An insurance company is analyzing the following three bonds, each with five year
ID: 2655958 • Letter: A
Question
An insurance company is analyzing the following three bonds, each with five years to maturity, annual interest payments, and is using duration as the measure of interest rate risk.
What is the duration of each of the three bonds? (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))
Duration of the bond
a.$10,000 par value, coupon rate = 9.5%, rb = 0.15years
b.$10,000 par value, coupon rate = 11.5%, rb = 0.15
c.$10,000 par value, coupon rate = 13.5%, rb = 0.15
Explanation / Answer
a.
Bond duration > 4.11 years
Period
Cash Flow
Discounting factor = 1/(1+R)^Y
PV of the cash flows = Cash flow x Df
Weighted cash flow = Period x Cash flow
Present value of weighted cash flow = Weighted Cash flow x Df
Y
CF
Df = 1/(1+15%)^Y
PV = CF x Df
WCF = CF x Y
WPV = WCF x Df
1
950
0.8696
826.0870
950.00
826.0870
2
950
0.7561
718.3365
1900.00
1436.6730
3
950
0.6575
624.6404
2850.00
1873.9213
4
950
0.5718
543.1656
3800.00
2172.6623
5
10950
0.4972
5444.0853
54750.00
27220.4263
Total = P =
8156.3147
Total = WP =
33529.7698
Duration = WP/P =
4.11
b.
Bond duration > 4.01 years
Period
Cash Flow
Discounting factor = 1/(1+R)^Y
PV of the cash flows = Cash flow x Df
Weighted cash flow = Period x Cash flow
Present value of weighted cash flow = Weighted Cash flow x Df
Y
CF
Df = 1/(1+15%)^Y
PV = CF x Df
WCF = CF x Y
WPV = WCF x Df
1
1150
0.8696
1000.0000
1150.00
1000.0000
2
1150
0.7561
869.5652
2300.00
1739.1304
3
1150
0.6575
756.1437
3450.00
2268.4310
4
1150
0.5718
657.5162
4600.00
2630.0649
5
11150
0.4972
5543.5206
55750.00
27717.6030
Total = P =
8826.7457
Total = WP =
35355.2294
Duration = WP/P =
4.01
#REF!
c.
Bond duration > 3.91 years
Period
Cash Flow
Discounting factor = 1/(1+R)^Y
PV of the cash flows = Cash flow x Df
Weighted cash flow = Period x Cash flow
Present value of weighted cash flow = Weighted Cash flow x Df
Y
CF
Df = 1/(1+15%)^Y
PV = CF x Df
WCF = CF x Y
WPV = WCF x Df
1
1350
0.8696
1173.9130
1350.00
1173.9130
2
1350
0.7561
1020.7940
2700.00
2041.5879
3
1350
0.6575
887.6469
4050.00
2662.9407
4
1350
0.5718
771.8669
5400.00
3087.4675
5
11350
0.4972
5642.9559
56750.00
28214.7797
Total = P =
9497.1767
Total = WP =
37180.6889
Duration = WP/P =
3.91
-----
Note:
+ or - 2 bps is possible
Period
Cash Flow
Discounting factor = 1/(1+R)^Y
PV of the cash flows = Cash flow x Df
Weighted cash flow = Period x Cash flow
Present value of weighted cash flow = Weighted Cash flow x Df
Y
CF
Df = 1/(1+15%)^Y
PV = CF x Df
WCF = CF x Y
WPV = WCF x Df
1
950
0.8696
826.0870
950.00
826.0870
2
950
0.7561
718.3365
1900.00
1436.6730
3
950
0.6575
624.6404
2850.00
1873.9213
4
950
0.5718
543.1656
3800.00
2172.6623
5
10950
0.4972
5444.0853
54750.00
27220.4263
Total = P =
8156.3147
Total = WP =
33529.7698
Duration = WP/P =
4.11
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