Question

Values for a bond bought at par with face value $1000, with yield to maturity of 5% initially, and 2% after 1 year.  

Values for a bond bought at par with face value $1000, with yield to maturity of 2% initially, and 5% after 1 year.  

Aug 28, 2018 10:49 AM

Instructions

The goal is to create a table for the rates or return on bonds of varying maturities like the one in the notes for Chapter 4. The bond has a face value of $1000 and is bought at par with a coupon rate of x%. After one year, the market yield on the bond changes to y%.

On your table, show the current yield, the resale price P(t+1) the rate of capital gain and the rate of return for bonds is 1,2,3, 5 and 7 years to maturity.

Do a second table for the situation where market yields go from y% to x%.

Answer 1

(a)

The initial bond price is calculated by summing the present values of the bond's coupon payments and par value redemption (at maturity) discounted at the YTM prevailing initially. After 1 year when the yield to maturity changes, the bond's resale price at Year 1 is equal to the total present value of the bond's REMAINING coupon payments and par value redemption (at maturity), discounted at the new changed yield to maturity. Further, as the bond is bought at par and the bond's par value is $ 1000, the bond's market value would be $ 1000 initially.

Initial Yield to Maturity = 5 % = Coupon Rate (as bonds selling at par have coupon rates equal to YTM)

Annual Coupon = 0.05 x 1000 = $ 50

New YTM after 1 year = 2 %

The table as asked for in the question is as shown below. Further, "after 1 year" meand at t=1 with current time being t = 0. Also, time remaining to maturity is calculated from t = 0 (current time again).

(b) Initial Yield to Maturity = 2 %, Par Value = Initial Bond Purchase Price = $ 1000 (as bond is purchased at par), New Changed Yield to Maturity = 5 %,

Also, as bond is purchased at par, Coupon Rate = Initial Yield to Maturity = 2 %

Annual Coupon = 0.02 x 1000 = $ 20

The calculation table asked for is shown below, with the assumption that current time is t=0, resale price is calculated at t=1 and time remaining to maturity is measured from t = 0.