Question

Using the three-step method, compute the dirty price (to 3 decimal places) of a $100 face-value bond maturing on 15-Feb-29, paying a 5%pa semi-annual coupons with a yield to maturity of 3%pa for settlement on 05-May-20. Set out the intermediate calculations for each of the three steps.

(Note there are 102 days between 05-May-20 and 15-Aug-2020. There are 182 days between 15-Feb-2020 and 15-Aug-2020)

Answer 1

Step 1:

Calculate present value of coupon payments:

Considering that first coupon payment will be made on August 15, 2020 i.e. 102 days from May 5, 2020. 2.5*(102/180) = 1.417

PV = 1.417/(1+(0.03/2))^(2*1)

And so on:

Please refer table below and excel screen shot for calculation.

Frequency	Settlement date	Days in between payments	Coupon payments	Present value
	5-May-20
1	15-Aug-20	102	1.417	1.375
2	15-Feb-21	184	2.556	2.408
3	15-Aug-21	181	2.514	2.299
4	15-Feb-22	184	2.556	2.269
5	15-Aug-22	181	2.514	2.166
6	15-Feb-23	184	2.556	2.137
7	15-Aug-23	181	2.514	2.041
8	15-Feb-24	184	2.556	2.014
9	15-Aug-24	182	2.528	1.934
10	15-Feb-25	184	2.556	1.897
11	15-Aug-25	181	2.514	1.812
12	15-Feb-26	184	2.556	1.788
13	15-Aug-26	181	2.514	1.707
14	15-Feb-27	184	2.556	1.684
15	15-Aug-27	181	2.514	1.608
16	15-Feb-28	184	2.556	1.587
17	15-Aug-28	182	2.528	1.524
18	15-Feb-29	184	2.556	1.495
	Sum of all coupon values			33.745

Step 2: Calculate present value of face value:

PVface= 100/(1+(0.03/2))^(2*18) = 58.509

Step 3: Add present value of coupon and face value

Bond value = 33.745 + 58.509 = 92.254

Hence bond value is $92.254.