Use the present value table in Appendix A and Appendix B to compute the NPV of each of the following cash outflows:

Required:

$40,250 paid at the end of four years. The discount rate is 3 percent.

$4,600 paid at the end of three years and $8,450 paid at the end of five years. The discount rate is 9 percent.

$14,700 paid annually at the end of each of the next four years. The discount rate is 3 percent.

$2,350 paid annually at the end of each of the next four years and $4,700 paid at the end of the fifth year. The discount rate is 6 percent.

APPENDIX A

Present Value of $1

Periods	3%	4%	5%	6%	7%	8%	9%
1	0.971	0.962	0.952	0.943	0.935	0.926	0.917
2	0.943	0.925	0.907	0.890	0.873	0.857	0.842
3	0.915	0.889	0.864	0.840	0.816	0.794	0.772
4	0.888	0.855	0.823	0.792	0.763	0.735	0.708
5	0.863	0.822	0.784	0.747	0.713	0.681	0.650
6	0.837	0.790	0.746	0.705	0.666	0.630	0.596
7	0.813	0.760	0.711	0.665	0.623	0.583	0.547
8	0.789	0.731	0.677	0.627	0.582	0.540	0.502
9	0.766	0.703	0.645	0.592	0.544	0.500	0.460
10	0.744	0.676	0.614	0.558	0.508	0.463	0.422
11	0.722	0.650	0.585	0.527	0.475	0.429	0.388
12	0.701	0.625	0.557	0.497	0.444	0.397	0.356
13	0.681	0.601	0.530	0.469	0.415	0.368	0.326
14	0.661	0.577	0.505	0.442	0.388	0.340	0.299
15	0.642	0.555	0.481	0.417	0.362	0.315	0.275
16	0.623	0.534	0.458	0.394	0.339	0.292	0.252
17	0.605	0.513	0.436	0.371	0.317	0.270	0.231
18	0.587	0.494	0.416	0.350	0.296	0.250	0.212
19	0.570	0.475	0.396	0.331	0.277	0.232	0.194
20	0.554	0.456	0.377	0.312	0.258	0.215	0.178

Periods	10%	11%	12%	13%	14%	15%	20%
1	0.909	0.901	0.893	0.885	0.877	0.870	0.833
2	0.826	0.812	0.797	0.783	0.769	0.756	0.694
3	0.751	0.731	0.712	0.693	0.675	0.658	0.579
4	0.683	0.659	0.636	0.613	0.592	0.572	0.482
5	0.621	0.593	0.567	0.543	0.519	0.497	0.402
6	0.564	0.535	0.507	0.480	0.456	0.432	0.335
7	0.513	0.482	0.452	0.425	0.400	0.376	0.279
8	0.467	0.434	0.404	0.376	0.351	0.327	0.233
9	0.424	0.391	0.361	0.333	0.308	0.284	0.194
10	0.386	0.352	0.322	0.295	0.270	0.247	0.162
11	0.350	0.317	0.287	0.261	0.237	0.215	0.135
12	0.319	0.286	0.257	0.231	0.208	0.187	0.112
13	0.290	0.258	0.229	0.204	0.182	0.163	0.093
14	0.263	0.232	0.205	0.181	0.160	0.141	0.078
15	0.239	0.209	0.183	0.160	0.140	0.123	0.065
16	0.218	0.188	0.163	0.141	0.123	0.107	0.054
17	0.198	0.170	0.146	0.125	0.108	0.093	0.045
18	0.180	0.153	0.130	0.111	0.095	0.081	0.038
19	0.164	0.138	0.116	0.098	0.083	0.070	0.031
20	0.149	0.124	0.104	0.087	0.073	0.061	0.026

APPENDIX B

Present Value of Annuity of $1

Periods	3%	4%	5%	6%	7%	8%	9%
1	0.971	0.962	0.952	0.943	0.935	0.926	0.917
2	1.913	1.886	1.859	1.833	1.808	1.783	1.759
3	2.829	2.775	2.723	2.673	2.624	2.577	2.531
4	3.717	3.630	3.546	3.465	3.387	3.312	3.240
5	4.580	4.452	4.329	4.212	4.100	3.993	3.890
6	5.417	5.242	5.076	4.917	4.767	4.623	4.486
7	6.230	6.002	5.786	5.582	5.389	5.206	5.033
8	7.020	6.733	6.463	6.210	5.971	5.747	5.535
9	7.786	7.435	7.108	6.802	6.515	6.247	5.995
10	8.530	8.111	7.722	7.360	7.024	6.710	6.418
11	9.253	8.760	8.306	7.887	7.499	7.139	6.805
12	9.954	9.385	8.863	8.384	7.943	7.536	7.161
13	10.635	9.986	9.394	8.853	8.358	7.904	7.487
14	11.296	10.563	9.899	9.295	8.745	8.244	7.786
15	11.938	11.118	10.380	9.712	9.108	8.559	8.061
16	12.561	11.652	10.838	10.106	9.447	8.851	8.313
17	13.166	12.166	11.274	10.477	9.763	9.122	8.544
18	13.754	12.659	11.690	10.828	10.059	9.372	8.756
19	14.324	13.134	12.085	11.158	10.336	9.604	8.950
20	14.877	13.590	12.462	11.470	10.594	9.818	9.129

Periods	10%	11%	12%	13%	14%	15%	20%
1	0.909	0.901	0.893	0.885	0.877	0.870	0.833
2	1.736	1.713	1.690	1.668	1.647	1.626	1.528
3	2.487	2.444	2.402	2.361	2.322	2.283	2.106
4	3.170	3.102	3.037	2.974	2.914	2.855	2.589
5	3.791	3.696	3.605	3.517	3.433	3.352	2.991
6	4.355	4.231	4.111	3.998	3.889	3.784	3.326
7	4.868	4.712	4.564	4.423	4.288	4.160	3.605
8	5.335	5.146	4.968	4.799	4.639	4.487	3.837
9	5.759	5.537	5.328	5.132	4.946	4.772	4.031
10	6.145	5.889	5.650	5.426	5.216	5.019	4.192
11	6.495	6.207	5.938	5.687	5.453	5.234	4.327
12	6.814	6.492	6.194	5.918	5.660	5.421	4.439
13	7.103	6.750	6.424	6.122	5.842	5.583	4.533
14	7.367	6.982	6.628	6.302	6.002	5.724	4.611
15	7.606	7.191	6.811	6.462	6.142	5.847	4.675
16	7.824	7.379	6.974	6.604	6.265	5.954	4.730
17	8.022	7.549	7.120	6.729	6.373	6.047	4.775
18	8.201	7.702	7.250	6.840	6.467	6.128	4.812
19	8.365	7.839	7.366	6.938	6.550	6.198	4.843
20	8.514	7.963	7.469	7.025	6.623	6.259	4.870