Hi denise!
The basic formula for answering all the questions you ask is the bond
valuation formula. That is, that the price of a bond should be the
present value (discounted at the yield to maturity rate) of its coupon
and face value payments. The formula is:
P = C1/(1+i) + C2/(1+i)^2 + C3/(1+i)^3 + ... + (F+Cn)/(1+i)^n
where
P is the price of the bond
C1, C2, ..., Cn are the coupon payments
i is the yield to maturity
F is the face value of the bond
n is the number of periods to maturity
Question 1
A. I assume for this question that the face value of the bond is
$1,000. The current yield is simply the coupon payment divided by the
price of the bond. Since the coupon rate is 8%, the payment is 8% of
$1,000, which is $80. Now, since the price of the bond is $1,100,
Current Yield = 80/1100 = 0.072 = 7.2%
B. Using the notation I described above, we have for this problem that:
P = 1100
C1 = C2 = ... = Cn = 80
i = unknown
F = 1000
n = 10
Thus, with the bond price formula, we have one equation with one
unknown, thus we can find the value of i. In order to do it, use a
financial calculator. Here's an online yield to maturity calculator:
Yield to Maturity Calculator
http://www.investopedia.com/calculator/AOYTM.aspx
Entering the values for this problem, we get that the YTM is 6.6%
Question 2
I assume again that this bond has a face value of $1,000.
A. Since the coupon rate is 8%, bondholders get $80 per year
B. Again we must solve the previous equation with one unknown,
although the unknown this time is P rather than i (which in this case
we know to be 7%). Again, you can use a financial calculator to get
this. Here's an online bond price calculator:
Bond Price Calculator
http://www.investopedia.com/calculator/BondPrice.aspx
Filling in the known values (use 1000 for "redemption value", which is
the same as face value), we get that the price of this bond is
$1,065.15
C. Using 6% yield instead of 7% gives that the bond price rises to $1,136.03.
Google search terms
"bond price" calculator
"yield to maturity" calculator
I hope this helps!
Best wishes,
elmarto |