In: Finance
You purchase a $13,000 3.875% Treasury bond maturing November 27, 2042. The bond is priced to yield 1.125% and settles January 10, 2017.
The base price of the bond is
Accrued Interest adds
The invoice price is thus
First of all, there are a couple of small data points which can however, be assumed and we proceed with the problem.
We need to know the periodicity of coupon payments (annual, semi annual or quarterly) and the date of transaction. We can safely assume that the date of transaction here is two days before settlement, i.e. January 8, 2017.
We are given following information:
Face value of bond = $ 13,000,
Coupon = 3.875% = 3.875/100*13000 = $ 503.75
For this sum, we assume coupon is annually paid
Time period remaining till maturity = Time period from January 8, 2017 to Nov 27, 2042 = 25.86 years apptoxapproxi
Yield to maturity = 1.125%
Current base price of bond has 2 components: Present value of all coupon payments and Present Value of Final Maturity Amount, i.e.
Price = Coupon * Present Value Interest Factor of Annuity (Yield to Maturity, time period) + Final Maturity Amount * PrePres Value Interest Factor (Yield to Maturity, time period)
= 503.75 * PVIFA(1.125%,25.86) + 13000 * PVIF(1.125%,25.86)
= 503.75*22.33 + 13000*0.7488
= 11248.74 + 9734.40
=$ 20983.14
This, the bond is trading at a good premium over Face Valuw, explaining why the Yield to Maturity is lower than Coupon Rate.
If we werr to assume semi annual coupons, coupon would half to 251.88 and time period would double to 51 .72. Rest of the calculation remains same.
Thus, base price of the bond is $ 20,983.14
However, since there would be a 2 day delay in settlement and receipt of money into the seller's account, he charges 2 day equivalent coupon amount on the base price to arrive at invoive price.
Thus, invoice price = 20983.14 + 503.75/360*2 (assuming a 360 day convention for interest computation)
= 20,985.90