The interest rate for the first year is $4\%($no uncertainty$).$

Each year the one$-$year interest rate could move up or down by $1\%.$

The likelihood that the rate moves higher is $70\%$; the rate that it moves lower is $30\%.$ Note the probability differs from the lecture examples.

All bonds have a face value of $$1,000.$

We will complete the following table by answering the following nine questions. Some of the cells are already complete so that you can verify your calculations against mine.

$\backslash$table$[[$Asset$,$Price,Yield,$\backslash$table$[[$Discount$],[$Factor$]]],[\backslash$table$[[1-$year zero$-$coupon$],[$face $$1,000.$ coupon $0\%$

What is the price or value of the bond?

What is the yield to maturity of the bond?

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

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.

Calculate the yield on the four$-$year coupon bond using your answer to question $7.$ I suggest using the IRR function in Excel.

The airline industry is currently considered very risky. I just paid $$900$ for a one$-$year zerocoupon airline bond with a face value of $$1,000.$ What default rate does the price imply? Be specific about your assumption on recovery and whether you are using an approximation or an exact formula.

Some fixed income instruments, mortgages are an example, have constant cash flow. What would be the price or value of a security paying $$25,000$ per year for four years in the uncertain interest rate environment described above?