In: Finance
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?
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