Question

Given the new found interest in nuclear power plants due to potential carbon taxes, you consider starting a company to build a nuclear power plant. Before you can build the plant, you need to gather permits, fight lawsuits and so forth. That will cost $800 million today and take 5 years to resolve with a 35% probability of success. If you build the plant, you must pay $9 billion the day you start building the plant, which is immediately after the lawsuits etc are resolved. The power plant itself takes 4 years to build. At that point the plant starts operating (exactly 4 years from when construction started). You receive $1 billion per year for 50 years starting one year from when the plant starts operating. At the end of the project, you have to pay $3 billion to shut down the plant. Your discount rate is 6% (annual rate, annual compounding).

Assume that you made the $800 million investment and the 5 years of permits, lawsuits and so forth have passed. The $800 million investment was successful. Now you are debating if you should make the plant or not today. What is the NPV of the plant?

Answer 1

Since project NPV is $$2,285 million, hence you should accept the project.

Amount in $ millions
Investment made five year before	-800
Value of investment after 5 years (year 0) at 6% interest rate	-1,071
Investment needed after 5 years (year 0)	-9,000
Project cash flow every year (from year 5)	1,000
Payment to shut the plant at the end of project (year 54)	-3,000
Discount rate	6%
Project NPV	2,285
Year	Cash flows	Discount factor (at 6%)	Discounted cash flow
0	-10,071	1.000	-10,071
1	0	0.943	0
2	0	0.890	0
3	0	0.840	0
4	0	0.792	0
5	1,000	0.747	747
6	1,000	0.705	705
7	1,000	0.665	665
8	1,000	0.627	627
9	1,000	0.592	592
10	1,000	0.558	558
11	1,000	0.527	527
12	1,000	0.497	497
13	1,000	0.469	469
14	1,000	0.442	442
15	1,000	0.417	417
16	1,000	0.394	394
17	1,000	0.371	371
18	1,000	0.350	350
19	1,000	0.331	331
20	1,000	0.312	312
21	1,000	0.294	294
22	1,000	0.278	278
23	1,000	0.262	262
24	1,000	0.247	247
25	1,000	0.233	233
26	1,000	0.220	220
27	1,000	0.207	207
28	1,000	0.196	196
29	1,000	0.185	185
30	1,000	0.174	174
31	1,000	0.164	164
32	1,000	0.155	155
33	1,000	0.146	146
34	1,000	0.138	138
35	1,000	0.130	130
36	1,000	0.123	123
37	1,000	0.116	116
38	1,000	0.109	109
39	1,000	0.103	103
40	1,000	0.097	97
41	1,000	0.092	92
42	1,000	0.087	87
43	1,000	0.082	82
44	1,000	0.077	77
45	1,000	0.073	73
46	1,000	0.069	69
47	1,000	0.065	65
48	1,000	0.061	61
49	1,000	0.058	58
50	1,000	0.054	54
51	1,000	0.051	51
52	1,000	0.048	48
53	1,000	0.046	46
54	-2,000	0.043	-86

Excel formula:

t in $ millions 2 Investment made five year before 3 Value of investment after 5 years (year 0) -82*(1+6%)"5 4 Investment needed after 5 years (year 0) 9000 5 Project cash flow every year (from year 5) 1000 6 Payment at the end of project (year 54) 7 Discount rate 0.06 8 Project NPV -SUM(D11:D65) Discount factor (at 6%) Discounted cash flow -1/(1+SBS7) A11 B11 C11 -1/(1+SBS7) A12 B12 C12 -1/(1+SBS7) A13 B13 C13 -1/(1+SBS7) A14 B14 C14 -1/(1+SBS7) A15 B15 C15 -1/(1+SBS7) A16 B16 C16 -1/(1+SBS7) A17 B17 C17 -1/(1+SBS7) A18 B18 C18 -1/(1+SBS7) A19 B19 C19 -1/(1+SB$7) A20B20 C20 -1/(1+SBS7) A21 B21 C21 -1/(1+SBS7) A22 B22 C22 -1/(1 SB$7) A23 B -1/(1+SB$7)2B24 C24 -1/(1 SB$7) 25 B25 C25 -1/(1 SB$7) A2 B26 C26 -1/(1+SBS7) A27 B27 C27 -1/(1+SB$7)A28 B -1/(1 SB$7)A29 B29 C29 -1/(1+SB$7)A30B30 C30 -1/(1+SB$7)A31B31 C31 Year Cash flows -B3+B4 11 0 12 A11+1 13 FA12+1 14A13+1 15 A14+1 -$B$5 16 A15+1 -$B$5 17 FA16+1 -SB$5 18 A17+1 -SB$5 19 =A1841 -SB$5 20 I-A19+1 -SB$5 21 -A20+1 -SB$5 22 A21+1 -SB$5 23 A22+1 -B23 C23 -SB$5 24 A23+1 -SB$5 25 A24+1 -SB$5 26 A25+1 -SB$5 27 -A26+1 28 A27+1 -B28 C28 -SB$5 29 A28+1 -SB$5 30 A29+1 -SB$5 31 A30+1

-1/(1 SB$7)3B32.C32 -1/(1 SB$7)33 B33 C33 -1/(1+SB$7)A34B34 C34 -1/(1 SB$7)35B35 C35 -1/(1 SB$7)A36 B36 C36 -1/(1+SBS7) A37 B37 C37 -1/(1+SB$7)38B38-C38 -1/(1 SB$7)A39B39 C39 -1/(1+SBS7)AA40 -1/(1+SBS7)AA41 -1/(1+SBS7)AA42 -1/(1+SBS7)AA43 -1/(1+SBS7)AA44 -1/(1+SBS7)AA45 -1/(1+SBS7)AA46 -1/(1+SBS7)AA47 -1/(1+SBS7)AA48 -1/(1+SBS7)AA49 -1/(1 SB$7)50B50 C50 -1/(1+SBS7) A51 B51 C51 -1/(1+SBS7) A52 B52 C52 -1/(1 SB$7)53 B53 C53 -1/(1 SB$7)5B54 C54 -1/(1 SB$7)55B55 C55 -1/(1 SB$7)56 B56 C56 -1/(1+SBS7) A57 B57 C57 -1/(1 SB$7)A58 B58-C58 -SB$5 32 A31+1 -SB$5 33 A32+1 -SB$5 34 A33+1 -SB$5 35 A34+1 -SB$5 36 -A35+1 -SB$5 37 A36+1 -SB$5 38 A37+1 -SB$5 39 A38+1 40 A39+1 -SB$5 -SB$5 41 -A40+1 -B41 041 -SB$5 42 A41+1 43 A42+1 44 A43+1 -B42 C42 -SB$5 -B43 C43 -SB$5 -SB$5 45 -A44+1 -B45 C45 -SB$5 46A45+1 47 A46+1 -SB$5 B47 C47 -SB$5 8A47+1 -SB$5 49 A48+1 -B49 C49 -SB$5 50 A49+1 -SB$5 51 A50+1 -SB$5 52 A51+1 -SB$5 53 A52+1 -SB$5 54 A53+1 -SB$5 55 A54+1 -SB$5 56 A55+1 -SB$5 57 A56+1 -SB$5 58 A57+1 -SB$5 59 A58+1 -SB$5 60 A59+1 -1/(1+SBS7)AA60 -B60 C60 1/1SB7) A61 B61*c61 61 A60+1

62 A61+1 63 -A62+1 SBS5 1/(1+SBS7)"A62-862°C62 -1/(1+SBS7)AA63 -1/(1+SBS7)AA64 -863°C63 SBS5 64 -A63+1 -B64 C64 65 EA64+1