Question

Excel Online Structured Activity: NPV profiles A company is considering two mutually exclusive expansion plans. Plan A requires a $39 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.23 million per year for 20 years. Plan B requires a $13 million expenditure to build a somewhat less efficient, more labor-intensive plant with an expected cash flow of $2.91 million per year for 20 years. The firm's WACC is 9%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below. Open spreadsheet a. Calculate each project's NPV. Round your answers to two decimal places. Do not round your intermediate calculations. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Plan A: $ million Plan B: $ million Calculate each project's IRR. Round your answer to two decimal places. Plan A: % Plan B: b. By graphing the NPV profiles for Plan A and Plan B, approximate the crossover rate to the nearest percent. % C. Calculate the crossover rate where the two projects' NPVs are equal. Round your answer to two decimal places. % d. Why is NPV better than IRR for making capital budgeting decisions that add to shareholder value? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

Answer 1

NPV is given by:

Σ Rt/(1 i)ttvaries from 1 to n NPV where Rt Cash flow netted (Inflow - Outflow) during the period "t" i Discount rate t number of periods

The Discount rate at which NPV = 0 is known as IRR

Answer a)

X V fx IRR(C3:C23) SUM А В Discount Rate Year 9% 1 Plan B Plan A 2 -$39.00 -$13.00 3 $6.23 $2.91 4 1 $6.23 $2.91 5 2 $6.23 $2.91 6 3 $6.23 $2.91 7 4 $6.23 $2.91 8 $6.23 $2.91 9 $6.23 $2.91 10 7 $6.23 $2.91 11 $6.23 $2.91 12 9 10 $6.23 $2.91 13 $6.23 $2.91 14 11 $6.23 $2.91 15 12 $6.23 $2.91 16 13 14 $6.23 $2.91 17 $6.23 $2.91 18 15 16 $6.23 $2.91 19 $6.23 $2.91 20 17 $6.23 $2.91 21 18 $6.23 $2.91 22 19 20 $6.23 $2.91 23 =IRR(C3:C23) IRR LO LO LO 24

X V fx =NPV(C1,C4:C23)+C3 SUM А В C E Discount Rate 9% Plan A Plan B 2 Year -$39.00 -$13.00 3 $6.23 $2.91 4 1 $6.23 $2.91 5 2 $6.23 $2.91 6 3 $6.23 $2.91 7 4 $6.23 $2.91 5 $6.23 $2.91 6 7 $6.23 $2.91 10 $6.23 $2.91 11 8 12 $6.23 $2.91 9 10 11 12 13 $6.23 $2.91 $6.23 $2.91 14 $6.23 $2.91 15 $6.23 $2.91 16 13 14 $6.23 $2.91 17 $6.23 $2.91 18 15 16 $6.23 $2.91 19 17 18 $6.23 $2.91 20 $6.23 $2.91 21 $6.23 $2.91 22 19 20 $6.23 $2.91 23 3.88% 15.00% 24 IRR NPV NPV(C1, C4:C23 )+ C3 25

X V fx =NPV(C1,D4:D23)+D3 SUM В E 9% Plan B -$13.00 Discount Rate Year 1 Plan A 2 -$39.00 3 0 $6.23 $2.91 4 1 $6.23 $2.91 5 2 $6.23 $2.91 6 3 $6.23 $2.91 7 4 $6.23 $2.91 8 5 $6.23 $2.91 6 $6.23 $2.91 10 7 $6.23 $2.91 11 8 $6.23 $2.91 12 9 $6.23 $2.91 13 10 $6.23 $2.91 14 11 15 $6.23 $2.91 12 $6.23 $2.91 16 13 17 $6.23 $2.91 14 $6.23 $2.91 18 15 $6.23 $2.91 19 16 $6.23 $2.91 20 17 $6.23 $2.91 18 $6.23 $2.91 19 $6.23 $2.91 20 IRR 15.00% 3.88% $17.87 NPV(C1, D4:D23)+ D3 NPV 222 322

