110. Yield to maturity--semiannual bond Answer: d Diff: M N
N = 8 2 = 16; I = ?; PV = ?; PMT = 0.095/2 1,000 = 47.50; FV = 1,000
Step 1: Determine the bond’s current price.
Current yield = Annual interest/Current bond price
8.2% = $95.00/VB
VB = $95.00/0.082
VB = $1,158.54.
Step 2: Determine the bond’s yield to maturity.
N = 16; PV = -1158.54; PMT = 47.50; FV = 1000; I = ? Solve for I = kd/2 = 3.44%; kd = 3.44% 2 = 6.89%.
111 . Annual interest payments remaining Answer: b Diff: M
Financial calculator solution:
Inputs: I = 10; PV = -847.88; PMT = 80; FV = 1000.
Output: N = 15 years.
112
. Current yield and capital gains yield Answer: c Diff: M
First, calculate the bond price as follows: N = 6 2 = 12; I = 8.5/2 = 4.25; PMT = 0.10/2 1,000 = 50; FV = 1000; and then solve for PV =
-$1,069.3780. VB = $1,069.378.
The current yield (CY) is then $100/$1,069.3780 = 9.35%. Recognizing that the CY and capital gains yield (CG) constitute the total return (YTM) on the bond or CY + CG = YTM, solve for CG in the following equation 9.35% + CG = 8.5%, CG = -0.85%.
113 . Current yield and YTM Answer: c Diff: M
Step 1: Calculate the price of the 16-year bond:
Current yield = Coupon/Price
8% = $100/Price
Price = $100/0.08 = $1,250.00.
This assumes a $1,000 face value. It doesn’t matter what face value you select as long as you are consistent throughout your calculations.
Step 2: Calculate the 16-year bond’s YTM:
Enter the following input data in the calculator:
N = 16; PV = -1250; PMT = 100; FV = 1000; and then solve for I = 7.3%.
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