In: Finance
A 10% semiannual bond was issued in June of 2014 with 10 years
to maturity. You purchased
the bond when it was issued. Immediately after the purchase, the
TYM changed to some new
level X and remained at this new level for 5 years. In June of 2019
you received your coupon,
the interest rates changed again to a new value of Y and you sold
your bond for 103 (all of this
happened in a single day).
a. If your realized return is 12.1% (annualized value), what is the
value of X?
b. What is the value of Y?
Pv | Selling Price of Bond in June 2019 after payment of dividend | $103 | ||||||||
Number of years to maturity | 5 | (10-5) | ||||||||
Nper | Number of semiannual periods to maturity | 10 | (5*2) | |||||||
Pmt | Semiannual coupon amount | $5.00 | (100*0.1)/2 | |||||||
Fv | Maturity payment | $100.00 | ||||||||
RATE | Semi annualInterest Rate | 4.6% | (Using Rate Function of excell with Nper=10, Pmt=5,Pv=-103, Fv=100) | |||||||
Y | AnnualInterest Rate=(4.6*2)% | 9.2% | ||||||||
Selling Price | $103.00 | |||||||||
Dividends received | $50 | (10*5) | ||||||||
Totalamount received | $153.00 | |||||||||
Purchase Price =P | ||||||||||
Realized return annualized=((153/P)-1)/5 | ||||||||||
((153/P)-1)/5=12.1%=0.121 | ||||||||||
((153/P)-1)=5*0.121= | 0.605 | |||||||||
153/P= | 1.605 | |||||||||
Pv | P=purchase Price =153/1.605= | $95.33 | ||||||||
Nper | Number of semiannual periods to maturity | 20 | (10*2) | |||||||
Pmt | Semiannual coupon amount | $5.00 | (100*0.1)/2 | |||||||
Fv | Maturity payment | $100.00 | ||||||||
RATE | Semi annualInterest Rate | 5.4% | (Using Rate Function of excell with Nper=20, Pmt=5,Pv=-95.33, Fv=100) | |||||||
Y | AnnualInterest Rate=(5.4*2)% | 10.8% | ||||||||
VALUE OF =X | 10.8% | |||||||||