A city issued a new series of bonds on Jan 1 2009. The bonds were sold at par ($

Question

A city issued a new series of bonds on Jan 1 2009. The bonds were sold at par ($1,000), have a 2.0% annual coupon rate and mature in 10years, 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 Jan 1 2012, assuming that you just paid $888.00 for it?

b) Assuming that the level of interest rates had risen to 4.5%, what should be the price of the bond on Jan 1 2011 (16 coupon payments left)?

c) On July 1,2012, you purchased the bond for $1,100 (purchased it just after the coupon payment was paid for june). what was the semi-annual yield to Maturity YIM at that date (13 coupon payments left)

Explanation / Answer

a) Semi-Annual Current Yield = Semi-Annual Coupon payment/price = (2%*1000/2)/888= 1.13%

b) Number of coupons left = 16

Coupon payment = 2%*1000/2= 10

price of the bond on Jan 1 2011 = 10/(1+4.5%/2) + 10/(1+4.5%/2)^2 + 10/(1+4.5%/2)^3 + 10/(1+4.5%/2)^4...........10/(1+4.5%/2)^16 + 1000/(1+4.5%/2)^16=$833.59

c) Number of coupons left = 13

Let semi-annual yield to Maturity = r

-1100 = 10/(1+r) + 10/(1+r) ^2 + 10/(1+r)^3 + 10/(1+r)^4.....................10/(1+r)^13 + 1000/(1+r)^13

semi-annual yield to Maturity,r= 0.22%

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