A 25-year, 8% semiannual coupon bond with a par value of $1,000 may be called in
ID: 2637438 • Letter: A
Question
A 25-year, 8% semiannual coupon bond with a par value of $1,000 may be called in 4 years at a call price of $1,100. The bond sells for $950. (Assume that the bond has just been issued.)
What is the bond's yield to maturity? Round your answer to two decimal places.
%
What is the bond's current yield? Round your answer to two decimal places.
%
What is the bond's capital gain or loss yield? Loss should be indicated with minus sign. Round your answer to two decimal places.
%
What is the bond's yield to call? Round your answer to two decimal places.
%
Explanation / Answer
Answer :
All calculations are considered that the bond is compunded semi- anuualy.
1. Yield to maturity (YTM)= Cash flow * 1- (1/ [1+ interest rate ]^n) / interest rate + [ (Maturity value)* 1/ {( 1+ interest rate )^n}, here, interest rate is interest rate divided by 100 , n = no. of period.
Therefore, YTM = 1000 * 1- ( 1/ [ 1+0.08]^4)/0.08 + [ (950)*1/{(1+0.08)^4}
Hence YTM = $ 4007.33
2. Current Yield = Annual cash inflows / Market Price ( Call Price)
Therefore, Current yield = 5.2 %
3. Capital gains Yield = (P1 - P0) / P0,
Where P0 = Original Price, P1= Selling Price.
Hence , Capital gains Yield = (950-1000)/ 1000
Therefore, Capital Gains Yielld = (-0.05), i. e here the bond yields a loss of -5%
4. Yield to call = [C/ {(1+r)^t} ] + [ F/ {(1+r)^n}]
Where, P = price of the bond
n = number of periods
C = coupon payment
r = rate of interest
F = principal at maturity
t = time period when payment is to be received,
Hence, Yield to call = 11.63 %
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