Question

In: Finance

Bond B and Bond T both have 7% coupon rate, bond B has 3 years to...

Bond B and Bond T both have 7% coupon rate, bond B has 3 years to maturity, bond T has 20 years to maturity. What is the percentage change of in the price of each bond if interest rate goes up by 2%? What is the percentage change if interest rate goes down by 2%? Which bond has higher interest rate risk?

Solutions

Expert Solution

Face Value is assumed as $1000

Coupon for Both Bonds = 1000*7% = $70

Interest Rate is assumed as 5%

Bond B:

5.00% 7.00% 3.00%
Period Cash
Flow
Discounting Factor
[1/(1.0425^year)]
PV of Cash Flows
(cash flows*discounting factor)
Discounting Factor
[1/(1.037^year)]
PV of Cash Flows
(cash flows*discounting factor)
Discounting Factor
[1/(1.03^year)]
PV of Cash Flows
(cash flows*discounting factor)
1 70 0.952380952 66.66666667 0.934579439 65.42056075 0.970873786 67.96116505
2 70 0.907029478 63.49206349 0.873438728 61.14071098 0.942595909 65.98171364
3 70 0.863837599 60.4686319 0.816297877 57.14085138 0.915141659 64.05991615
3 1300 0.863837599 1122.988878 0.816297877 1061.18724 0.915141659 1189.684157
Price of the Bond =
Sum of PVs
1313.61624 Price of the Bond =
Sum of PVs
1244.889363 Price of the Bond =
Sum of PVs
1387.686952
% Change =
[(1244.889-1313.616)/1313.616]
-0.052318839 = -5.23% % Change =
[(1387.6869-1313.616)/1313.616]
0.056386873 = 5.64%

Bond T:

5.00% 7.00% 3.00%
Period Cash
Flow
Discounting Factor
[1/(1.0425^year)]
PV of Cash Flows
(cash flows*discounting factor)
Discounting Factor
[1/(1.037^year)]
PV of Cash Flows
(cash flows*discounting factor)
Discounting Factor
[1/(1.03^year)]
PV of Cash Flows
(cash flows*discounting factor)
1 70 0.952380952 66.66666667 0.934579439 65.42056075 0.970873786 67.96116505
2 70 0.907029478 63.49206349 0.873438728 61.14071098 0.942595909 65.98171364
3 70 0.863837599 60.4686319 0.816297877 57.14085138 0.915141659 64.05991615
4 70 0.822702475 57.58917324 0.762895212 53.40266484 0.888487048 62.19409335
5 70 0.783526166 54.84683165 0.712986179 49.90903256 0.862608784 60.38261491
6 70 0.746215397 52.23507776 0.666342224 46.64395567 0.837484257 58.62389797
7 70 0.71068133 49.74769311 0.622749742 43.59248193 0.813091511 56.91640579
8 70 0.676839362 47.37875534 0.582009105 40.74063732 0.789409234 55.2586464
9 70 0.644608916 45.12262414 0.543933743 38.07536198 0.766416732 53.64917126
10 70 0.613913254 42.97392775 0.508349292 35.58445045 0.744093915 52.08657404
11 70 0.584679289 40.92755024 0.475092796 33.25649575 0.722421277 50.56948936
12 70 0.556837418 38.97861927 0.444011959 31.08083715 0.70137988 49.09659161
13 70 0.530321351 37.12249455 0.414964448 29.04751135 0.68095134 47.6665938
14 70 0.505067953 35.35475671 0.387817241 27.14720687 0.661117806 46.27824641
15 70 0.481017098 33.67119687 0.36244602 25.37122137 0.641861947 44.93033632
16 70 0.458111522 32.06780654 0.338734598 23.71142185 0.623166939 43.62168575
17 70 0.436296688 30.54076813 0.31657439 22.16020733 0.605016446 42.35115121
18 70 0.415520655 29.08644584 0.295863916 20.71047414 0.587394608 41.11762253
19 70 0.395733957 27.70137699 0.276508333 19.35558331 0.570286027 39.92002188
20 70 0.376889483 26.3822638 0.258419003 18.0893302 0.553675754 38.75730279
20 1300 0.376889483 489.9563277 0.258419003 335.9447037 0.553675754 719.7784804
Price of the Bond =
Sum of PVs
1362.311052 Price of the Bond =
Sum of PVs
1077.525701 Price of the Bond =
Sum of PVs
1761.201721
% Change =
[(1077.5257-1362.311)/1362.311]
-0.209045761 = -20.90% % Change =
[(1761.2017-1362.311)/1362.311]
0.292804399 = 29.28%

Accordingly, Bond T has Higher Interst Rate Risk


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