(Related to Checkpoint 9.2 and Checkpoint 9.3) (Bond valuation) The 12-year $1,000 par bonds of Vail Inc. pay 9 percent interest. The market's required yield to maturity on a comparable-risk bond is 12 percent. The current market price for the bond is $910.
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?
(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 9%] |
PMT |
90 |
Yield to Maturity [YTM] |
1/Y |
? |
Time to Maturity [12 Years] |
N |
12 |
Bond Price [-$910] |
PV |
-910 |
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 = 10.34%.
“Hence, the yield-to-maturity of the Bond will be 10.34%”
(b)-The value of the Bond at market's required yield to maturity on a comparable-risk bond rate of 12%
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 = $90 [$1,000 x 9%]
Annual Yield to Maturity of the Bond = 12%
Maturity Period = 12 Years
The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value
= $90[PVIFA 12%, 12 Years] + $1,000[PVIF 12%, 12 Years]
= [$90 x 6.19437] + [$1,000 x 0.25668]
= $557.49 + $256.68
= $814.17
“Hence, the Value of the Bond will be $814.17”
(c)-Decision
“YES”. We should purchase the bond, since the bond is trading at Discount price of $814.17 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.
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