Question

You are given the following information with respect to a bond: par value: 1000 term to maturity: 3 years annual coupon rate 6% payable annually You are also given that the one, two, and three year annual spot interest rates are 7%, 8%, and 9% respectively. The bond is sold at a price equal to its value. Calculate the annual effective yield rate for the bond i.

Answer 1

To calculate the annual effective yield rate for the bond, you need to calculate the present value of the bond's cash flows and then use that value to calculate the yield rate. Here are the steps: Calculate the present value of the bond's cash flows, Calculate the bond's value, Calculate the annual effective yield rate.

Step-by-step explanation:

To calculate the annual effective yield rate for the bond, you need to calculate the present value of the bond's cash flows and then use that value to calculate the yield rate. Here are the steps:

1. Calculate the present value of the bond's cash flows: At the end of the first year, you receive a coupon payment of $60 (which is 6% of the bond's par value of $1000). At the end of the second year, you receive another coupon payment of $60. And at the end of the third year, you receive a coupon payment of $60 plus the bond's par value of $1000. To calculate the present value of these cash flows, you need to discount each cash flow using the corresponding spot interest rate. The present value of the first cash flow is $60/(1+0.07) = $56.07, the present value of the second cash flow is $60/(1+0.08)² = $52.80, and the present value of the third cash flow is ($60+$1000)/(1+0.09)³ = $904.85.
2. Calculate the bond's value: The bond's value is the sum of the present values of its cash flows. In this case, the bond's value is $56.07 + $52.80 + $904.85 = $1013.72.
3. Calculate the annual effective yield rate: The annual effective yield rate is the rate that makes the bond's value equal to its price. In this case, the bond is sold at a price equal to its value, so the yield rate is 0%. However, if the bond was sold at a price different from its value, you would need to solve for the yield rate using an iterative method or a financial calculator.

Answer 2

Tha annual effective yield rate for the bond is:

= 6.2%

Step-by-step explanation:

a) Data and Calculations:

Bond par value = $1,000

Annual coupon rate = 6%

Annual spot interest rates = 7%, 8%, and 9% for year 1, year 2, and year 3 respectively

Current value of bond = $970 ($1,000 * 99% * 99% * 99%)

Annual coupon payments = $60 * 3 = $180

Effective rate for the three years = $180/$970 * 100 = 18.6%

Annualized effective yield rate = 6.2% (18.6%/3)

OR

Annualized effective yield rate = (Annual coupon payments/Current value of bonds)

= 6.2% ($60/$970)