Chapter 8, Problem 22P

(a)

To determine

To construct:A choice table for interest tables from 0% to 100% assuming doing nothing is allowed.

Answer to Problem 22P

From table below, from 0% to 4.7%, Alternative C should be preferred. Between 4.7% to 6.9%; Alternative B should be preferred. Alternative A should be preferred for interest rate between 6.9% to 8.2%.

Explanation of Solution

NPV of Alternative A $=\left[450-800(A/P,i,2)\right](P/A,i,8)$

NPV of Alternative B $=\left[450-1,500(A/P,i,4)\right](P/A,i,8)$

NPV of Alternative C $=450(P/A,i,8)-2,750$

Choice table for interest from 0% to 100%

Interest rate	(A/P,i,2)	(A/P,i,4)	(P/A,i,8)	A	B	C
0%	0.500	0.250	8.000	400	600	850
1%	0.508	0.256	7.652	337	502	693
2%	0.515	0.263	7.325	278	411	546
3%	0.523	0.269	7.020	224	326	409
4%	0.530	0.275	6.733	174	248	280
5%	0.538	0.282	6.463	128	174	158
6%	0.545	0.289	6.210	85	106	44
7%	0.553	0.295	5.971	45	43	(63)
8%	0.561	0.302	5.747	8	(17)	(164)
9%	0.568	0.309	5.535	(26)	(72)	(259)
10%	0.576	0.315	5.335	(58)	(124)	(349)
11%	0.584	0.322	5.146	(88)	(172)	(434)
12%	0.592	0.329	4.968	(116)	(218)	(515)
13%	0.599	0.336	4.799	(142)	(261)	(591)
14%	0.607	0.343	4.639	(166)	(301)	(663)
15%	0.615	0.350	4.487	(189)	(338)	(731)
16%	0.623	0.357	4.344	(210)	(374)	(795)
17%	0.631	0.365	4.207	(230)	(407)	(857)
18%	0.639	0.372	4.078	(249)	(439)	(915)
19%	0.647	0.379	3.954	(266)	(469)	(971)
20%	0.655	0.386	3.837	(283)	(497)	(1,023)
21%	0.662	0.394	3.726	(298)	(523)	(1,073)
22%	0.670	0.401	3.619	(313)	(548)	(1,121)
23%	0.678	0.408	3.518	(326)	(572)	(1,167)
24%	0.686	0.416	3.421	(339)	(595)	(1,210)
25%	0.694	0.423	3.329	(351)	(616)	(1,252)
26%	0.702	0.431	3.241	(363)	(637)	(1,292)
27%	0.711	0.439	3.156	(374)	(656)	(1,330)
28%	0.719	0.446	3.076	(384)	(675)	(1,366)
29%	0.727	0.454	2.999	(394)	(692)	(1,401)
30%	0.735	0.462	2.925	(403)	(709)	(1,434)
31%	0.743	0.469	2.854	(412)	(725)	(1,466)
32%	0.751	0.477	2.786	(420)	(740)	(1,496)
33%	0.759	0.485	2.721	(428)	(755)	(1,526)
34%	0.767	0.493	2.658	(436)	(769)	(1,554)
35%	0.776	0.501	2.598	(443)	(782)	(1,581)
36%	0.784	0.509	2.540	(450)	(795)	(1,607)
37%	0.792	0.517	2.485	(456)	(808)	(1,632)
38%	0.800	0.525	2.432	(462)	(819)	(1,656)
39%	0.808	0.533	2.380	(468)	(831)	(1,679)
40%	0.817	0.541	2.331	(474)	(842)	(1,701)
41%	0.825	0.549	2.283	(479)	(852)	(1,723)
42%	0.833	0.557	2.237	(484)	(862)	(1,743)
43%	0.842	0.565	2.193	(489)	(872)	(1,763)
44%	0.850	0.573	2.150	(494)	(881)	(1,783)
45%	0.858	0.582	2.109	(499)	(891)	(1,801)
