Rolling Company bonds have a coupon rate of 5.00 percent, 19 years to maturity,

Question

Rolling Company bonds have a coupon rate of 5.00 percent, 19 years to maturity, and a current price of $1,136. What is the YTM? The current yield? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Rolling Company bonds have a coupon rate of 5.00 percent, 19 years to maturity, and a current price of $1,136. What is the YTM? The current yield? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

Let the Face Value=1000

Coupon Rate=5% , So coupon is 50

Price of the bond=PV of the coupons plus the PV of the face value at maturity

or 1136=50/(1+YTM)^1+50/(1+YTM)^2+50/(1+YTM)^3+50/(1+YTM)^4+50/(1+YTM)^5+50/(1+YTM)^6+50/(1+YTM)^7+50/(1+YTM)^8+50/(1+YTM)^9+50/(1+YTM)^10+50/(1+YTM)^11+50/(1+YTM)^12+50/(1+YTM)^13+50/(1+YTM)^14+50/(1+YTM)^15+50/(1+YTM)^16+50/(1+YTM)^17+50/(1+YTM)^18+50/(1+YTM)^19+1000/(1+YTM)^19

By solving through trial and eroor in excel , we get YTM=0.0398 or 3.98% . It is obvious that YTM will be lower than the coupon rate as the bond is selling at a premium.

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