1. What is the value of a $1,000 par value bond with annual payments of a(n) a.
ID: 2659506 • Letter: 1
Question
1. What is the value of a $1,000 par value bond with annual payments of a(n)
a. 10% coupon with a maturity of 10 years and a 15% required return?
b. 8% coupon with a maturity of 10 years and a 8% required return?
c. 11% semiannual coupon with a maturity of 20 years and a 11% required return?
d. 8% semiannual coupon with a maturity of 20 years and a 9% required return?
2. What is the yield to maturity of a $1000 par value bond with a(n)
a. 10% annual coupon and 10 years to maturity and a $1,000 price?
b. 9.5% annual coupon and 20 years to maturity and a $788 price?
c. 5.0% annual coupon and 8 years to maturity and a $800 price?
Can I please get the answer with the formula so I can better understand? Thank you.
Explanation / Answer
1. Formula PV = PMT * (1 - (1 + i) ^ -n) / i + M * (1+i) ^ -10
a. PV = 100 * (1 - (1 + 0.15) ^ -10) / 0.15 + 1,000 (1 + 0.15) ^ -10 = $749.06 (when our required rate of return is higher than the coupon rate of the bond, we will buy the bond at a discount. This means we will pay less than face value for it, which should always be $1,000.)
b. $1,000 (this is because our required return is the exact same as the bond payment, so we would pay face value)
c. $1,000 (same thing)
d. $907.99 (here be careful, because it is semiannual, your coupon rate is really 4%, your number of periods is 40, and your required rate is 4.5%)
2. Formula YTM = (C + (F - P) / n) / ((F + P) / 2)
a. YTM = (100 + (1,000 - 1,000) / 10) / ((1,000 + 1,000) / 2) = 10% (when a bond is purchased at face value, the YTM is equal to the coupon rate)
b. 12.41% (if the bond is selling below the face value, the YTM must be more than the coupon rate)
c. 8.55%
Please let me know if you need help setting up the other parts.
Hope that helps!
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