46%	0.867	0.590	2.069	(503)	(899)	(1,819)
47%	0.875	0.598	2.030	(507)	(908)	(1,836)
48%	0.883	0.606	1.993	(511)	(916)	(1,853)
49%	0.892	0.615	1.957	(515)	(924)	(1,869)
50%	0.900	0.623	1.922	(519)	(931)	(1,885)
51%	0.908	0.631	1.888	(523)	(939)	(1,900)
52%	0.917	0.640	1.856	(526)	(946)	(1,915)
53%	0.925	0.648	1.824	(529)	(953)	(1,929)
54%	0.934	0.657	1.793	(533)	(960)	(1,943)
55%	0.942	0.665	1.764	(536)	(966)	(1,956)
56%	0.951	0.674	1.735	(539)	(973)	(1,969)
57%	0.959	0.682	1.707	(542)	(979)	(1,982)
58%	0.968	0.691	1.680	(544)	(985)	(1,994)
59%	0.976	0.699	1.653	(547)	(991)	(2,006)
60%	0.985	0.708	1.628	(550)	(996)	(2,017)
61%	0.993	0.717	1.603	(552)	(1,002)	(2,029)
62%	1.002	0.725	1.579	(555)	(1,007)	(2,039)
63%	1.010	0.734	1.555	(557)	(1,013)	(2,050)
64%	1.019	0.743	1.533	(559)	(1,018)	(2,060)
65%	1.027	0.751	1.510	(562)	(1,023)	(2,070)
66%	1.036	0.760	1.489	(564)	(1,028)	(2,080)
67%	1.045	0.769	1.468	(566)	(1,032)	(2,089)
68%	1.053	0.778	1.447	(568)	(1,037)	(2,099)
69%	1.062	0.786	1.427	(570)	(1,042)	(2,108)
70%	1.070	0.795	1.408	(572)	(1,046)	(2,116)
71%	1.079	0.804	1.389	(574)	(1,050)	(2,125)
72%	1.088	0.813	1.371	(576)	(1,055)	(2,133)
73%	1.096	0.822	1.353	(578)	(1,059)	(2,141)
74%	1.105	0.831	1.335	(579)	(1,063)	(2,149)
75%	1.114	0.840	1.318	(581)	(1,067)	(2,157)
76%	1.122	0.848	1.301	(583)	(1,071)	(2,164)
77%	1.131	0.857	1.285	(585)	(1,074)	(2,172)
78%	1.140	0.866	1.269	(586)	(1,078)	(2,179)
79%	1.148	0.875	1.254	(588)	(1,082)	(2,186)
80%	1.157	0.884	1.239	(589)	(1,085)	(2,193)
81%	1.166	0.893	1.224	(591)	(1,089)	(2,199)
82%	1.175	0.902	1.209	(592)	(1,092)	(2,206)
83%	1.183	0.911	1.195	(594)	(1,096)	(2,212)
84%	1.192	0.920	1.181	(595)	(1,099)	(2,218)
85%	1.201	0.929	1.168	(596)	(1,103)	(2,224)
86%	1.210	0.938	1.155	(598)	(1,106)	(2,230)
87%	1.218	0.947	1.142	(599)	(1,109)	(2,236)
88%	1.227	0.957	1.129	(600)	(1,112)	(2,242)
89%	1.236	0.966	1.117	(602)	(1,115)	(2,247)
90%	1.245	0.975	1.105	(603)	(1,118)	(2,253)
91%	1.254	0.984	1.093	(604)	(1,121)	(2,258)
92%	1.262	0.993	1.081	(605)	(1,124)	(2,264)
93%	1.271	1.002	1.070	(607)	(1,127)	(2,269)
94%	1.280	1.011	1.059	(608)	(1,130)	(2,274)
95%	1.289	1.021	1.048	(609)	(1,132)	(2,279)
96%	1.298	1.030	1.037	(610)	(1,135)	(2,283)
97%	1.307	1.039	1.026	(611)	(1,138)	(2,288)
98%	1.316	1.048	1.016	(612)	(1,140)	(2,293)
99%	1.324	1.057	1.006	(613)	(1,143)	(2,297)
100%	1.333	1.067	0.996	(614)	(1,146)	(2,302)

(b)

To determine

To construct:A choice table for interest tables from 0% to 100% assuming A, B o r C must be chosen.

