Chapter 11.pdf

Contemporary Engineering Economics, Fifth Edition, by Chan S. Park. ISBN: 0-13-611848-8 © 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Chapter 11 Inflation and Its Impact on Project Cash Flows Measure of Inflation 11.1

2.5(1 + 0.08)(1 + 0.10)(1 + 0.12) = 3.3264 3.3264 = 2.5(1 + f )3 f = 9.99%

11.2 1.2(1 + f )10 = 3.62 f = 11.674%

100(1 + 0.11674)10 = 301.67 11.3 (a) Average (geometric) price index 150.6(1 + f )4 = 165.8 f = 2.433%

(b) 165.8(1 + 0.02433)1 = 169.83 11.4


Actual versus Constant Dollars 11.6 Given: i = 11%, f = 5% , 10 annuity payments in actual dollars 500(P / A,11%,10) P = $6, 50

= $38,280 Comments: Since the annuity payments are made in actual dollars, we use the market interest rate to find its equivalent lump sum amount in today’s dollars. 11.7 Given: i = 13%, f = 5%, maintenance costs are given in constant dollars. i' =

i − f

1 + f

=

0.13 − 0.05 1 + 0 .05

= 7.62%

000( P / F , 7. 7.62%,1) + $25, 00 000(P / F , 7. 7.6 2%, 2) 2) P = $20, 00 000( P / F , 7. 7.62%, 3) 3) + $34, 00 000(P / F , 7. 7.6 2%, 4) 4) +$28, 00 000( P / F , 7. 7.62%, 5) 5) +$38, 00 = $114,300 300( A / P,13%, 5) 5) A = $114, 30 = $32,497 11.8 Given: i = 14%, f = 5%


11.10 (a) Constant-dollar analysis: we need to find the inflation-free interest rate. i'=

i − f

1 + f

= 7.477%

Then, find the equivalent present worth of this geometric series at i ' . P = $10, 000(P / A1 , 8%, 7.477%, 4)

= $37,490 (b) Actual-dollar analysis

1

Net Cash Flow in Constant $ $10,000

Conversion factor (1 + 0.07)1

Net Cash Flow in Actual $ $10,700

2

10,800

(1 + 0.07)2

12,365

3

11,664

(1 + 0.07)3

14,289

4

12,597

(1 + 0.07)4

16,512

Period

P = $10, 700( P / F ,15%,1) + $12,365(P / F ,15%, 2) 4) +$14, 289( P / F ,15%, 3) + $16,512(P / F ,15%, = $37,490


First compute the equivalent present worth of the constant dollar series ati ' : P = $1, 000( P / A, 5.01%, 4)

= $3,545.13 Then, we compute the equivalent annual payment in actual dollars using i: A = $3, 545.13( A / P, 9%, 4)

= $1,094.27 11.12 Given: i = 12%, f = 6% , bond interest rate = 9% compounded semiannually, face value = $1,000

• The 15th interest payment in actual dollars: I 15 = $1,000(0.045) = $45

• The 15th interest payment (7.5th year) in constant dollars: I '15 = $45( P / F , 6%, 7.5) = $29.07

Equivalence Calculation Under Inflation


11.15 Given: i ' = 6%, f = 5%, N = 5 years, A = $2.2 million in constant dollars

• Market interest rate: i = 0.06 + 0.05 + (0.06)(0.05) = 11.3%

• Actual dollar analysis: Period

Net Cash Flow in Actual $

Equivalent Present Worth

1

Net Cash Flow in Constant $ $2,200,000

$2,310,000

$2,075,472

2

2,200,000

2,425,500

1,957,992

3

2,200,000

2,546,775

1,847,162

4

2,200,000

2,674,114

1,742,606

5

2,200,000

2,807,819

1,643,968

$9,267,200 P = $2, 310, 000(P / F ,11.3%,1)

+  + $2, 807, 819(P / F ,11.3%, 5) = $9,267,200 11.16 Given: i = 12%, f = 5%, g = 7%, N = 5 years, A1 = $5, 000 in constant dollars


11.17 Given: i = 0.75% per month, f = 0.5% per month, P = $8,000, N = 24 months (a) Inflation-free interest rate: 0.0075 − 0.005 = 0.2488% per month 1 + 0.005 i ' = 3.0263% per year im ' =

(b) Equal monthly payment in constant dollars: A ' = $8, 000( A / P, 0.2488%, 24)

= $343.79 11.18 Given: i = 6% compounded monthly, f = 5% compounded annually, number of months to deposit = 240 months, number of annual withdrawals = 10, first withdrawal = 6 months after retirement.

