A $25 000, 10% bond redeemable at par on December 1, 2025, is purchased on September 25, 2014, to yield 7.6% compounded semi-annually. Bond interest is payable semi-annually. a)What is the quoted or market price? b)What is the accrued interest? c)What is the cash or purchase price?
To calculate the quoted or market price, accrued interest, and cash or purchase price of the bond, we need to consider the following:
1) Quoted or market price: This refers to the actual price at which the bond is traded in the market. It can be calculated using the present value formula and the yield to maturity (YTM).
2) Accrued interest: This is the interest earned by the bondholder from the last interest payment date to the date of purchase. It is calculated based on the interest rate and the number of days between the last payment date and the purchase date.
3) Cash or purchase price: This is the total amount paid by the investor to purchase the bond, including both the quoted price and the accrued interest.
Now, let's calculate each of these:
a) Quoted or market price:
To calculate the quoted price, we need to calculate the present value of the bond's future cash flows (interest payments and the principal amount) using the yield to maturity. In this case, the bond is purchased to yield 7.6% compounded semi-annually.
To calculate the present value, we can use the formula:
Quoted Price = ∑ [Cash Flow / (1 + Yield/2)^(n*2)]
Where:
Cash Flow = coupon payment (10% of $25,000 = $2,500) and principal payment ($25,000)
Yield = yield to maturity rate (7.6% divided by 2 = 3.8%)
n = number of periods until payment (number of semi-annual periods)
Since the bond matures on December 1, 2025, and it's purchased on September 25, 2014, there are 11 years and 2 months remaining until maturity, which is equal to 22 semi-annual periods.
Calculating the quoted price:
Quoted Price = ($2,500 / (1 + 3.8%)^1) + ($2,500 / (1 + 3.8%)^2) + ... + ($2,500 / (1 + 3.8%)^44) + ($25,000 / (1 + 3.8%)^44)
Using a financial calculator or spreadsheet software, perform the above calculations to determine the quoted or market price.
b) Accrued interest:
To calculate the accrued interest, we need to determine the number of days from the last interest payment date to the date of purchase and then calculate the interest earned for that period.
To do this, count the number of full semi-annual periods from the last interest payment date (June 1, 2014) to the purchase date (September 25, 2014), which is approximately 0.25 of a semi-annual period.
Accrued Interest = (0.25 * $2,500) = $625
c) Cash or purchase price:
The cash or purchase price is the sum of the quoted price and the accrued interest.
Cash or Purchase Price = Quoted Price + Accrued Interest
Now, using the previously calculated quoted price from part a) and the accrued interest from part b), calculate the cash or purchase price.