Question

A bond with face value $1,000 has a current yield of 6% and a coupon rate of 8%. a. If interest is paid annually, what is the bond’s price? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. Is the bond’s yield to maturity more or less than 8%? More Less

Answer 1

Answer:

a. Price of Bond is $1,333.33

b. Less

Explanation:

a.

Current yield is the ratio of coupon payment to the market value of the bond. It is the rate of income received from bond at current market rate.

As given

Coupon Payment = $1,000 x 8% = $80

Current Yield formula is as follow

Current Yield = Coupon Payment / Market Value

6% = $80 / Market Value

Market Value = $80 / 6%

Market Value = $1,333.33

b.

As we know that

if Price > Face value then YTM < Coupon rate

if Price < Face value then YTM > Coupon rate

if Price = Face value then YTM = Coupon rate

According to given condition

$1,333.33 > $1,000 then YTM < 8%

The bond’s yield to maturity is less than 8%.

Answer 2

Bond current yield is the annual interest paid by a bond expressed in %

• The formulae for Bond Current Yield is Annual Coupon payment of bond / Current selling or market price of the bond

6% = ($1,000 * 8%) / Current selling price of the bond

6% = $80 / Current selling price of the bond

Current selling price of the bond = $80 / 6%

Current selling price of the bond = $80 / 0.06

Current selling price of the bond = $1333.33333333

Current selling price of the bond = $1,333.33

Therefore, the bond’s price is $1,333.33.

if Price > Face value then YTM < Coupon rate

if Price < Face value then YTM > Coupon rate

if Price = Face value then YTM = Coupon rate

Now, $1,333.33 > $1,000 then YTM < 8%. Therefore, the bond’s yield to maturity is less than 8% because it is a premium bond.

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