•

Effective inflation rate per semiannual: Since the first withdrawals is made after 6 months from retirement, it is necessary to calculate the effective inflation rate per semiannual.

⎛ 1.05 ⎞ f = ⎜ ⎟ ⎝ 1 ⎠ •

1/ 2

− 1 = 2.4695% per semiannual

Annual withdrawals in actual dollars: On semiannual basis, the first withdrawal will be made after 41 semiannual periods. Then, we can calculate the equivalent


•

Equivalence calculation: To find the required equal monthly deposit amount (A), we establish the following equivalence relationship: 1

⎛ 0.06 ⎞ im = ⎜1 + ⎟ − 1 = 0.5% 12(1) ⎝ ⎠ 12

⎛ 0.06 ⎞ ia = ⎜1 + ⎟ − 1 = 6.168% 12 ⎝ ⎠ A( F / A, 0.5%, 240)( F / P, 0.5%, 6) = $135, 941+ $142, 738(P / F , 6.168%,1) +$149, 875(P / F , 6.168%, 2) + ⋅⋅⋅ +$210,888(P / F , 6.168%, 9) A = $1, 294, 043.01/ 476.08 = $2,718.12 per month.

$210,888 $200,846

$135,941 (240 months) 0

Years

20 21

22

29

30


(b)

• Effective annual interest rate: ia = (1 + 0.08 / 4) − 1 = 8.243% 4

• Equivalent value of $1,000,000 in actual dollars at the end of 65th birthday: $1, 000, 000(F / P , 6%, 40) = $10, 285, 718

• Conversion of gradient series to equivalent uniform series: A = G ( A / G,8.243%, 40)

= $1,000(10.3746) = $10,374 • Amount of the first deposit ( A1 ) : ( A1 + $10,374)( F / A,8.243%, 40) = $10, 285, 718 ( A1 + $10, 374)(276.21) = $10, 285, 718 A1 + $10,374 = $37,237 A1 = $26,862


Effects of Inflation on Project Cash Flows 11.21 Consider the following project’s after-tax cash flow and the expected annual general inflation rate during the project period: End of year 0

Cash flow in actual dollars -$45,000

Expected general inflation rate

1

32,000

3.5%

2

32,000

4.2%

3

32,000

5.5%

(a) The average annual general inflation rate: (1 + 0.035)(1 + 0.042)(1 + 0.055) = 1.1378 (1 + f )3 = 1.1378 f = 4.40%

(b) Constant dollars:

0

Actual dollars -$45,000

Constant dollars -$45,000

1

32,000

32,000(0.9662) = 30,918

n


11.22 (a) and (b) 0

1

2

Income Statement

Revenue Expenses: O&M Depreciation Interest

$114,000

$114,000

$ $ $

56,490 $ 11,000 $ 5,000 $

59,315 8,800 2,619

Taxable Income Income Taxes

$ $

41,510 $ 16,604 $

43,266 17,306

Net Income

$

24,906 $

25,960

$ $

24,906 $ 11,000 $ $ (600) $ $ (23,810) $

25,960 8,800 29,768 12,600 2,173 (26,190)

($17,000) ($17,000)

$11,496 $10,949

$53,110 $48,172

PW (18%) = $ IRR (%) =

30,885 103.59%

Cash Flo w Statement

Cash from operation Net Income Depreciation Investment / Salvage Working capital Gains Tax Loan repayment Net Cash Flow (actual) Net Cash Flow (constant)

