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Q4. FYI bonds have a par value of $1,000. The bonds pay $40 in interest every...

Q4. FYI bonds have a par value of $1,000. The bonds pay $40 in interest every six months and will mature in 10 years.

a. Calculate the price if the yield to maturity on the bonds is 7, 8, and 9 percent, respectively.

b. Explain the impact on price if the required rate of return decreases.

c. Compute the coupon rate on the bonds. How does the relationship between the coupon rate and the yield to maturity determine how a bond's price will compare to it par value?

Expert Solution

a)

PRICE OF BOND = C x 1 - (1+r)^-n / r + F / (1+r)

YTM = 7%(PREMIUM) = 40 x 1 - (1+0.035)^-20 / 0.035 + 1000 / (1+0.035)

= 1071.06

YTM = 8%(PAR) = 40 x 1 - (1+0.04)^-20 / 0.04 + 1000 / (1+0.04)

= 1000

YTM = 9%(DISCOUNT) = 40 x 1 - (1+0.045)^-20 / 0.045 + 1000 / (1+0.045)

= 934.96

b)

as the required rate decreses the price of bond increases , they share inverse relationship that is because as the required rate decreases the investor is now willing for accept lower rate of return also so as the required rate decreases the price of bond in value shall increase

c)

COUPON RATE = COUPON AMOUNT PER ANNUM / PAR VALUE OF BOND

COUPON AMOUNT = 40 x 2 =80

PAR VALUE OF BOND = 1000

COUPON RATE (IN ALL 3 CASES ) = 80 / 1000

= 8%

relationship between the coupon rate and the yield to maturity determine how a bond's price will compare to it par value

If the yield to maturity for a bond is less than the bond’s coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa).

If a bond’s coupon rate is less than its YTM, then the bond is selling at a discount.
If a bond’s coupon rate is more than its YTM, then the bond is selling at a premium.
If a bond’s coupon rate is equal to its YTM, then the bond is selling at par.

jeff jeffy answered 2 years ago

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