If there a two bonds issued and each pay $100.annual interest plus $1000. at maturity, Bond L has maturity of 15yrs.; Bond S maturity of 1 yr., what will be the value of each bond when the interest rate is 5%, 8% and12%? Assuming only one payment left to be made.
Bond value and time—Constant required returns Pecos Manufacturing has just
issued a 15-year, 12% coupon interest rate, $1,000-par bond that pays interest
annually. The required return is currently 14%, and the company is certain it will
remain at 14% until the bond matures in 15 years.
a. Assuming that the required return does remain at 14% until maturity, find the
value of the bond with (1) 15 years, (2) 12 years, (3) 9 years, (4) 6 years,
(5) 3 years, and (6) 1 year to maturity.
To calculate the value of each bond at different interest rates, we can use the formula for the present value of a bond:
PV = I / (1+r)^n + F / (1+r)^n
Where:
PV is the present value of the bond
I is the annual interest payment
F is the face value or final payment at maturity
r is the interest rate
n is the number of years until maturity
Let's calculate the values of Bond L and Bond S at interest rates of 5%, 8%, and 12%, assuming only one payment is left.
For Bond L:
- Annual interest payment (I) = $100
- Face value at maturity (F) = $1000
- Maturity (n) = 15 years
For Bond S:
- Annual interest payment (I) = $100
- Face value at maturity (F) = $1000
- Maturity (n) = 1 year
Now, using the formula, we can calculate the present value (PV) for each bond at different interest rates:
Interest rate of 5%:
PV(L) = $100 / (1+0.05)^15 + $1000 / (1+0.05)^15
PV(S) = $100 / (1+0.05)^1 + $1000 / (1+0.05)^1
Interest rate of 8%:
PV(L) = $100 / (1+0.08)^15 + $1000 / (1+0.08)^15
PV(S) = $100 / (1+0.08)^1 + $1000 / (1+0.08)^1
Interest rate of 12%:
PV(L) = $100 / (1+0.12)^15 + $1000 / (1+0.12)^15
PV(S) = $100 / (1+0.12)^1 + $1000 / (1+0.12)^1
Calculating these values will give us the present value of each bond at the different interest rates.