$ $

(55,000) (12,000) $

$

50,000 $


11.23 (a) and (b) (a) Project Cash Flows with Inflation 0

1

2

3

4

5

6

Income Statement


$152,250

$159,863 $167,856 $176,248 $185,061 $194,314

$ 86,100 $ 90,405 $ 94,925 $ 99,672 $ 104,655 $ 109,888 $ 24,000 $ 38,400 $ 23,040 $ 13,824 $ 13,824 $ 6,912 $ 10,800 $ 10,800

Taxable Income Income Taxes (40%)

$31,350 $12,540

$20,258 $8,103

$49,891 $19,956

$62,752 $25,101

$66,582 $26,633

$77,514 $31,006

Net Income

$18,810

$12,155

$29,935

$37,651

$39,949

$46,508

$18,810 $24,000

$12,155 $38,400

$29,935 $23,040

$37,651 $13,824

$39,949 $13,824

$46,508 $6,912

Cash Flow Statement

Cash from operation Net Income Depreciation Cash from investing activities: Investment / Salvage $ (120,000) Gains Tax Working Capital Cash from financing activities: Loan repayment $ 120,000 Net Cash Flow (actual)

PW(18%) = $92,959

$0

$ 20,101 $ (8,041)

$ (120,000) $42,810

($69,445)

$52,975

$51,475

$53,773

$65,481


Project Cash Flows without Inflation 0

1

2

3

4

5

6

Income Statement


$145,000

$145,000 $145,000 $145,000 $145,000 $145,000

$ 82,000 $ 82,000 $ 82,000 $ 82,000 $ 82,000 $ 82,000 $ 24,000 $ 38,400 $ 23,040 $ 13,824 $ 13,824 $ 6,912 $ 10,800 $ 10,800


$28,200 $11,280

$13,800 $5,520

$39,960 $15,984

$49,176 $19,670

$49,176 $19,670

$56,088 $22,435

Net Income

$16,920

$8,280

$23,976

$29,506

$29,506

$33,653

$16,920 $24,000

$8,280 $38,400

$23,976 $23,040

$29,506 $13,824

$29,506 $13,824

$33,653 $6,912

Cash Flow Statement

Cash from operation Net Income Depreciation Cash from investing activities: Investment / Salvage $(120,000) Gains Tax Working Capital Cash from financing activities: Loan repayment $ 120,000 Net Cash Flow (actual) PW (12.38%) =

$0

$ 15,000 $ (6,000)

$ (120,000) $40,920

($73,320) $47,016

$43,330

$43,330

$49,565

$87,429

Note: Amount of interest payments remain unchanged with or without inflation. (d) Present value gain due to borrowing:


11.24 Effects of inflation on cash flows: (a) Project Cash Flows with Inflation 0

1

2

3

4

5

Income Statement

Revenue Expenses: Depreciation Interest Taxable Income Income Taxes Net Income

$23,100

$20,948

$17,364

$18,233

$19,144

$4,000 $2,000 $17,100 $6,840 $10,260

$6,400 $1,396 $13,152 $5,261 $7,891

$3,840 $731 $12,793 $5,117 $7,676

$2,304

$1,152

$15,929 $6,371 $9,557

$17,992 $7,197 $10,795

$10,260 $4,000

$7,891 $6,400

$7,676 $3,840

$9,557 $2,304

$10,795 $1,152 $2,553 ($100)

($6,042) $8,218

($6,647) $7,644

($7,311) $4,205

$11,861

$14,401

2

3

4

5

$19,000

$15,000

$15,000

$15,000

6 400

3 840

2 304

1 152

Cash Flow Statement

Cash from operation Net Income Depreciation Investment / Salvage Gains Tax Loan repayment Net Cash Flow (actual) PW (20%) =

($20,000) $20,000 $0 $26,098

(b) Income Statement (without inflation) 0 1 Income Statement Revenue $22,000 Expenses: Depreciation 4 000


11.25 (a), (b), and (c); The project is acceptable Income Statement 0 Income Statement

Revenue (Labor Savings) Expenses: O&M Depreciation Interest

1

inflation 5%

2

$84,000

$

21,435 $

3

$88,200

36,735 $

$92,610

13,118

Taxable Income Income Taxes (40%)

