Question
The Robinson Corporation has $38 million of bonds outstanding that were issued at a coupon rate of 12.050 percent seven years ago. Interest rates have fallen to 11.050 percent. Mr. Brooks, the Vice-President of Finance, does not expect rates to fall any further. The bonds have 17 years left to maturity, and Mr. Brooks would like to refund the bonds with a new issue of equal amount also having 17 years to maturity. The Robinson Corporation has a tax rate of 30 percent. The underwriting cost on the old issue was 3.80 percent of the total bond value. The underwriting cost on the new issue will be 2.40 percent of the total bond value. The original bond indenture contained a five-year protection against a call, with a call premium of 8 percent starting in the sixth year and scheduled to decline by one-half percent each year thereafter. (Consider the bond to be seven years old for purposes of computing the premium.) Use Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. Assume the discount rate is equal to the aftertax cost of new debt rounded up to the nearest whole percent (e.g. 4.06 percent should be rounded up to 5 percent)
a. Compute the discount rate. (Do not round intermediate calculations. Input your answer as a percent rounded up to the nearest whole percent.)
b. Calculate the present value of total outflows. (Do not round intermediate calculations and round your answer to 2 decimal places.)
c. Calculate the present value of total inflows. (Do not round intermediate calculations and round your answer to 2 decimal places.)
d. Calculate the net present value. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)
Appendix D Present value of an annuity of $1, PVA PV = A Period 1% g 8 * N o @ : a un Edo no on co 0.990 1.970 2.941 3.902 4.853 5.795 6.728 7.652 8.566 9.471 10.368 11.255 12.134 13.004 13.865 14.718 15.562 16.398 17.226 18.046 22.023 25.808 32.835 39.196 2% 3% 4% 0.980 0.971 0.962 1.942 1.913 1.886 2.884 2.829 2.775 3.808 3.717 3.630 4.713 4.580 4.452 5.601 5.417 5.242 6.472 6.230 6.002 7.325 7.020 6.733 8.162 7.786 7.435 8.983 8.530 8.111 9.787 9.253 8.760 10.575 9.954 9.385 11.348 10.635 9.986 12.106 11.296 10.563 12.849 11.938 11.118 13.578 12.561 11.652 14.292 13.166 12.166 14.992 13.754 12.659 15.678 14.324 13.134 16.351 14.877 13.590 19.523 17.413 15.622 22.396 19.600 17.292 27.355 23.115 19.793 31.424 25.730 21.482 5% 6% 7% 8% 9% 10% 11% 12% 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811 10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974 11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.120 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7.366 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469 14.094 12.783 11.654 10.675 9.823 9.077 8.422 7.843 15.372 13.765 12.409 11.258 | 10.274 9.427 8.694 8.055 17.159 15.046 13.332 | 11.925 10.757 9.779 8.951 8.244 18.256 15.762 13.801 12.233 10.962 9.915 9.042 8.304 Appendix D (concluded) Period 4.031 958 SO GA NE o w 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 35% 40% 50% 0.885 0.877 0.870 0.855 0.847 0.840 0.8330.800 0.769 0.741 0.714 0.667 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528 1.440 1.361 1.289 | 1.224 1.111 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 1.952 1.816 1.696 1.589 1.407 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589 2.362 2.166 1.997 | 1.849 1.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 2.689 2.436 2.220 2.035 1.737 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326 2.951 2.643 2.385 2.168 1.824 4,423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 3.161 2.802 2.508 2.263 1.883 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 3.329 2.925 2.598 2.331 1.922 5.132 4.946 4.772 4.607 4.451 4.303 4.163 3.463 3.019 2.665 2.379 1.948 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192 3.571 3.092 2.715 2.414 1.965 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 3.656 3.147 2.752 2.438 1.977 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439 3.725 3.190 2.779 2.456 1.985 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 3.780 3.223 2.799 2.469 1.990 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 3.824 3.249 2.814 2.478 1.993 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 3.859 3.268 2.825 2.484 1.995 6.604 6.265 5.954 5.668 5.405 5.162 4.938 4.730 3.887 3.283 2.834 2.489 1.997 6.729 6.373 6.047 5.749 5.475 5.222 4.988 4.775 3.910 3.295 2.840 2.492 1.998 6.840 6.467 6.128 5.818 5.534 5.273 5.033 4.812 3.928 3.304 2.844 2.494 1.999 6.938 6.550 6.198 5.877 5.584 5.316 5.070 4.843 3.942 3.311 2.848 2.496 1.999 7.025 6.623 6.259 5.929 5.628 5.353 5.101 4.870 3.954 3.316 2.850 2.497 1.999 7.330 6.873 6.464 6.097 5.766 5.467 5.195 4.948 3.985 3.329 2.856 2.499 2.000 7.496 7.003 6.566 6.177 5.829 5.517 5.235 4.979 3.995 3.332 2.857 2.500 2.000 7.634 7.105 6.642 6.233 5.871 5.548 5.258 4.997 3.999 3.333 2.857 2.500 2.000 7.675 7.133 6.661 6.246 5.880 5.554 5.262 4.999 4.000 3.333 2.857 2.500 2.000
Explanation / Answer
a.) Discount Rate = Prevailing Interest Rates x (1-T)
= 11.05 x (1-0.30)
= 7.735%
= 8%
b.) Call Premium after 7 years = 8% - 2x0.5% =7%
Assuming Annual Interest Payments and $1000 be par value of bond
New Annual Interest Liability =$0.1105x38 mil =$4.199 mil
Present Value of Total Outflows = Returning Money to Existing Investors Today + New Issue Underwriting Cost + Future Interest Payments + Future Redemption of Bonds
= (Redemption Amount + Call Premium) + 2.40% of Bond Value + 4.199x{(1-(1+0.08)-17)/0.08} + 38/(1+0.08)17
= (38 + 0.07x38) + 0.024x38 + 4.199x9.1216 + 38/3.7000
= 41.572 + 38.3017 + 10.2702
= 90.1439
c.) Present Value of Total Cash Inflows = Money raised Under New Issue =$38 million
d.) Net Present Value = - PV of Total Outflows + PV of Total Inflows
=$ -90.1439 + 38.0000
=$ -52.1439 million
