Solution:
Data given: Par value of Bond $ 1,000
Annual coupon rate 8%
Maturity period 11 years
Part 5a)
i) To find current price -
if the yield to maturity (YTM) is 7%
The general formula for current price of a bond is explained in Exhibit 1 below:
Further, the present value of an annuity (viz. the annual coupon payment) is explained in Exhibit 2 below and applied to the above formula to enable you to calculate the current price
Now applying the formula P = C [ {(1 + r)n - 1} / r(1 + r)n ] + F / (1 + r)n
where Face value, F = $ 1000
Coupon payment, C = $1000 x 8% = $ 80
Yield to maturity, r = 7% or 0.07
Maturity period, n = 11
P = $ 80 x [{(1 + 0.07)11 - 1} / 0.07 x (1 + 0.07)11] + $ 1000 / (1 + 0.07)11
= $ 80 x [(1.0711 - 1) / 0.07 x 1.0711 ] + $1000 / 1.0711
= $ 80 x 1.1048 / (0.07 x 2.1048) + $1000 / 2.1048
= $ 80 x 1.1048 / 0.1473 + $ 1000 / 2.1048
= $ 80 x 7.500 + $ 475.10
= $ 600 + $ 475.10
= $ 1,075.10
Similarly if we apply 8 % or 9 % as r in above formula we get the results:
if the yield to maturity (YTM) is 8% the current price is $ 1,000
if the yield to maturity (YTM) is 9% the current price is $ 931.95
ii) Find yield if the YTM is 7%, 8% and 9%
The yield is the coupon payment divided by the current price
So Yield if rate is 7% is 80 / 1075.10 = 0.0744 i.e 7.44%
… is 8% is 80 / 1000 = 8%
… is 9% is 80 / 931.95 = 0.0858 i.e. 8.58%
iii) If the required rate of return or the yield to maturity increases (as we have seen from 7% to 9%), the current price has an inverse relationship i.e. it decreases. Hence, if the required rate on a bond (or intrinsic rate of return) is higher the bond is discounted further to a lower price.
Part 5b) Solution is provided in Exhibit 3 viz the answers are $ 935.81, $ 961.10 and $ 990.83 in the three cases:
5a FYI bonds have a par value of $1,000. The bonds pay an 8% annual coupon...
8. Croft Inc, bonds have a par value of $1,000. The bonds have a 4% coupon rate and will mature in 10 years. Assume the bond is semi-annual 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. How does the relationship between the coupon rate and the yield to maturity determine how a bond's price will...
Croft Inc, bonds have a par value of $1000. The bonds have a 4% coupon rate and will mature in 10 years. Assume the bond is semi-annual. 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.
1) Bond with a $1.000 par value has an 8 percent annual coupon rate. It will mature in 4 years, and annual coupon payments are made at the end of each year. Present annual yields on similar bonds are 6 percent. What should be the current price? - a. S1.069.31 b. S1.000.00 c. $9712 d. $927.66 e. none of the above 2) A bond with a ten percent coupon rate bond pays interest semi-annually. Par value is $1.000. The bond...
1.A 30-year, $1,000 par value bond has a 9.5% annual payment coupon. The bond currently sells for $875. If the yield to maturity remains at its current rate, what willthe price be 9 years from now?2.Knapp Bros, LLC is planning to issue new 20-year bonds. The current plan is to make the bonds non-callable, but this may be changed. If the bonds are made callableafter 7 years at a 7% call premium, how would this affect their required rate of...
Harbuck’s Coffee semi-annual coupon, $1,000 par value bonds have 15 years to maturity. The bond’s annual coupon rate is 7% and they sell for $1,035 each. These bonds can be called in 3 years at a call price of $1,050. What is the bond’s yield to call? What is the bond’s yield to maturity? Which return would you expect to earn?
A.Zero Coupon Bonds A 7 year maturity zero coupon corporate bond has an 8% promised yield. The bond's price should equal B.The Fishing Pier has 6.40 percent, semi-annual bonds outstanding that mature in 12 years. The bonds have a face value of $1,000 and a market value of $1,027. What is the yield to maturity? C.Bond Yields Find the promised yield to maturity for a 7% coupon, $1,000 par 20 year bond selling at $1115.00. The bond makes semiannual coupon...
Company M has issued bonds previously. The bonds have a par value of $1,000 and offer an annual coupon rate of 6%. The bond has 9 years remaining until its maturity date. Calculate the value (price) of the bond assuming: The current market interest rate (also called the discount rate, required rate of return, Yield to Maturity) is... (A) 4% (B) 8% (C) 6%
Messenger, Inc. bonds have a 4% coupon rate with annual coupon payments and a $1,000 par value. The bonds have 5 years until maturity, and expected to yield 4.90%. What is the current yield for Messenger's bonds? 4.51% 4.33% 4.42% 4.16%
QUESTION 4 IBM's bonds currently sell for $1,040 and have a par value of $1,000. They pay $65 annual coupon and have a 15 year maturity, but may be called in 5 years at $1,000. What is their Yield to Maturity (YTM)? 5.78% 6.39% 6.71% 6.09% QUESTION 5 Bob's corporation's bonds make an annual payment of 7.35%. The bonds have a par value of $1,000, a current price of $1,130, and mature in 12 years. What is the yield to...
5. A firm's bonds have a maturity of 8 years with a $1,000 par value,, have an 11% coupon rate, are callable in 4 years at $1,154 and currently sell at a price of $1,283.09. Suppose the coupon payments are made quarterly a) What is the yield to maturity? N= 1/YR= 1/YR= PMT= PMT= FV= FV= PV= PV= Yield to maturity= b) What is the yield to call? N= I/YR PMT= FV= PV= Yield to call