114. Length of time until annual bonds called Answer: b Diff: M N
For these kinds of problems, set up the two valuations (without call and with call). Use the yield to maturity information to solve for the price of the bond. Then, use the price of the bond to solve for the time until the call may be exercised.
Step 1: Solve for the price of the bond. Input the following data into your calculator: N = 10; I = 7.4; PMT = 90; FV = 1000; and solve for PV = -$1,110.3285. VB = $1,110.3285.
Step 2: Use the price calculated in the first step to solve for the time until the bond can be called. Input the following data into your calculator: I = 6.5; PV = -1110.3285; PMT = 90; FV = 1050; and solve for N = 3.1569 or 3.16 years.
115 . Market value of semiannual bonds Answer: a Diff: M
Financial calculator solution:
Inputs: N = 20; I = 6; PMT = 20; FV = 1000.
Output: PV = -$541.20; VB = $541.20.
Since there are 10,000 bonds outstanding the total value of debt is $541.20(10,000) = $5,412,000.
116 . Future bond value--annual payment Answer: c Diff: M
The YTM = Current yield + Capital gain.
Thus: Capital gain = YTM - Current yield
= 9.7072% - 10% = -0.2928%.
The price in 1 year = Price now (1 + CG%).
Price now:
Current yield = Annual coupon/Price.
Thus: Price = Annual coupon/Current yield
= $110/0.10 = $1,100.
Price in one year = $1,100 (1 + CG%)
= $1,100 (1 - 0.002928) (Remember to express the
= $1,096.78 $1,097. capital gain as a decimal.)
117 . Bond coupon rate Answer: c Diff: M
Financial calculator solution:
Inputs: N = 10; I = 5; PV = -768; FV = 1000.
Output: PMT = $19.955 (semiannual PMT).
Annual coupon rate = (PMT 2)/M = ($19.955 2)/$1,000 = 3.99% 4%.
118 . Bond coupon rate Answer: d Diff: M
Financial calculator solution:
Inputs: N = 20; I = 7; PV = -1158.91; FV = 1000.
Output: PMT = $85.00 (semiannual PMT).
Annual coupon rate = $85(2)/$1,000 = 17.0%.
119 . Bond value Answer: d Diff: T
Burger King V B:
Calculate EAR to apply to Burger King bonds using interest rate conversion feature, and calculate the value, VBK, of Burger King bonds:
Inputs: P/YR = 2; NOM% = 12. Output: EFF% = EAR = 12.36%. (Remember to switch P/YR back to 1.)
Inputs: N = 20; I = 12.36; PMT = 80; FV = 1000.
Output: PV = -$681.54. V B = $681.54.
McDonalds V B:
Inputs: N = 40; I = 6; PMT = 40; FV = 1000.
Output: PV = -$699.07. V B = $699.07.
Calculate the difference between the two bonds' PVs:
Difference: VB(McD) - VB(BK) = $699.07 - $681.54 = $17.53.
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