Bond at market's required yield to maturity on a​ comparable-risk bond rate of 17%

The Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Annual Coupon Amount = $140 [$1,000 x 14%]

Annual Yield to Maturity of the Bond = 17%

Maturity Period = 10 Years

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $140[PVIFA 17%, 10 Years] + $1,000[PVIF 17%, 10 Years]

= [$140 x 4.65860] + [$1,000 x .20804]

= $652.20 + $208.04

= $860.24

“Hence, the Value of the Bond will be $860.24”

(c)-Decision

“YES”. We should purchase the bond, since the bond is trading at Discount price of $860.24 per Bond.

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.

-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.