$62,565 $25,026

$51,465 $20,586

$79,493 $31,797

Net Income

$37,539

$30,879

$47,696

$37,539 $21,435

$30,879 $36,735

$47,696 $13,118

Cash Flow Statement

Cash from operation Net Income Depreciation Cash from investing activities: Investment / Salvage Gains Tax Working capital Cash from financing activities: Loan repayment Net Cash Flow (actual) Net Cash Flow (constant)

$ 8%

$

(150,000) (10,000) $

($160,000) ($160,000) PW (20%) = $ PW (14.29%) = $

(800) $

$58,174 $55,404 22,773 22,773

$ $ (864) $

$66,750 $60,544

80,000 (515) 11,664

$151,962 $131,270


Rate of Return Analysis under Inflation 11.26 (a) Project's IRR with no inflation 0

1

2

3

4

5

6

7

8

Income Statement

Revenue Expenses: O&M Depreciation

$22,000 $ $

$22,000

$22,000

9,500 $ 9,500 $ 9,500 $ 8,860 $ 15,184 $ 10,844 $

$22,000 9,500 $ 7,744 $

$22,000 9,500 $ 5,537 $

$22,000 9,500 $ 5,530 $

$22,000 9,500 $ 5,537 $

$22,000 9,500 2,765


$3,640 1,274

($2,684) (939)

$1,656 580

$4,756 1,665

$6,963 2,437

$6,970 2,439

$6,963 2,437

$9,735 3,407

Net Income

$2,366

($1,744)

$1,077

$3,092

$4,526

$4,530

$4,526

$6,328

Cash Flow Statement

Cash from operation Net Income Depreciation Investment / Salvage Gains Tax Working capital Net Cash Flow

$ $ $

(62,000)

$

(10,000) ($72,000)

PW (12.38%)=

2,366 $ (1,744) $ 1,077 $ 8,860 $ 15,184 $ 10,844 $

$11,226 ($12,340.64)

$13,439

$11,920 IRR (%)

3,092 $ 7,744 $

$10,835

4,526 $ 5,537 $

$10,063

4,530 $ 5,530 $

$10,061

4,526 $ 6,328 5,537 $ 2,765 $ 5,000 $ (1,750) $ 10,000 $10,063

$22,343

7.47%

Page | 15


(b) Project's IRR with inflation Income Statement 0

2

3

4

5

6

7

8

$23,760

$25,661

$27,714

$29,931

$32,325

$34,911

$37,704

$40,720

10,070 8,860

10,674 15,184

11,315 10,844

11,994 7,744

12,713 5,537

13,476 5,530

14,284 5,537

15,142 2,765


$4,830 1,691

($197) (69)

$5,555 1,944

$10,193 3,568

$14,075 4,926

$15,905 5,567

$17,883 6,259

$22,814 7,985

Net Income Cash Flow Statement Cash from operation Net Income Depreciation Investment / Salvage Gains Tax Working capital Loan repayment

$3,140

($128)

$3,611

$6,626

$9,149

$10,338

$11,624

$14,829

$3,140 $8,860

($128) $15,184

$3,611 $10,844

$6,626 $7,744

$9,149 $5,537

$10,338 $5,530

$11,624 $5,537

($10,000)

($800)

($864)

($933)

($1,008)

($1,088)

($1,175)

($1,269)

$14,829 $2,765 $7,387 ($2,586) $17,138

($72,000) ($72,000)

$11,199 $10,666

$14,192 $12,872

$13,522 $11,680

$13,362 $10,993

$13,597 $10,654

$14,693 $10,964

$15,891 $11,293

$39,534 $26,758

Income Statement Revenue Expenses: O&M Depreciation

Net Cash Flow (in actual $) Net Cash Flow (in constant $)

1

($62,000)

PW (18%)= ($10,303) The project is not acceptable.

