• The interest rate for the first year is 4% (no uncertainty).
• The one-year interest rate could move up or down by 1% each year.
• The probability that the rate moves higher is 70%; it moves lower is 30%. Note the values differ from the lecture examples.
• All bonds have a face value of $1,000.
• Coupon bonds have a coupon rate of 5%, paid annually at the end of each year.

Complete the table by answering the following questions. Some cells are complete so that you can verify your calculations against mine. Perform your calculations on a calculator or with Excel. Round your final answer as in the table below. Do not round intermediate values; use all the decimal places in subsequent computations.

Asset	Price	Yield	Discount Factor
1-year zero-coupon face $1,000. coupon 0%
2-year zero-coupon face $1,000, coupon 0%	$921.0854	4.20%	$0.9211
3-year zero-coupon face $1,000, coupon 0%	$879.1023	4.39%	$0.8791
4-year zero-coupon face $1,000, coupon 0%
4-year coupon face $1,000, coupon 5%

1. Consider a one-year zero-coupon bond with a face value of $1000.
2. What is the price or value of the bond?

1. What is the yield to maturity of the bond?

1. What is the one-year discount factor (present value of $1 delivered in the future)?

1. Consider a four-year zero-coupon bond. Use a binomial tree for this calculation. The probability that the rate moves higher is 70%; it moves lower is 30%. Note the values differ from the lecture examples. Do not round intermediate values.

1. What is the price or value of the bond?

Node6

7%

Node3

6%

Node1 Node7

5% 5%

Node0 Node4

4% 4%

Node2 Node8

3% 3%

Node5

2%

Node9

1%

1. What is the yield to maturity of the bond?

1. What is the four-year discount factor (present value of $1 delivered in the future)?

1. Use the discount factors to value a four-year coupon bond (face value of $1,000 and a coupon rate of 5%). You do not need to use the binomial tree, but you can verify your calculation using the tree if you are unsure of the answer.

1. What is the price or value of the bond?

1. What is the yield to maturity of the bond?