Question

In: Finance

A 10% semiannual bond was issued in June of 2014 with 10 years to maturity. You...

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?

Solutions

Expert Solution

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%

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