The default-free yield curve on zero-coupon U.S. Government Treasury securities
ID: 2742976 • Letter: T
Question
The default-free yield curve on zero-coupon U.S. Government Treasury securities is given below. Maturity (in years) Rate 1 .01 2 .015 3 .02 4 .025 5 .0275 6 .03 Currently you can buy a corporate bond sold by a company that has some chance of defaulting in the future. This corporate bond matures in 5 years, pays a 5 percent coupon once a year, and has a face value of $1000. A. If there is no change of default what would be the price of this corporate bond? Hint: if there is no chance of default, then the required rates of return for money at various horizons is given by the Treasury zero yield curve above. Given these rates, what would be the price of the corporate bond? B. If there was a default-free bond with the same cash flows as the corporate bond described above, what would its price be? What would its yield to maturity be? Hint: Use goal seek to figure out the single rate YTM when applied to the cash flows implied a present value equal to the price you just derived. C. The current price of the corporate bond with default risk is $1075 per $1000 in face value. What is the YTM on this bond? What is the annualized default risk premium on this bond (that is, what is the extra return per annum that this bond would return over a default free bond with the same payment stream)?
Explanation / Answer
Bond Value = FV { 1/(1+R/m)mN + (Cr/R) (1 - (1+R/m)-mN)}
FV = Par Value
Cr = Annual Coupon Rate
M = Coupon Per Year
R = Yield to Maturity
N = Number of Years to maturity
So, Price of bond = $1,000 {1/(1+0.0275)5 + (0.05/0.0275) (1 - (1+0.0275)-1)}
= $1,104
Par Value
$1000
interest Rate
2.75%
Periodic Payments
50
No. of Period
5
Present Value
$1103.783092
Dividend Yield (Current Yield)
4.53%
Par Value
$1000
interest Rate
2.75%
Periodic Payments
50
No. of Period
5
Present Value
$1103.783092
Dividend Yield (Current Yield)
4.53%
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.