fx NPV(C1,D4:D23)+D3 D25 А В C E Discount Rate 9% Plan A Plan B 2 Year -$39.00 -$13.00 3 0 $6.23 $2.91 4 $6.23 $2.91 5 2 $6.23 $2.91 6 $6.23 $2.91 7 4 $6.23 $2.91 5 $6.23 $2.91 6 $6.23 $2.91 10 7 $6.23 $2.91 11 12 $6.23 $2.91 13 $6.23 $2.91 10 11 $6.23 $2.91 14 12 $6.23 $2.91 15 $6.23 $2.91 16 13 $6.23 $2.91 17 14 $6.23 $2.91 18 15 $6.23 $2.91 19 16 $6.23 $2.91 20 17 $6.23 $2.91 21 18 $6.23 $2.91 22 19 $6.23 $2.91 23 20 15.00% 3.88% 24 IRR $13.56 NPV $17.87 25 26

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Answer b)

NPV profile

X V fx =NPV(F5,$C$6: $c$25)+$C$5 SUM D. A В E Н 1 2 3 Discount Rate NPV of plan A NPV of plan B 0%=NPV(F5, $C$6:$C$25 )+ $C$5 Year Cashflows for the Plan B Cashflows for the Plan A 4 -$39.00 -$13.00 5 0 $6.23 $2.91 $73.42 $39.51 1% 6 $6.23 $2.91 $62.87 $34.58 2% 7 2 $6.23 $2.91 $53.69 $30.29 3% $6.23 $2.91 $45.67 $26.55 4% 9 4 $6.23 $2.91 $38.64 $23.27 5% 10 $6.23 $2.91 $32.46 $20.38 6% 11 6 $27.00 7 8 $6.23 $2.91 $17.83 7% 12 $6.23 $2.91 $22.17 $15.57 8% 13 $6.23 $2.91 $17.87 $13.56 9% 14 9 $6.23 $2.91 $14.04 $11.77 15 10% 10 $6.23 $2.91 $10.61 $10.17 11% 16 11 $6.23 $2.91 $7.53 $8.74 12% 17 12 $6.23 $2.91 $4.76 $7.44 13% 18 13 $6.23 $2.91 $2.26 $6.27 14% 19 14 $6.23 $2.91 -$0.00 $5.21 15% 20 15 16 $6.23 $2.91 -$2.06 $4.25 16% 21 $6.23 $2.91 -$3.94 $3.38 22 17% 17 $6.23 $2.91 -$5.65 $2.58 18% 23 18 $6.23 $2.91 -$7.22 $1.84 24 19% 19 20 $6.23 $2.91 -$8.66 $1.17 20% 25 -$9.99 $0.55 21% 26 $11 21 So 02 22% 27

X V fxNPV(F5,$ D$6:$D$25)+$D$5 SUM В D E G 2 3 Year Discount Rate NPV of plan A NPV of plan B $85.60 NPV(F5, $D$6:$D$25)+ $D$5 Cashflows for the Plan A Cashflows for the Plan B 4 -$39.00 -$13.00 0% 5 0 $6.23 $2.91 $73.42 $39.51 1% 6 1 $6.23 $2.91 $62.87 $34.58 2% 7 2 $6.23 $2.91 $53.69 $30.29 3% 3 $6.23 $2.91 $45.67 $26.55 4% 9 4 $38.64 $6.23 $2.91 $23.27 5% 10 5 $6.23 $2.91 6% $32.46 $20.38 11 6 $6.23 $2.91 $27.00 $17.83 7% 12 7 $6.23 $2.91 $22.17 $15.57 8% 13 8 $6.23 $2.91 $17.87 $13.56 9% 14 $14.04 $6.23 $2.91 $11.77 10% 15 10 $6.23 $2.91 $10.61 $10.17 11% 16 11 $6.23 $2.91 $7.53 $8.74 17 12 12% $6.23 $2.91 $4.76 $7.44 13% 18 13 $6.23 $2.91 $2.26 $6.27 19 14% 14 15% -$0.00 $6.23 $2.91 $5.21 20 15 11. $6.23 $2.91 16% -$2.06 $4.25 21 16 $6.23 $2.91 -$3.94 $3.38 22 17% 17 $6.23 $2.91 18% -$5.65 $2.58 23 18 $6.23 $2.91 -$7.22 $1.84 24 19% 19 $6.23 $2.91 -$8.66 $1.17 25 20% 20 -$9.99 $0.55 21% 26

