BONDS PLEASE ANSWER ALL QUESTIONS AND SHOW WORK. Bond Questions 1 Consider the f
ID: 2802091 • Letter: B
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BONDS
PLEASE ANSWER ALL QUESTIONS AND SHOW WORK.
Bond Questions 1 Consider the following four bonds: Coupon Issue 5 years Zero Coupon PerpetualConvertible 5 yearsInfinity Maturity Coupon rate 5 years 5% | 6% zero 6% If the market yield is(7%, what is the value of the three first bonds (assuming that the face value is $1,000)?Jolc fon pv Why are the values of the bonds lower than their face values? Why is the coupon rate for the convertible bond lower than that of the nonconvertible, coupon issue? Suppose that the market yield rises to 7.5%, what are the bond values at that yield? a. b. c. d.Explanation / Answer
a. If the market yield is 7%;
for a coupon issue bond:
N= 5 years; Coupon = 6% of 1000 = $60; YTM = 7%; Future Value = Par value = $1000
value of the bond = Present Value.
Substituting the above values in financial calculator, and calculating for PV gives:
PV = $958.998 = ~ $958.99
For a Zero coupon Bond:
N= 5 years; Coupon = 0; YTM = 7%; Future Value = Par value = $1000
value of the bond = Present Value.
Substituting the above values in financial calculator, and calculating for PV gives:
PV = $712.986 = ~ $712.99
for a perpetual bond:
N= Infinity; Coupon = 6% of 1000 = $60; YTM = 7%;
Value of bond = Coupon per period / YTM
= 60 / 0.07 = $857.14
b. why are the values of the bonds lower than their face values?
values of these bonds are lower because the YTM is greater than the coupon rate.
Theoreticaly:
YTM is the required rate of return on a bond investment and coupon is the rate that you currently get from the investment. If the rate you require is less than the rate you get, you would obviously pay less than what you would pay if you get the expected return.
Accordingly, if the required rate of return = Coupon rate; bonds trade at par
if the required rate of return > Coupon rate; bonds trade at discount
if the required rate of return < Coupon rate; bonds trade at premium.
Mathematically:
Value of Bond for a 1 year maturity = Coupon / (1 + YTM)
when YTM > coupon, the bond value is less than when both are equal since the denominator is higher and numerator lower
C. why is coupon rate for convertible bond lower than that of the nonconvertible, coupon issue:
The holder of the convertible bond can convert his bond into a specified number of shares. This gives the holder an extra opportunity and reduces the interest rate risk. This reduction in risk is accordingly captured in the coupon rate with a reduced return.
D.
If the YTM = 7.5%, then same as per question (a) but modifying the YTM, we would get:
for a coupon issue bond:
N= 5 years; Coupon = 6% of 1000 = $60; YTM = 7.5%; Future Value = Par value = $1000
value of the bond = Present Value.
Substituting the above values in financial calculator, and calculating for PV gives:
PV = $939.311 = ~ $939.31
For a Zero coupon Bond:
N= 5 years; Coupon = 0; YTM = 7.5%; Future Value = Par value = $1000
value of the bond = Present Value.
Substituting the above values in financial calculator, and calculating for PV gives:
PV = $696.5586 = ~ $696.56
for a perpetual bond:
N= Infinity; Coupon = 6% of 1000 = $60; YTM = 7.5%;
Value of bond = Coupon per period / YTM
= 60 / 0.075 = $800.00
As the YTM increases and coupon remains same, the value of the bond decreases.
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