IRR' (%)

8.49%

Page | 16


11.27

Income Statement 0 Income Statement Revenue Expenses: O&M Rent Depreciation

1

2

3

4

5

6

$35,000

$38,000

$55,000

$60,000

$70,000

$60,000

$16,000 $10,080 $11,000

$21,000 $10,584 $17,600

$23,000 $11,113 $10,560

$32,000 $11,669 $6,336

$33,000 $12,252 $6,336

$33,000 $12,865 $3,168


($2,080) ($11,184) $10,327 ($624) ($3,355) $3,098

$9,995 $2,999

$18,412 $5,524

$10,967 $3,290

Net Income Cash Flow Statement Cash from operation Net Income Depreciation Investment / Salvage Gains Tax Working capital

($1,456)

($7,829)

$7,229

$6,997

$12,888

$7,677

($1,456) $11,000

($7,829) $7,229 $17,600 $10,560

$6,997 $6,336

$12,888 $6,336

$7,677 $3,168 $13,401 ($4,020)

$13,333 $10,969

$19,224 $15,063

$20,226 $15,093

Net Cash Flow (Actual Dollar) Net Cash Flow (Constant Dollar)

5%

($55,000)

($55,000) ($55,000)

$9,544 $9,090

$9,771 $8,863

$17,789 $15,367


11.28 (a) Real after-tax yield on bond investment:

• Nontaxable municipal bond: ′ imunicipal =

0.09 − 0.03

1 + 0.03 • Taxable corporate bond:

′ icorporate =

= 5.825%

0.12(1 − 0.3) − 0.03 1 + 0.03

= 5.243%

(b) Given i = 6%, and f = 3% ′ isavings = 2.91%

′ ′ Since imunicipal > 2.91% and icorporate > 2.91% , both bond investments are better than the savings account. The real return is best with the municipal bond because the initial investment is the same in both cases, $10,000. But of course if MARR is high enough, one or both bonds may be unacceptable and then it is time to seek a better investment. 11.29 (a), (b), and (c) Engine A 0

1

2

3

4

5


Engine B 0

1

2

3

4

5

Income Statement

Revenue Expenses: O&M Depreciation

$117,504 $24,000

$126,904 $24,000

$137,057 $24,000

$148,021 $24,000

$159,863 $24,000


($141,504) ($56,602)

($150,904) ($60,362)

($161,057) ($64,423)

($172,021) ($68,808)

($183,863) ($73,545)

($84,902)

($90,543)

($96,634)

($103,213)

($110,318)

($84,902) $24,000

($90,543) $24,000

($96,634) $24,000

($103,213) $24,000

($110,318) $24,000 $80,000

($200,000)

($60,902)

($66,543)

($72,634)

($79,213)

($6,318)

PW (20%)=

($379,735)

AE (20%)=

($126,976)

FW (20%)=

($944,903)

Net Income Cash Flow Statement

Cash from operation Net Income Depreciation Investment / Salvage Gains Tax Net Cash Flow

($200,000)

11.30 (a) & (b) Actual and constant dollar analysis: 0 Income Statement Revenue

1

2

$126,000

$132,300


11.31 (a) & (b) Project cash flows in actual and constant dollars:

0

2

3

4

5

6

$84,800

$89,888

$95,281

$100,998

$107,058

$113,482

20,000

32,000

19,200

11,520

11,520

5,760


$64,800 $25,920

$57,888 $23,155

$76,081 $30,432

$89,478 $35,791

$95,538 $38,215

$107,722 $43,089

Net Income Cash Flow Statement Cash from operation Net Income Depreciation Investment / Salvage Gains Tax Working capital Loan repayment

$38,880

$34,733

$45,649

$53,687

$57,323

$64,633

38,880 20,000

34,733 32,000

45,649 19,200

53,687 11,520

57,323 11,520

$58,880 $55,547

$66,733 $59,392

$64,849 $54,448

$65,207 $51,650

$68,843 $51,443

Income Statement Revenue Expenses: O&M Depreciation Interest

Net Cash Flow (actual $) Net Cash Flow (constant $)

1

(100,000)

($100,000) ($100,000) PW (18%) = IRR'(%) =

64,633 5,760 42,556 (17,022)