Discount Rate	NPV of plan A	NPV of plan B
0%	$85.60	$45.20
1%	$73.42	$39.51
2%	$62.87	$34.58
3%	$53.69	$30.29
4%	$45.67	$26.55
5%	$38.64	$23.27
6%	$32.46	$20.38
7%	$27.00	$17.83
8%	$22.17	$15.57
9%	$17.87	$13.56
10%	$14.04	$11.77
11%	$10.61	$10.17
12%	$7.53	$8.74
13%	$4.76	$7.44
14%	$2.26	$6.27
15%	-$0.00	$5.21
16%	-$2.06	$4.25
17%	-$3.94	$3.38
18%	-$5.65	$2.58
19%	-$7.22	$1.84
20%	-$8.66	$1.17
21%	-$9.99	$0.55
22%	-$11.21	-$0.02
23%	-$12.34	-$0.55
24%	-$13.39	-$1.04
25%	-$14.37	-$1.49
26%	-$15.27	-$1.92
27%	-$16.12	-$2.31
28%	-$16.91	-$2.68
29%	-$17.65	-$3.03
30%	-$18.34	-$3.35
31%	-$18.99	-$3.66
32%	-$19.61	-$3.94
33%	-$20.18	-$4.21
34%	-$20.73	-$4.47
35%	-$21.24	-$4.71
36%	-$21.73	-$4.93
37%	-$22.19	-$5.15
38%	-$22.63	-$5.35
39%	-$23.05	-$5.55
40%	-$23.44	-$5.73
41%	-$23.82	-$5.91
42%	-$24.18	-$6.08
43%	-$24.52	-$6.24
44%	-$24.85	-$6.39
45%	-$25.16	-$6.54
46%	-$25.46	-$6.68
47%	-$25.75	-$6.81
48%	-$26.03	-$6.94
49%	-$26.29	-$7.06
50%	-$26.54	-$7.18
51%	-$26.79	-$7.30
52%	-$27.02	-$7.41
53%	-$27.25	-$7.51
54%	-$27.47	-$7.61
55%	-$27.67	-$7.71
56%	-$27.88	-$7.80
57%	-$28.07	-$7.90
58%	-$28.26	-$7.98
59%	-$28.44	-$8.07
60%	-$28.62	-$8.15
61%	-$28.79	-$8.23
62%	-$28.95	-$8.31
63%	-$29.11	-$8.38
64%	-$29.27	-$8.45
65%	-$29.42	-$8.52
66%	-$29.56	-$8.59
67%	-$29.70	-$8.66
68%	-$29.84	-$8.72
69%	-$29.97	-$8.78
70%	-$30.10	-$8.84
71%	-$30.23	-$8.90
72%	-$30.35	-$8.96
73%	-$30.47	-$9.01
74%	-$30.58	-$9.07
75%	-$30.69	-$9.12
76%	-$30.80	-$9.17
77%	-$30.91	-$9.22
78%	-$31.01	-$9.27
79%	-$31.11	-$9.32
80%	-$31.21	-$9.36
81%	-$31.31	-$9.41
82%	-$31.40	-$9.45
83%	-$31.49	-$9.49
84%	-$31.58	-$9.54
85%	-$31.67	-$9.58
86%	-$31.76	-$9.62
87%	-$31.84	-$9.66
88%	-$31.92	-$9.69
89%	-$32.00	-$9.73
90%	-$32.08	-$9.77
91%	-$32.15	-$9.80
92%	-$32.23	-$9.84
93%	-$32.30	-$9.87
94%	-$32.37	-$9.90
95%	-$32.44	-$9.94
96%	-$32.51	-$9.97
97%	-$32.58	-$10.00
98%	-$32.64	-$10.03
99%	-$32.71	-$10.06
100%	-$32.77	-$10.09

