Final answer:
The price of the 5-year $1000 par value bond with a 10% annual coupon rate, paid semiannually, when seeking a 14% annual simple rate of return, is calculated by summing the present value of all future cash flows discounted at 7% per semiannual period. Market conditions, such as interest rates, affect the bond's price: it falls when rates rise and increases when they fall.
Step-by-step explanation:
To determine the price paid for a $1000 par value bond with a 10 percent annual coupon rate and semiannual payments, where the buyer seeks a 14 percent annual simple rate of return, we need to calculate the present value of the bond's future cash flows discounted at the desired yield to maturity (YTM).
The bond pays semiannual interest, so the coupon payment is 10 percent of $1000 divided by 2, which equals $50 every six months. Because the desired YTM is 14 percent per annum, we will use 7 percent per semiannual period for discounting the future cash flows.
To find the present value of the bond, we use the present value formula for each coupon payment and the face value, and then sum them up:
Present Value (PV) = C / (1 + r)^t + ... + C / (1 + r)^n + F / (1 + r)^n
Where:
C = Coupon payment ($50)
r = Discount rate per period (7%)
t = Time period
n = Total number of periods
F = Face value ($1000)
Since there are 5 years with 2 periods each, n equals 10. After calculating the present value of each payment and the face value, we sum them to get the price paid for the bond.
As market conditions change, such as fluctuations in interest rates, the price of existing bonds will adjust accordingly. If interest rates rise, the bond's market value will generally fall to provide a yield comparable to newly issued bonds with higher rates. Conversely, if interest rates decline, the value of the bond will rise.