Heymann Company bonds have 4 years left to maturity. Interest is paid annually,
ID: 2718596 • Letter: H
Question
Heymann Company bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 9%.
What is the yield to maturity at a current market price of
$834? Round your answer to two decimal places.
%
$1,081? Round your answer to two decimal places.
%
Would you pay $834 for each bond if you thought that a "fair" market interest rate for such bonds was 14%-that is, if rd = 14%?
A) You would not buy the bond as long as the yield to maturity at this price is less than the coupon rate on the bond.
B) You would buy the bond as long as the yield to maturity at this price is greater than your required rate of return.
C) You would buy the bond as long as the yield to maturity at this price is less than your required rate of return.
D) You would buy the bond as long as the yield to maturity at this price equals your required rate of return.
E) You would not buy the bond as long as the yield to maturity at this price is greater than your required rate of return.
Explanation / Answer
Given data,
Par value of Bond = $1000
Coupon Rate = 9%
Remaining period of maturity = 4 years
Redeemed value = $1000 (since no information is available, par value is taken)
Market Value = Net PV of Cashflows
Computation of Yield To Maturity when market value is $834:
Market Price = [(1000*9/100) * PVAF (YTM, 4 yrs)] + (1000 * PVF (YTM, 4 yrs))
Applying trial and error method,
At YTM = 15%,
Market Price
= [(1000*9/100) * PVAF (15%, 4 yrs)] + (1000 * PVF (15%, 4 yrs))
= 256.948 + 571.753
= $828.701
At YTM = 14%,
Market Price
= [(1000*9/100) * PVAF (14%, 4 yrs)] + (1000 * PVF (14%, 4 yrs))
= 262.234 + 592.080
= $854.314
For 1% decrease in YTM, market price increased by $25.613.
For how much increase in YTM, market price increases by $ 5.299?
5.299 / 25.613 = 0.2068%
Therefore, YTM = 15 – 0.2068 = 14.7932%
YTM = 14.7932%
Computation of Yield To Maturity when market value is $1081:
Market Price = [(1000*9/100) * PVAF (YTM, 4 yrs)] + (1000 * PVF (YTM, 4 yrs))
Applying trial and error method,
At YTM = 7%,
Market Price
= [(1000*9/100) * PVAF (7%, 4 yrs)] + (1000 * PVF (7%, 4 yrs))
= 304.849 + 762.895
= $1067.744
At YTM = 6%,
Market Price
= [(1000*9/100) * PVAF (6%, 4 yrs)] + (1000 * PVF (6%, 4 yrs))
= 311.859 + 792.094
= $1103.953
For 1% decrease in YTM, market price increased by $36.209.
For how much increase in YTM, market price increases by $13.256?
13.256 / 36.209 = 0.3661%
Therefore, YTM = 7 – 0.3661 = 6.6339%
YTM = 6.6339%
If coupon rate is less than the yield to maturity, the expected market value is less than the fair market value and if coupon rate is more than the yield to maturity, the expected market value is more than the fair market value.
If fair market value is less than the expected market value, it is recommended to pay for the bond and purchase it, otherwise it is not preferrable.
Fair market value is less than the expected market value when coupon rate is more than the yield to maturity.
Therefore, correct option is A) You would not buy the bond as long as yield to maturity at this price is less than the coupon rate on the bond