NPV Profile $140.00 $120.00 $100.00 $80.00 $60.00 $40.00 $20.00 Plan B $0.00 Plan A -$20.00 -$40.00 -$60.00 Discount Rate %00T %06 %08 %S9 %09 %0 NPV

Hence, cross over rate is near 11%

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Answer c)

For crossover rate

Step 1: Subtract cash flows of 2 project

Step 2: Find IRR of difference

X V fx =D3-C3 SUM A B C E F Discount Rate 9% 1 Plan A Plan B Plan A - Plan B 2 Year -$39.00 -$13.00 0 D3- C3 3 $6.23 $2.91 -$3.32 $6.23 $2.91 -$3.32 5 2

A A = EE Cut Calibri Percenta 11 В IU Merge and Wrap Copy Format Painter Paste Center Тext X V fx =IRR(F3:F23) SUM A В C D F G 9% Discount Rate 1 Plan A Plan B Plan A - Plan B 2 Year -$39.00 -$13.00 $26.00 3 0 $6.23 $2.91 -$3.32 4 1 $6.23 $2.91 -$3.32 5 2 $6.23 $2.91 -$3.32 6 3 $6.23 $2.91 -$3.32 7 4 $6.23 $2.91 -$3.32 8 5 $6.23 $2.91 -$3.32 9 $6.23 $2.91 -$3.32 10 7 $6.23 $2.91 -$3.32 11 $6.23 $2.91 -$3.32 12 9 $6.23 $2.91 -$3.32 13 10 $6.23 $2.91 -$3.32 14 11 $6.23 $2.91 -$3.32 15 12 $6.23 $2.91 -$3.32 16 13 $6.23 $2.91 -$3.32 17 14 $6.23 $2.91 -$3.32 18 15 $6.23 $2.91 -$3.32 19 16 $6.23 $2.91 -$3.32 20 17 $6.23 $2.91 -$3.32 21 18 $6.23 $2.91 -$3.32 22 19 -$3.32 $6.23 $2.91 23 20 IRR =IRR(F3:F23) 15.00% 3.88% 24 Cross Over Rate $17.87 $13.56 25 NPV H LL st LC LO OY st Ln LC

fxIRR(F3:F23) F24 А В C E F G Discount Rate 9% Plan A Plan B Plan A Plan B 2 Year -$39.00 -$13.00 $26.00 3 0 $6.23 $2.91 -$3.32 4 $6.23 $2.91 -$3.32 5 2 $6.23 $2.91 -$3.32 6 $6.23 $2.91 -$3.32 7 4 $6.23 $2.91 -$3.32 5 $6.23 $2.91 -$3.32 6 $6.23 $2.91 -$3.32 10 7 $6.23 $2.91 -$3.32 11 12 $6.23 $2.91 -$3.32 13 $6.23 $2.91 -$3.32 10 11 $6.23 $2.91 -$3.32 14 12 $6.23 $2.91 -$3.32 15 $6.23 $2.91 -$3.32 16 13 $6.23 $2.91 -$3.32 17 14 $6.23 $2.91 -$3.32 18 15 $6.23 $2.91 -$3.32 19 16 $6.23 $2.91 -$3.32 20 17 $6.23 $2.91 -$3.32 21 18 $6.23 $2.91 -$3.32 22 19 $6.23 $2.91 -$3.32 23 20 3.88% 11,26%---- 15.00% 24 IRR Cross Over Rate $17.87 $13.56 25 NPV

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