$95,927 $67,625

$136,553 51.53%

Page | 20


(c) The effects of project financing under inflation: 0

1

2

3

4

5

6

Income Statement


$84,800

$89,888

$95,281

$100,998

$107,058

$113,482

20,000 12,000

32,000 10,521

19,200 8,865

11,520 7,010

11,520 4,933

5,760 2,606


$52,800 21,120

$47,367 18,947

$67,216 26,886

$82,468 32,987

$90,605 36,242

$105,116 42,046

Net Income

$31,680

$28,420

$40,330

$49,481

$54,363

$63,070

31,680 20,000

28,420 32,000

40,330 19,200

49,481 11,520

54,363 11,520

63,070 5,760 42,556 (17,022)

(12,323)

(13,801)

(15,457)

(17,312)

(19,390)

(21,717)

$39,357 $37,130

$46,619 $41,491

$44,072 $37,004

$43,688 $34,605

$46,493 $34,743

$72,646 $51,213

Cash Fl ow Statement

Cash from operation Net Income Depreciation Investment / Salvage Gains Tax Working capital Loan repayment

(100,000)

100,000


$0 $0 PW (18%) =

$163,425

Page | 21


(e) The present value loss due to inflation: 0

1

2

3

4

5

6

Income Statement


$80,000

$80,000

$80,000

$80,000

$80,000

$80,000

20,000

32,000

19,200

11,520

11,520

5,760


$60,000 24,000

$48,000 19,200

$60,800 24,320

$68,480 27,392

$68,480 27,392

$74,240 29,696

Net Income

$36,000

$28,800

$36,480

$41,088

$41,088

$44,544

36,000 20,000

28,800 32,000

36,480 19,200

41,088 11,520

41,088 11,520

44,544 5,760 30,000 (12,000)

$56,000

$60,800

$55,680

$52,608

$52,608

$68,304

Cash Fl ow Statement

Cash from operation Net Income Depreciation Investment / Salvage Gains Tax Working capital Loan repayment

(100,000)

Net Cash Flow (actual $)

($100,000) PW (11.32%) =

$140,656

Present value loss = $136,553 - $140,656 = ($4,103) (e) Required additional before-tax annual revenue in actual dollars (equal amount) to make-up the inflation loss. $4,103( A / P,18%, 6) 1 − 0.40

= $1,955

Page | 22


Short Case Studies ST 11.1 Based on 2009 data, we may compute the average inflation rates as follows: C o n s u m e r P u r c h a se s

2003

2009

184 $170,000

2 1 3 .2 $215,900

A v g . in f la t io n rate 2 .4 9 % 4.06%

$19,560

$20,125

0.48%

$1.61

$2.32

6.28%

$39.50

$39.50

0.00%

$42.95

$42.95

0.00%

T a x P r e p a r a ti o n

$130

$151

2 .5 3 %

A v e r a g e c o s t o f f e d e r a l , s t a te , a n d l o c a l t a x - r e tu r n p r e p a r a ti o n b y H & R B l o c k M c D o n a ld ’ s B i g M a c

$2.22

$2.39

1.24%

$189

$212

1 .9 3 %

$8.08

$8.52

0.89%

$246

$235

-0 . 7 6 %

$1,162

$1,315

2.08%

$3,889

$4,848

3.74%

$6,696

$7,907

2.81%

$15,441

$17,799

2.40%

$6,366

$6,725

0.92%

N e w C P I S i n g le - F a m i ly H o m e M e d i a n r e s a le p r i c e Toyota Cam ry S t i c k e r p r ic e , p l u s d e s t in a t i o n c h a r g e , fo r L E 5 - s p e e d U n l e a d e d G a s o l in e A v e r a g e n a t i o n a l p r i c e p e r g a l l o n f o r a l l g r a d e s c o m b i n e d , in c l u d i n g a l l t a x e s , s e l f -s e r v i c e Pa ir of Jeans G ap’s Easy Fit, stonewa shed, national price I n te r n e t S e r v i c e A v e r a g e m o n t h l y s u b s c r ip t i o n f o r u s e o f c a b l e s e r v i c e f ro m C o m c a s t , s t a n d a r d t i e r

Average recommend ed price C l e a r in g C l o g g e d S i n k R o t o - R o o t e r s e w e r a n d d r a i n se r v ic e M o v ie T i c k e t

r e si d e n ti a l n a t ’ l a v .

