The City of Davenport issued a new series of bonds on Jan 1, 2009. The bonds wer
ID: 2375041 • Letter: T
Question
The City of Davenport issued a new series of bonds on Jan 1, 2009. The bonds were sold at par ($1,000), have a 2.8% annual coupon rate and mature in 10 years, on Jan 1, 2019. Coupon interest payments are made semi-annually (on June 30 and December 31).
(A) What was the Semi-Annual Current Yield of this bond on January 1, 2012 assuming that you just paid $788.00 for it? _________________
(B) Assuming that the level of interest rates had risen to 4.0%, what should be the price of the bond on January 1, 2011 (16 coupon payments left)? _________________
(C) On July 1, 2012, you purchased the bond for $1,300 (you purchased it just after the coupon payment was paid for June). What was the semi-annual Yield to Maturity (YTM) at that date (13 coupon payments left)? _________________
Explanation / Answer
semi-annual payment = 28 / 2 = $14
so the cash flows are :
jan 1,2012 : -788
june 30 , 2012 : 14
Dec , 2012 : 14
.
.
.
.
Jan 1, 2019 : 14 + 1000
so the IRR for the above cash flows is : 3.318 %
so the semi-annual YTM = 3.318 %
B)
The cash flows are :
june 30 , 2011 : 14
Dec , 2011 : 14
.
.
.
.
Jan 1, 2019 : 14 + 1000
The NPV for the above cash flow at 4% is 697.0403
so the bond price should be $ 697.0403
C)
july 1,2012 : -1300
Dec , 2012 : 14
.
.
.
.
Jan 1, 2019 : 14 + 1000
so the IRR for the above cash flows is : -0.7832 %
so the semi-annual YTM = -0.7832 %