Question

Question 1 5 Use the example in the video tutorial for the bond duration of a 10-year semi-annual coupon bond, what is the Macalay Duration of the bond if the coupon rate is 5% and YTM is 9%?

Group of answer choices

7.448

6.84

7.895

7.59

Question 2 Using the same bond maturity, now change the coupon rate to 3% and YTM to 5%. What is Macalay Duration?

Group of answer choices

8.571

8.163

7.762

7.392

Answer both if possible but the first person I asked got question 1 wrong!

Answer 1

Question 1
Semi annual coupon = 1000*(5%/2) = 25
Years	Cash flow	Present value formula	Present value	Duration D = (PV*T)
0.5	25	25/(1+9%)^0.5	23.95	11.97
1.0	25	25/(1+9%)^1	22.94	22.94
1.5	25	25/(1+9%)^1.5	21.97	32.95
2.0	25	25/(1+9%)^2	21.04	42.08
2.5	25	25/(1+9%)^2.5	20.15	50.39
3.0	25	25/(1+9%)^3	19.30	57.91
3.5	25	25/(1+9%)^3.5	18.49	64.72
4.0	25	25/(1+9%)^4	17.71	70.84
4.5	25	25/(1+9%)^4.5	16.96	76.34
5.0	25	25/(1+9%)^5	16.25	81.24
5.5	25	25/(1+9%)^5.5	15.56	85.60
6.0	25	25/(1+9%)^6.0	14.91	89.44
6.5	25	25/(1+9%)^6.5	14.28	92.81
7.0	25	25/(1+9%)^7.0	13.68	95.73
7.5	25	25/(1+9%)^7.5	13.10	98.24
8.0	25	25/(1+9%)^8.0	12.55	100.37
8.5	25	25/(1+9%)^8.5	12.02	102.15
9.0	25	25/(1+9%)^9.0	11.51	103.60
9.5	25	25/(1+9%)^9.5	11.03	104.74
10.0	1025	1025/(1+9%)^10.0	432.97	4329.71
Total	750.36	5713.77
Macaulay Duration = Duration D / Present value of cash flows
Macaulay Duration = 5713.77/ 750.36
Macaulay Duration = 7.615
Answer : 7.59
Question 2
Semi annual coupon = 1000*(3%/2) = 15
Years	Cash flow	Present value formula	Present value	Duration D = (PV*T)
0.5	15	15/(1+5%)^0.5	14.64	7.32
1.0	15	15/(1+5%)^1	14.29	14.29
1.5	15	15/(1+5%)^1.5	13.94	20.91
2.0	15	15/(1+5%)^2	13.61	27.21
2.5	15	15/(1+5%)^2.5	13.28	33.19
3.0	15	15/(1+5%)^3	12.96	38.87
3.5	15	15/(1+5%)^3.5	12.65	44.26
4.0	15	15/(1+5%)^4	12.34	49.36
4.5	15	15/(1+5%)^4.5	12.04	54.19
5.0	15	15/(1+5%)^5	11.75	58.76
5.5	15	15/(1+5%)^5.5	11.47	63.08
6.0	15	15/(1+5%)^6.0	11.19	67.16
6.5	15	15/(1+5%)^6.5	10.92	71.00
7.0	15	15/(1+5%)^7.0	10.66	74.62
7.5	15	15/(1+5%)^7.5	10.40	78.02
8.0	15	15/(1+5%)^8.0	10.15	81.22
8.5	15	15/(1+5%)^8.5	9.91	84.22
9.0	15	15/(1+5%)^9.0	9.67	87.02
9.5	15	15/(1+5%)^9.5	9.44	89.64
10.0	1015	1015/(1+5%)^10.0	623.12	6231.22
Total	848.43	7275.59
Macaulay Duration = Duration D / Present value of cash flows
Macaulay Duration = 7275.59 / 848.43	8.575
Macaulay Duration = 8.575
Answer : 8.571