Question

4) Suppose there is a 3-year bond with a $1000 face value, 30% annual coupon payments and a 20% annual yield to maturity.

a) Without any calculation, briefly explain whether this bond will be selling a premium or a discount.

b) Calculate the price of this bond.

c) Calculate the duration of this bond.

d) Suppose the interest rates in the economy rise by 5 percentage points immediately after someone bought this bond. Show a calculation using duration for what should happen to the price of this bond immediately.

e) Suppose now one year passes and the interest rates in the economy are still 5 percentage points higher. If the person that owns this bond sells it for fair value, what would be their one year rate of return? Show a calculation.

5) For each of the following state whether it is True or False and provide a brief explanation (1 or 2 sentences) as to why it is true or false.

a) All else the same, a higher coupon rate will mean a higher price for a standard coupon bond.

b) All else the same, a higher coupon rate will mean a higher duration for a standard coupon bond.

c) All else the same, a shortage in the money market will lead to the price of bonds falling.

Answer 1

(4) (a) The bond has an annual yield to maturity of 20% and a coupon payment of 30%. The yield to maturity is equivalent to the required return on the bond whereas the annual coupon rate is the return being actually provided. As the return being actually provided is greater than the required return, the bond buyers will pay a premium for gaining this extra return. Hence, the bonds will sell at a premium.

(b) Bond Tenure = 3 years, Coupon Rate = 30 %, Yield to Maturity = 20 % and Par Value = $ 1000

Annual Coupon = 0.3 x 1000 = $ 300

Therefore, Bond Price = 300 x (1/0.2) x [1-{1/(1.2)^(3)}] + 1000 / (1.2)^(3) = $ 1210.65

(c)

(d) Modified Duration = 2.012 years (from part(c))

Change in YTM = + 5 percentage points

% Change in Price = - Modified Duration x % Change in YTM (expressed in decimals) = - 2.012 x 0.05 ~ - 1006 or - 10.06 %

New Changed Bond Price = (1-0.1006) x 1210.65 ~ $ 1088.86

NOTE: Please raise separateq queries for solutions to the remaining unrelated questions as one query is restricted to the solution of only one complete question (with a maximum of four sub-parts)