Answer to Problem 22P

From table below, from 0% to 4.7%, Alternative C should be preferred. Between 4.7% to 6.9%; Alternative B should be preferred. Beyond that Alternative A should be preferred for interest rate between 6.9% to 100%.

Explanation of Solution

NPV of Alternative A $=\left[450-800(A/P,i,2)\right](P/A,i,8)$

NPV of Alternative B $=\left[450-1,500(A/P,i,4)\right](P/A,i,8)$

NPV of Alternative C $=450(P/A,i,8)-2,750$

Choice table for interest from 0% to 100%

Interest rate	(A/P,i,2)	(A/P,i,4)	(P/A,i,8)	A	B	C
0%	0.500	0.250	8.000	400	600	850
1%	0.508	0.256	7.652	337	502	693
2%	0.515	0.263	7.325	278	411	546
3%	0.523	0.269	7.020	224	326	409
4%	0.530	0.275	6.733	174	248	280
5%	0.538	0.282	6.463	128	174	158
6%	0.545	0.289	6.210	85	106	44
7%	0.553	0.295	5.971	45	43	(63)
8%	0.561	0.302	5.747	8	(17)	(164)
9%	0.568	0.309	5.535	(26)	(72)	(259)
10%	0.576	0.315	5.335	(58)	(124)	(349)
11%	0.584	0.322	5.146	(88)	(172)	(434)
12%	0.592	0.329	4.968	(116)	(218)	(515)
13%	0.599	0.336	4.799	(142)	(261)	(591)
14%	0.607	0.343	4.639	(166)	(301)	(663)
15%	0.615	0.350	4.487	(189)	(338)	(731)
16%	0.623	0.357	4.344	(210)	(374)	(795)
17%	0.631	0.365	4.207	(230)	(407)	(857)
18%	0.639	0.372	4.078	(249)	(439)	(915)
19%	0.647	0.379	3.954	(266)	(469)	(971)
20%	0.655	0.386	3.837	(283)	(497)	(1,023)
21%	0.662	0.394	3.726	(298)	(523)	(1,073)
22%	0.670	0.401	3.619	(313)	(548)	(1,121)
23%	0.678	0.408	3.518	(326)	(572)	(1,167)
24%	0.686	0.416	3.421	(339)	(595)	(1,210)
25%	0.694	0.423	3.329	(351)	(616)	(1,252)
26%	0.702	0.431	3.241	(363)	(637)	(1,292)
27%	0.711	0.439	3.156	(374)	(656)	(1,330)
28%	0.719	0.446	3.076	(384)	(675)	(1,366)
29%	0.727	0.454	2.999	(394)	(692)	(1,401)
30%	0.735	0.462	2.925	(403)	(709)	(1,434)
31%	0.743	0.469	2.854	(412)	(725)	(1,466)
32%	0.751	0.477	2.786	(420)	(740)	(1,496)
33%	0.759	0.485	2.721	(428)	(755)	(1,526)
34%	0.767	0.493	2.658	(436)	(769)	(1,554)
35%	0.776	0.501	2.598	(443)	(782)	(1,581)
36%	0.784	0.509	2.540	(450)	(795)	(1,607)
37%	0.792	0.517	2.485	(456)	(808)	(1,632)
38%	0.800	0.525	2.432	(462)	(819)	(1,656)
39%	0.808	0.533	2.380	(468)	(831)	(1,679)
40%	0.817	0.541	2.331	(474)	(842)	(1,701)
41%	0.825	0.549	2.283	(479)	(852)	(1,723)
42%	0.833	0.557	2.237	(484)	(862)	(1,743)
43%	0.842	0.565	2.193	(489)	(872)	(1,763)
44%	0.850	0.573	2.150	(494)	(881)	(1,783)
45%	0.858	0.582	2.109	(499)	(891)	(1,801)
