Question

Assume that you are a financial analyst in the fixed income department of an investment bank. You are given the following information: the 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are, respectively, 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum, with continuous compounding. Your task is to answer the following questions.

1. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 4% per annum semiannually.
2. Calculate the yield rate of this bond.

Answer 1

GIVEN IN THE QUESTION -

• FACE VALUE = 100
• MATURITY PERIOD = 30 MONTHS
• COUPON RATE = 4% p.a.
• INTEREST AMOUNT (SEMI-ANNUALLY) = 2 (which is calculated as = 100 * 4% * 6/12)
• CASHFLOWS AT THE END OF YEAR 1 TO YEAR 4 = INTEREST AMOUNT = 2
• CASHFLOWS AT THE END OF YEAR 5 = INTEREST AMOUNT + PRINCIPAL REPAYMENT = 2 + 100 = 102

CASH PRICE OF BOND = 98.173 which is calculated as follows -

YIELD RATE OF BOND = 4.074 % which is calculated as follows -

%