Chapter 8, Problem 9P

To determine

i.

Choice Table for interest rate from 0% to 100%.

Answer to Problem 9P

Till 13% interest rate, Combined stores are beneficial

From 13% to 100%, South end store is profitable.

Explanation of Solution

Given:

Annual Profit = $370000

Leasing Period = 5 years

Expenditure on store fixtures = $1200000

Combined Profit = $560000.

Calculation:

Formula: NPV = R x {[1 − (1+i)^- n] / i} + [Salvage value / (1+i)n] − Initial Investment.

R is the net cash inflow expected to be received in each period;

i is the required rate of return per period;

n are the number of periods during which the project is expected to operate and generate cash inflows.

For illustration, let’s assume that the interest rate is 1% and calculate the NPV for combined stores:

NPV = $\begin{array}{l}\$560,000\times \left\{\frac{[1–{\left(1+0.01\right)}^{-5}]}{0.01}\right\}+(\frac{\$1,000,000}{{1.01}^5})–\$1,200,000\\ = \$2,469,387.18\end{array}$

Year	Cash Flow from South end	Combined Cash Flow
0	0	-1200000
1	370000	560000
2	370000	560000
3	370000	560000
4	370000	560000
5	370000	1560000
Interest Rate	NPV for South End	NPV for Combined stores
0%	$1,850,000.00	$2,600,000.00
1%	$1,795,769.56	$2,469,387.18
2%	$1,743,980.02	$2,345,268.13
3%	$1,694,491.66	$2,227,244.81
4%	$1,647,174.26	$2,114,947.61
5%	$1,601,906.37	$2,008,033.10
6%	$1,558,574.60	$1,906,181.89
7%	$1,517,073.05	$1,809,096.74
8%	$1,477,302.71	$1,716,500.82
9%	$1,439,170.97	$1,628,136.09
10%	$1,402,591.10	$1,543,761.91
11%	$1,367,481.90	$1,463,153.66
12%	$1,333,767.19	$1,386,101.53
13%	$1,301,375.57	$1,312,409.44
14%	$1,270,239.96	$1,241,894.01
15%	$1,240,297.39	$1,174,383.59
16%	$1,211,488.65	$1,109,717.46
17%	$1,183,758.08	$1,047,745.00
18%	$1,157,053.28	$988,324.99
19%	$1,131,324.91	$931,324.91
20%	$1,106,526.49	$876,620.37
21%	$1,082,614.20	$824,094.52
22%	$1,059,546.71	$773,637.52
23%	$1,037,285.00	$725,146.08
24%	$1,015,792.23	$678,523.01
25%	$995,033.60	$633,676.80
26%	$974,976.19	$590,521.24
27%	$955,588.89	$548,975.08
28%	$936,842.24	$508,961.70
29%	$918,708.35	$470,408.80
30%	$901,160.81	$433,248.14
31%	$884,174.57	$397,415.25
32%	$867,725.90	$362,849.23
33%	$851,792.28	$329,492.50
34%	$836,352.32	$297,290.57
35%	$821,385.73	$266,191.90
36%	$806,873.22	$236,147.69
37%	$792,796.46	$207,111.70
38%	$779,138.04	$179,040.13
39%	$765,881.36	$151,891.43
40%	$753,010.65	$125,626.23
41%	$740,510.89	$100,207.12
42%	$728,367.78	$75,598.62
43%	$716,567.67	$51,767.02
44%	$705,097.58	$28,680.30
45%	$693,945.10	$6,308.00
46%	$683,098.42	-$15,378.80
47%	$672,546.25	-$36,407.67
48%	$662,277.81	-$56,804.80
49%	$652,282.82	-$76,595.14
50%	$642,551.44	-$95,802.47
51%	$633,074.27	-$114,449.42
52%	$623,842.33	-$132,557.59
53%	$614,847.02	-$150,147.54
54%	$606,080.11	-$167,238.91
55%	$597,533.73	-$183,850.44
56%	$589,200.35	-$200,000.00
57%	$581,072.73	-$215,704.67
58%	$573,143.97	-$230,980.76
59%	$565,407.43	-$245,843.85
60%	$557,856.75	-$260,308.84
61%	$550,485.83	-$274,389.98
62%	$543,288.83	-$288,100.89
63%	$536,260.12	-$301,454.62
64%	$529,394.32	-$314,463.64
65%	$522,686.24	-$327,139.90
66%	$516,130.92	-$339,494.84
67%	$509,723.57	-$351,539.44
68%	$503,459.61	-$363,284.20
69%	$497,334.62	-$374,739.19
70%	$491,344.34	-$385,914.07
71%	$485,484.70	-$396,818.12
72%	$479,751.76	-$407,460.22
73%	$474,141.74	-$417,848.91
74%	$468,650.99	-$427,992.38
75%	$463,276.02	-$437,898.49
76%	$458,013.42	-$447,574.82
77%	$452,859.96	-$457,028.63
78%	$447,812.48	-$466,266.88
79%	$442,867.97	-$475,296.31
80%	$438,023.51	-$484,123.36
81%	$433,276.27	-$492,754.24
82%	$428,623.55	-$501,194.92
83%	$424,062.71	-$509,451.17
84%	$419,591.25	-$517,528.51
85%	$415,206.70	-$525,432.28
86%	$410,906.71	-$533,167.60
87%	$406,689.01	-$540,739.44
88%	$402,551.38	-$548,152.55
89%	$398,491.71	-$555,411.52
90%	$394,507.93	-$562,520.80
91%	$390,598.07	-$569,484.66
92%	$386,760.18	-$576,307.20
93%	$382,992.42	-$582,992.42
94%	$379,292.99	-$589,544.15
95%	$375,660.14	-$595,966.10
96%	$372,092.19	-$602,261.83
97%	$368,587.51	-$608,434.80
98%	$365,144.51	-$614,488.36
99%	$361,761.67	-$620,425.72
100%	$358,437.50	-$626,250.00

Conclusion:

Till 13% interest rate, Combined stores are beneficial

From 13% to 100%, South end store is profitable.

To determine

ii.

Rate of return if North-end store is open.

Answer to Problem 9P

Rate of return is 13.28%.

Explanation of Solution

Given:

Annual Profit = $370000

Leasing Period = 5 years

Expenditure on store fixtures = $1200000.

Combined Profit = $560000.

Calculation:

Return from North End − Here, we need to calculate the IRR for North end store alone.

Formula for IRR: 0 = -Initial Investment + [(Cash Inflow₁)/(1+IRR)1] + [(Cash Inflow₂)/(1+IRR)2] +

[(Cash Inflow₃)/(1+IRR)3].....+ [(Cash Inflow_n)/(1+IRR)n]

Cash flow from North End from Year 1 to 4 = $\$560,000-\$370,000=\$190,000$

Cash flow from North End in Year 5 = $\$190,000+\$1,000,000=\$1,190,000$

Initial Investment = $1,200,000

IRR:

$\begin{array}{l}0= -\$1,200,000+\left[\frac{\left(\$190,000\right)}{\left(1+IRR\right)}\right]+[\frac{\left(\$190,000\right)}{{\left(1+IRR\right)}^2}\left]+\right[\frac{\left(\$190,000\right)}{{\left(1+IRR\right)}^3}\left]+\right[\\ \frac{\left(\$190,000\right)}{{\left(1+IRR\right)}^4}\left]+\right[\frac{\left(\$190,000\right)}{{\left(1+IRR\right)}^5}]= 13.28\%\end{array}$.

Conclusion:

IRR = 13.28%.