120. Bond value and effective annual rate Answer: b Diff: T
Since the securities are of equal risk, they must have the same effective rate. Since the comparable 10-year bond is selling at par, its nominal yield is 8 percent, the same as its coupon rate. Because it is a semiannual coupon bond, its effective rate is 8.16 percent. Using your calculator, enter NOM% = 8; P/YR = 2; and solve for EFF%.
(Remember to change back to P/YR = 1.) So, since the bond you are considering purchasing has quarterly payments, its nominal rate is calculated as follows: EFF% = 8.16; P/YR = 4; and solve for NOM%. NOM% = 7.9216%. (Again, remember to change back to P/YR = 1.) To determine the quarterly payment bond’s price you must use the cash flow register because the payment amount changes. CF0 = 0, CF1 = 20; Nj = 20; CF2 = 25; Nj = 19; CF3 = 1025; I = 7.9216/4 = 1.9804; and then solve for NPV = $1,060.72.
121 . Bond value after reorganization Answer: d Diff: T
Financial calculator solution:
Inputs: CF0 = 0; CF1 = 0; Nj = 5; CF2 = 100; Nj = 4; CF5 = 1600; I = 20.
Output: NPV = $362.44. VB = $362.44.
122 . Bond sinking fund payment Answer: d Diff: T
The company must call 5 percent or $50,000 face value each year. It could call at par and spend $50,000 or buy on the open market. Since the interest rate is higher than the coupon rate (14% vs. 12%), the bonds will sell at a discount, so open market purchases should be used.
Financial calculator solution:
Inputs: N = 30; I = 7; PMT = 60; FV = 1000.
Output: PV = -$875.91. VB = $875.91.
The company would have to buy $50,000/$1,000 = 50 bonds at $875.91 each = $43,795.50 $43,796.
123 . Bond coupon payment Answer: b Diff: T
Calculate YTM or kd for first issue:
Inputs: N = 20; PV = -701.22; PMT = 80; FV = 1000.
Output: I = kd = YTM = 12%.
Calculate PMT on second issue using 12% = kd = YTM:
Inputs: N = 5; I = 12; PV = -701.22; FV = 1000.
Output: PMT = $37.116 ≈ $37.12.
124 . Bonds with differential payments Answer: c Diff: T
Step 1: Calculate the EAR of 9% nominal yield bond compounded semi-annually. Use interest rate conversion feature.
Inputs: P/YR = 2; NOM% = 9. Output: EFF% = 9.2025%. (Remember to change back to P/YR = 1.)
Step 2: Calculate the nominal rate, k Nom, of a 9.2025% EAR but with quarterly compounding.
Inputs: P/YR = 4; EFF% = 9.2025. Output: NOM% = 8.90%. (Remember to change back to P/YR = 1.)
Step 3: Calculate the quarterly periodic rate from kNom of 8.9% and calculate the quarterly payment.
kPER = kNom/4 = 8.90%/4 = 2.225%.
Inputs: N = 80; I = 2.225; PV = -1000; FV = 1000.
Output: PMT = $22.25.
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