46%	0.867	0.590	2.069	(503)	(899)	(1,819)
47%	0.875	0.598	2.030	(507)	(908)	(1,836)
48%	0.883	0.606	1.993	(511)	(916)	(1,853)
49%	0.892	0.615	1.957	(515)	(924)	(1,869)
50%	0.900	0.623	1.922	(519)	(931)	(1,885)
51%	0.908	0.631	1.888	(523)	(939)	(1,900)
52%	0.917	0.640	1.856	(526)	(946)	(1,915)
53%	0.925	0.648	1.824	(529)	(953)	(1,929)
54%	0.934	0.657	1.793	(533)	(960)	(1,943)
55%	0.942	0.665	1.764	(536)	(966)	(1,956)
56%	0.951	0.674	1.735	(539)	(973)	(1,969)
57%	0.959	0.682	1.707	(542)	(979)	(1,982)
58%	0.968	0.691	1.680	(544)	(985)	(1,994)
59%	0.976	0.699	1.653	(547)	(991)	(2,006)
60%	0.985	0.708	1.628	(550)	(996)	(2,017)
61%	0.993	0.717	1.603	(552)	(1,002)	(2,029)
62%	1.002	0.725	1.579	(555)	(1,007)	(2,039)
63%	1.010	0.734	1.555	(557)	(1,013)	(2,050)
64%	1.019	0.743	1.533	(559)	(1,018)	(2,060)
65%	1.027	0.751	1.510	(562)	(1,023)	(2,070)
66%	1.036	0.760	1.489	(564)	(1,028)	(2,080)
67%	1.045	0.769	1.468	(566)	(1,032)	(2,089)
68%	1.053	0.778	1.447	(568)	(1,037)	(2,099)
69%	1.062	0.786	1.427	(570)	(1,042)	(2,108)
70%	1.070	0.795	1.408	(572)	(1,046)	(2,116)
71%	1.079	0.804	1.389	(574)	(1,050)	(2,125)
72%	1.088	0.813	1.371	(576)	(1,055)	(2,133)
73%	1.096	0.822	1.353	(578)	(1,059)	(2,141)
74%	1.105	0.831	1.335	(579)	(1,063)	(2,149)
75%	1.114	0.840	1.318	(581)	(1,067)	(2,157)
76%	1.122	0.848	1.301	(583)	(1,071)	(2,164)
77%	1.131	0.857	1.285	(585)	(1,074)	(2,172)
78%	1.140	0.866	1.269	(586)	(1,078)	(2,179)
79%	1.148	0.875	1.254	(588)	(1,082)	(2,186)
80%	1.157	0.884	1.239	(589)	(1,085)	(2,193)
81%	1.166	0.893	1.224	(591)	(1,089)	(2,199)
82%	1.175	0.902	1.209	(592)	(1,092)	(2,206)
83%	1.183	0.911	1.195	(594)	(1,096)	(2,212)
84%	1.192	0.920	1.181	(595)	(1,099)	(2,218)
85%	1.201	0.929	1.168	(596)	(1,103)	(2,224)
86%	1.210	0.938	1.155	(598)	(1,106)	(2,230)
87%	1.218	0.947	1.142	(599)	(1,109)	(2,236)
88%	1.227	0.957	1.129	(600)	(1,112)	(2,242)
89%	1.236	0.966	1.117	(602)	(1,115)	(2,247)
90%	1.245	0.975	1.105	(603)	(1,118)	(2,253)
91%	1.254	0.984	1.093	(604)	(1,121)	(2,258)
92%	1.262	0.993	1.081	(605)	(1,124)	(2,264)
93%	1.271	1.002	1.070	(607)	(1,127)	(2,269)
94%	1.280	1.011	1.059	(608)	(1,130)	(2,274)
95%	1.289	1.021	1.048	(609)	(1,132)	(2,279)
96%	1.298	1.030	1.037	(610)	(1,135)	(2,283)
97%	1.307	1.039	1.026	(611)	(1,138)	(2,288)
98%	1.316	1.048	1.016	(612)	(1,140)	(2,293)
99%	1.324	1.057	1.006	(613)	(1,143)	(2,297)
100%	1.333	1.067	0.996	(614)	(1,146)	(2,302)