Question

A bond is callable at the end of 10 years for $6910 or at the end of 15 years for $8365. If the bond pays interest at j4=7%, matures at 95 in 20 years and has a face value of $8000, what price will guarantee the investor a yield of j4 =12%?

Answer 1

Quarterly coupon = $8000*7%/4 =$140

Redemption price after 20 years if the bond is not called = 8000*95/100 = $7600

If the bond is called after 10 years for $6910 and the investor should get 12% quarterly compounded return

Return required per quarter = 12%/4 = 3% =0.03

No of coupons = 10*4 =40

Price = 140/0.03*(1-1/1.03^40)+6910/1.03^40

=$5354.38

If the bond is called after 15 years for $8365 and the investor should get 12% quarterly compounded return

Return required per quarter = 12%/4 = 3% =0.03

No of coupons = 15*4 =60

Price = 140/0.03*(1-1/1.03^60)+8365/1.03^60

=$5294.40

If the bond is never called ,and the investor should get 12% quarterly compounded return

Return required per quarter = 12%/4 = 3% =0.03

No of coupons = 20*4 =80

Price = 140/0.03*(1-1/1.03^80)+7600/1.03^80

=$4942.33

So, the investors, by purchasing the bond at the minimum of the three prices as above i,e at a price of $4942.33 , will guarantee themselves a yield of 12%

Price is $4942.33 to guarantee the investor a yield of j4= 12%.