Question

purchased a coupon bond on January 2, 2020 with the following information: You purchased Coupon rate: 6.00% Interest payment: annual Maturity: 5 years Par Amount: $10,000 Yield to Maturity: 6.20% 33.1 - What price did you pay for this bond? Show all calculations. 33.2 - If you sold the bond exactly two years later at a price of $101, what is your annualized rate of return for the two years, assuming you did not reinvest any coupon payments? You must show your work to receive full credit.

Answer 1

Q33.1

$Price = \frac{coupon \ rate \times par \ value}{(1+YTM)^1}+....\frac{coupon \ rate \times par \ value}{(1+YTM)^5}+\frac{par \ value}{(1+YTM)^5}$

$Price = \frac{0.06 \times 10000}{(1+0.062)^1}+....\frac{0.06 \times 10000}{(1+0.062)^5}+\frac{10000}{(1+0.062)^5}$

So the price of the bond would be 9,916.21

Q33.2

When the selling price given is $101 and the par value is 10000, the SP is 101% x 10000 = 10100

When the selling price is $10100 and the purchase price is $9916.21 the annualized rate of return is calculated as follows:

$r = (\frac{SP}{Purcahse \ Price})^{\frac{1}{2}}-1$

$r = (\frac{10100}{9916.21})^{\frac{1}{2}}-1$