In: Finance
6) Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of $1,000, have 12 years remaining to maturity, and have a required rate of return of 8 percent.
a. The bond has a 6 percent coupon rate.
b. The bond has a 8 percent coupon rate.
c. The bond has a 10 percent coupon rate.
d. What do your answers to part (a) through (c) say about the relation between coupon rates and present values?
For a, b and c:
Using financial calculator BA II Plus - Input details: |
a. |
b. |
c. |
I/Y = Rate/Frequency = |
4.000000 |
4.000000 |
4.000000 |
PMT = Coupon rate / Frequency x FV = |
-$30.00 |
-$40.00 |
-$50.00 |
N = Number of years remaining x frequency = |
24 |
24 |
24 |
FV = Future Value = |
-$1,000.00 |
-$1,000.00 |
-$1,000.00 |
CPT > PV = Present value = |
$847.53 |
$1,000.00 |
$1,152.47 |
Formula based present value of annuity: |
|||
PV = |PMT| x ((1-(1+R%)^-N)/R% + |FV|/(1+R%)^N = |
$847.53 |
$1,000.00 |
$1,152.47 |
d. Rest all remains equal, as we increase coupon rate the price of the bond increasing. The coupon rates and PVs or bond prices are positively related.