Question

A 5% Treasury note matures in 12 months and has $10,000 face value. If the 6‐months and 12‐months zero‐ coupon rates are 3% and 4% respectively, what is the YTM on the Treasury note? Specify your answer as a percentage with 4 digits after the decimal point.

Answer 1

Coupon rate = 5%, Time to maturity = 12 months = 1 year, Face value = 10000, 6 months zero rate = 3%, 12 month zero rate = 4%

Since bond is Treasury note, therefore it pays semi-annual coupon

Coupon paid semi-annually = (Coupon rate x Face value)/ 2 = (5% x 10000) / 2 = 250

Price of Treasury note = Sum of present values of future cash flows

Let C1, C2 be two coupons of the note paid semi annually and F be the face value

Price = C1 / (1 + 3%/2) + (C2 + F) / (1 + 4%)

= 250 / ( 1 + 1.5%) + (250 + 10000) / (1 + 4%)

250 / 1.015 + 10250 / 1.04 = 246.305419 + 9855.769231 = 10102.074650

For calculating YTM of treasury note,

No of half year to maturity = 2

First we will calculate the semi annual yield to maturity

We will use rate function in excel to calculate semi annual YTM of treasury note

Formula to be used in excel: =rate(nper,-pmt,pv,-fv)

Below is the excel screen shot

Using rate function in excel, we get semi annual yield to maturity = 1.9744%

YTM = 2 x semi annual yield to maturity = 1.9744% x 2 = 3.9488%