Question

A bond has a $1000 par value and issued 5 years ago. The bond has 10 years to maturity and an annual 8% annual coupon and sells for $990.

i) Estimate the bond's current yield

ii) Estimate the bond's yield-to-maturity

iii) Explain the relationship of the bond price and its yield

(Please explain the answer in detail, thank you)

Answer 1

(i)-Bond’s Current Yield

Current Yield of the Bond = (Annual Coupon Amount / Selling Price of the Bond) x 100

= [($1,000 x 8%) / $990] x 100

= [$80 / $990] x 100

= 8.08%

“The bond's current yield = 8.08%”

(ii)- Bond's yield-to-maturity

Yield to Maturity [YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [(Par Value + Bond Price)/2]

Par Value = $1,000

Annual Coupon Amount = $80 [$1,000 x 8%]

Bond Price = $990

Maturity Years = 5 Years [10 Years – 5 Years]

Therefore, Yield to Maturity [YTM] = Coupon Amount + [(Par Value – Bond Price) / Maturity Years] / [(Par Value + Bond Price)/2]

= [$80 + {($1,000 – $990) / 5 Years)] / [($1,000 + $990) / 2]

= [($80 + $2.00) / $995]

= [$82 / $995]

= 0.0825

= 8.25%

“The Bond's yield-to-maturity = 8.25%”

(iii)- Relationship of the bond price and its yield

- If the Yield To Maturity [YTM] of the Bond is equal to the Coupon rate of the bond, then the Selling price of the bond will be equal to the par Value or Face Value of the Bond

- If the Yield To Maturity [YTM] is greater than the coupon rate, then the selling price of the bond will be less than it’s par value, since the bonds are selling at discount

- If the Yield To Maturity [YTM] is less than the coupon rate, then the selling price of the bond will be more than it’s par value, since the bonds are selling at premium.