A d u l t t i c k e t ; f i r st - ru n t h e a t e r ; e v e n i n g , n a t i o n a l a v e r a g e A i rl in e T i c k e t D o m e s ti c r o u n d t r ip , b a s e d o n a 2 , 0 0 0 - m i le t r i p , e x c l u d i n g a v i a t i o n t a x e s Vacation O n e w e e k f o r a n a d u l t a t C l u b M e d ’ s P u n t a C a n a r e s o rt , i n c l u d i n g a i r fa r e f r o m N e w Y o r k H o s p it a l S t a y A v e r a g e c o s t o f o n e d a y i n a s e m i p r i v a t e r o o m , i n c l u d i n g a n c i l l a r y s e r v i c e s e x c e p t p r iv a t e p h y s i c i a n ’ s f e e ( C l e v e l a n d ) Birth A verage hospital cost for m other and child, excluding private physician’s fee (Clevelan d) A Y e a r in C o l le g e In - st a t e , i n c l u d i n g r o o m a n d b o a r d a n d f e e s, u n d e r g r a d u a t e s t u d e n t a t P e n n S t a t e Funeral N a t i o n a l a v e r a g e , e x c l u d i n g c e m e t e r y c o s t s

Page | 23


ST.11.2 (a) & (b) The project cash flows and IRR with no inflation: 1 $80,000

2 $80,000

3 $80,000

4 $80,000

5 $80,000

6 $80,000

7 $80,000

8 $80,000

9 $80,000

10 $80,000

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$3,000 $15,000 $9,000 $4,500

$15,719 $3,333

$26,939 $4,445

$19,239 $1,481

$13,739 $741

$9,823 $0

$9,812 $3,333

$9,823 $4,445

$4,906 $1,481

$0 $741

$0 $0


$29,448 $10,307

$17,116 $5,991

$27,780 $9,723

$34,020 $11,907

$38,677 $13,537

$35,355 $12,374

$34,232 $11,981

$42,113 $47,759 $48,500 $14,740 $16,716 $16,975

Net Income Cash Flow Statement Cash from operation Net Income Depreciation Building Milling machine Jigs & dies Investment / Salvage Building Milling machine Jigs & dies (Replacement) Gains Taxes: Building Milling machine Jigs & dies

$19,141

$11,125

$18,057

$22,113

$25,140

$22,981

$22,251

$27,373

$31,043

$31,525

$19,141

$11,125

$18,057

$22,113

$25,140

$22,981

$22,251

$27,373

$31,043

$31,525

$15,719 $3,333

$26,939 $4,445

$19,239 $1,481

$13,739 $741

$9,823 $0

$9,812 $3,333

$9,823 $4,445

$4,906 $1,481

$0 $741

$0 $0

Income Statement Revenue Expenses: O&M Labor Material Energy Depreciation : Building Milling machine Jigs & dies

Net Cash Flow

0

($110,000) ($10,000)

$10,000 $300 ($10,000)

$300

($3,500) ($105)

($105) ($120,000)

$38,193

PW (11.32%)

$90,992

$42,509

$38,777

$36,593

IRR (%) =

28.40%

$25,158

$36,126

$36,519

$33,760

$31,784

$38,220

Page | 24


(c), (d) & (e): The economic gain in present worth due to inflation = $108,404 - $90,988 = $17,416. 0

