Question

Consider a one-year 6% semi-annual coupon bond with a face value of $1,000 that costs $950?

a) What are the bond’s cash flows?

b) Find the yield to maturity of this bond algebraically being sure to show your work.

Hint: You will have to use the quadratic formula to solve for the YTM.

Recall: If there is an equation in the following form: ax2 + bx + c = 0

Then the quadratic equation gives X

c) Use Goal Seek or Solver in Excel to check your answer to part b. Excel Note: Solver is an “Add-In” that is found under the “Files” menu and then choosing “Options”. Once the “Options” window is open, you need to click on “Add-ins” and then click “Go”. Another window should pop up at that point, and you need to select “Solver” (and also add the “Analysis ToolPak” to run regressions) and click “Ok”. Once you have installed Solver, you can use it to solve for the YTM. You will need to set up the YTM as a variable in its own cell that you can refer to as the choice variable for Solver to adjust.

Answer 1

One Year Bond that pays 6% coupon semi annually has face value $1000 with market price $950

Bond Cash Flow will be $30 after the purchase of bond and $1030 at Maturity these 2 cash flows will take place in transaction,

Answer for B)

We have following equation

950=30/(1+x)^(0.5)+1030/(1+x).....x=YTM

950(1+x)=30(1+x)^0.5+1030

950(1+x)-30(1+x)^0.5-1030=0

Let (1+x)=z^2

950z^2-30z-1030=0

z=1.05716 toer root is -1.0226

z^2=(1.05716)^2=1+x

1+x=1.1176

x=11.76%=YTM

Answer for C)

I got 10.82% as YTM Kindly confirm