Chapter 8, Problem 9P

(a)

To determine

To construct:A choice table for interest tables from 0% to 100%

Answer to Problem 9P

From table below, from 0% to 7.98%, South end + North end should be preferred on account of higher NPV. Beyond that from 7.98% to 100%, South end should be preferred.

Explanation of Solution

NPV of South end $=\$285,000(P/A,i,5)$

NPV of South & North end $=-950,000+395,000(P/A,i,5)+750,000(P/F,i,5)$

Choice table for interest from 0% to 100%

Interest rate	(P/A,i,5)	(P/F,i,5)	South end	South + North end
0%	5.00	1.00	1,425,000	1,775,000
1%	4.85	0.95	1,383,228	1,680,705
2%	4.71	0.91	1,343,336	1,591,115
3%	4.58	0.86	1,305,217	1,505,941
4%	4.45	0.82	1,268,769	1,424,915
5%	4.33	0.78	1,233,901	1,347,788
6%	4.21	0.75	1,200,524	1,274,327
7%	4.10	0.71	1,168,556	1,204,318
8%	3.99	0.68	1,137,922	1,137,558
9%	3.89	0.65	1,108,551	1,073,861
10%	3.79	0.62	1,080,374	1,013,052
11%	3.70	0.59	1,053,331	954,968
12%	3.60	0.57	1,027,361	899,457
13%	3.52	0.54	1,002,411	846,376
14%	3.43	0.52	978,428	795,593
15%	3.35	0.50	955,364	746,984
16%	3.27	0.48	933,174	700,431
17%	3.20	0.46	911,814	655,825
18%	3.13	0.44	891,244	613,064
19%	3.06	0.42	871,426	572,053
20%	2.99	0.40	852,324	532,700
21%	2.93	0.39	833,906	494,921
22%	2.86	0.37	816,137	458,637
23%	2.80	0.36	798,990	423,773
24%	2.75	0.34	782,435	390,258
25%	2.69	0.33	766,445	358,026
26%	2.64	0.31	750,995	327,014
27%	2.58	0.30	736,062	297,164
28%	2.53	0.29	721,622	268,421
29%	2.48	0.28	707,654	240,732
30%	2.44	0.27	694,137	214,047
31%	2.39	0.26	681,053	188,320
32%	2.35	0.25	668,383	163,507
33%	2.30	0.24	656,110	139,566
34%	2.26	0.23	644,217	116,458
35%	2.22	0.22	632,689	94,145
36%	2.18	0.21	621,510	72,592
37%	2.14	0.21	610,668	51,766
38%	2.11	0.20	600,147	31,636
39%	2.07	0.19	589,936	12,170
40%	2.04	0.19	580,022	(6,659)
41%	2.00	0.18	570,394	(24,879)
42%	1.97	0.17	561,040	(42,515)
43%	1.94	0.17	551,951	(59,591)
44%	1.91	0.16	543,116	(76,132)
45%	1.88	0.16	534,525	(92,157)
46%	1.85	0.15	526,170	(107,689)
47%	1.82	0.15	518,042	(122,748)
48%	1.79	0.14	510,133	(137,352)
49%	1.76	0.14	502,434	(151,520)
50%	1.74	0.13	494,938	(165,267)
51%	1.71	0.13	487,638	(178,612)
52%	1.69	0.12	480,527	(191,570)
53%	1.66	0.12	473,598	(204,154)
54%	1.64	0.12	466,845	(216,381)
55%	1.61	0.11	460,262	(228,262)
56%	1.59	0.11	453,844	(239,811)
57%	1.57	0.10	447,583	(251,040)
58%	1.55	0.10	441,476	(261,962)
59%	1.53	0.10	435,517	(272,586)
60%	1.51	0.10	429,700	(282,925)
61%	1.49	0.09	424,023	(292,987)
62%	1.47	0.09	418,479	(302,784)
63%	1.45	0.09	413,065	(312,325)
64%	1.43	0.08	407,777	(321,618)
65%	1.41	0.08	402,610	(330,672)
66%	1.39	0.08	397,560	(339,495)
67%	1.38	0.08	392,625	(348,095)
68%	1.36	0.07	387,800	(356,481)
69%	1.34	0.07	383,082	(364,658)
70%	1.33	0.07	378,468	(372,634)
71%	1.31	0.07	373,954	(380,417)
72%	1.30	0.07	369,539	(388,011)
73%	1.28	0.06	365,217	(395,423)
74%	1.27	0.06	360,988	(402,660)
75%	1.25	0.06	356,848	(409,726)
76%	1.24	0.06	352,794	(416,628)
77%	1.22	0.06	348,825	(423,370)
78%	1.21	0.06	344,937	(429,958)
79%	1.20	0.05	341,128	(436,396)
80%	1.18	0.05	337,396	(442,689)
81%	1.17	0.05	333,740	(448,841)
82%	1.16	0.05	330,156	(454,857)
83%	1.15	0.05	326,643	(460,741)
84%	1.13	0.05	323,199	(466,497)
85%	1.12	0.05	319,821	(472,129)
86%	1.11	0.04	316,509	(477,640)
87%	1.10	0.04	313,260	(483,034)
88%	1.09	0.04	310,073	(488,314)
89%	1.08	0.04	306,946	(493,484)
90%	1.07	0.04	303,878	(498,547)
91%	1.06	0.04	300,866	(503,505)
92%	1.05	0.04	297,910	(508,363)
93%	1.04	0.04	295,008	(513,122)
94%	1.03	0.04	292,158	(517,786)
95%	1.02	0.04	289,360	(522,357)
96%	1.01	0.03	286,612	(526,838)
97%	1.00	0.03	283,912	(531,231)
98%	0.99	0.03	281,260	(535,538)
99%	0.98	0.03	278,654	(539,763)
100%	0.97	0.03	276,094	(543,906)

(b)

To determine

To compute:The expected rate of return when North end is open.

Answer to Problem 9P

Expected rate of return if North end is openis 7.98%.

Explanation of Solution

IRR is the rate of return at which NPV of two alternatives is equal. To compute the rate of return if North end is opened, we will equate the NPV of both the alternatives.

NPV of south end = NPV of south & north end

  $\begin{array}{l}\$285,000(P/A,i,5)=-950,000+395,000(P/A,i,5)+750,000(P/F,i,5)\\ 950,000=110,000(P/A,i,5)+750,000(P/F,i,5)\end{array}$

Solving the above equation by taking interest rates on hit and trial basis, i falls between 7% and 8%. Interpolating the two interest rates, i = 7.98%.

If interest rate is between 0% to 7.98%, then it is better to open north end, otherwise it is better to continue with the existing one.