1 $85,600

2 $91,592

3 $98,003

4 $104,864

5 $112,204

6 $120,058

7 $128,463

8 $137,455

9 $147,077

10 $157,372

3,090 15,750 9,360 4,635

3,183 16,538 9,734 4,774

3,278 17,364 10,124 4,917

3,377 18,233 10,529 5,065

3,478 19,144 10,950 5,217

3,582 20,101 11,388 5,373

3,690 21,107 11,843 5,534

3,800 22,162 12,317 5,700

3,914 23,270 12,810 5,871

4,032 24,433 13,322 6,048

15,719 3,333

26,939 4,445

19,239 1,481

13,739 741

9,823 0

9,812 3,333

9,823 4,445

4,906 1,481

0 741

0 0


$33,713 11,800

$25,979 9,093

$41,599 14,560

$53,181 18,613

$63,592 22,257

$66,468 23,264

$72,021 25,207

$87,088 30,481

$100,470 35,165

$109,537 38,338

Net Income Cash Flow Statement Cash from operation Net Income Depreciation Building Milling machine Jigs & dies Investment / Salvage Building Milling machine Jigs & dies (Replacement) Gains Taxes: Building Milling machine Jigs & dies

$21,913

$16,887

$27,040

$34,568

$41,335

$43,204

$46,814

$56,607

$65,306

$71,199

21,913

16,887

27,040

34,568

41,335

43,204

46,814

56,607

65,306

71,199

15,719 3,333

26,939 4,445

19,239 1,481

13,739 741

9,823 0

9,812 3,333

9,823 4,445

4,906 1,481

0 741

0 0

Revenue Expenses: O&M Labor Material Energy Depreciation : Building Milling machine Jigs & dies


(110,000) (10,000)

10,000 300 (10,000)

300

(3,500) (105)

(105) ($120,000) ($120,000) PW (18%) =

$40,965 $38,647 $108,407

$48,271 $42,960

$47,760 $40,100 IRR' (%) =

$49,048 $38,850

$41,353 $30,899

$56,349 $39,724

$61,082 $40,620

$62,994 $39,523

$66,047 $39,093

$77,894 $43,496

30.53%

Page | 25


ST.11.3 (a) & (b): Assumption: The building will be placed in service in January. Expenses: Fixed costs Variable costs Depreciation : Building Equipment Amortization Taxable Income Income Taxes Net Income Cash Flow Statement Operating Avtivities: Net Income Depreciation Amortization Investment activities Opportunity cost* Land Building Equipment Gains Taxes Land Building Equipment Working capital Net Cash Flow (actual) Net Cash Flow (constant)

$5,000,000 $114,000,000

$5,250,000 $119,700,000

$5,512,500 $125,685,600

$5,788,125 $131,968,800

$6,077,531 $138,567,600

$6,381,408 $145,496,400

$122,863 $1,214,650 $250,000 $69,412,487 $27,764,995

$128,205 $2,081,650 $250,000 $72,090,145 $28,836,058

$128,205 $1,486,650 $250,000 $76,413,045 $30,565,218

$128,205 $1,061,650 $250,000 $80,751,220 $32,300,488

$128,205 $759,050 $250,000 $85,163,614 $34,065,446

$122,863 $379,100 $250,000 $89,864,229 $35,945,692

$41,647,492

$43,254,087

$45,847,827

$48,450,732

$51,098,168

$53,918,537

$41,647,492 $1,337,513 $250,000

$43,254,087 $2,209,855 $250,000

$45,847,827 $1,614,855 $250,000

$48,450,732 $1,189,855 $250,000

$51,098,168 $887,255 $250,000

$53,918,537 $501,963 $250,000

($600,000) ($1,500,000) ($1,000,000)

($4,000,000) ($8,500,000)

$2,000,000 $3,000,000 $1,500,000

($1,000,000)

($200,000) $496,581 $6,900 $8,874,100

($1,425,000)

($1,496,400)

($1,570,800)

($1,649,700)

($1,732,200)

($2,100,000) ($1,000,000) ($13,500,000) $41,810,005 ($2,100,000) ($952,381) ($12,244,898) $36,117,055 IRR" = PW (20%) = 137.08%

$44,217,542 $36,377,881 $98,365,719

$46,141,882 $36,153,372

$48,240,887 $35,998,093

$50,503,223 $35,891,698

$70,348,082 $47,614,351

(c) The project is acceptable.

Page | 26

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