Industrial Engineering Chapter 10 Excel Problem Inflation Rate Eoy Thencurrent Constant Worth Problem Growth Rate Inflation Rate

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PROBLEM 10.30

INFLATION RATE 5.00%

EOY THEN-CURRENT CONSTANT WORTH

1$10,000.00 $10,000.00

2$12,000.00 $11,428.57

3$15,000.00 $13,605.44

4$17,500.00 $15,117.16

PROBLEM 10.31

GROWTH RATE 12.00%

INFLATION RATE 5.00%

EOY THEN-CURRENT CONSTANT

0$420,000.00 $420,000.00

1$470,400.00 $448,000.00

2$526,848.00 $477,866.67

3$590,069.76 $509,724.44

4$660,878.13 $543,706.07

5$740,183.51 $579,953.15

6$829,005.53 $618,616.69

PROBLEM 10.32

REAL REQUIRED RETURN 8.00%

INFLATION RATE 3.00%

COMBINED RATE 11.24%

PROBLEM 10.33

REAL INTEREST RATE 9.5238% SOLVER CHANGED CELL

INFLATION RATE 5.0000%

COMBINED RATE 15.0000% SOLVER TARGET CELL

9.5238% SOLVING MATHEMATICALLY

PROBLEM 10.34

REAL MARR 7.00%

INFLATION RATE 4.00%

EOY THEN-CURRENT CONSTANT

1$9,000.00 $8,653.85

2$11,000.00 $10,170.12

3$14,000.00 $12,445.95

4$18,000.00 $15,386.48

5$23,000.00 $18,904.32

PW = $52,347.07 $52,347.07

PROBLEM 10.35

YEAR INFLATION RATE REAL DISCOUNT RATE THEN-CURRENT LABOR COST CONSTANT DOLLAR LABOR COST PW

13% 6% $1,000 $970.87 $915.92

23% 5% $1,500 $1,413.89 $1,270.34

34% 4% $2,000 $1,812.68 $1,566.01

45% 5% $1,000 $863.18 $710.21

PW = $4,462.48

PROBLEM 10.36

FIRST COST $270,000.00

FIRST YEAR COST OF O&M $40,000.00

YEARLY INCREASE IN O&M 11.00%

ACTUAL INCOME PER YEAR $120,000.00

HORIZON 10

INFLATION RATE 4.50%

REAL RETURN DESIRED 3.60%

COMBINED RETURN DESIRED 8.26%

a EOY THEN-CURRENT THEN-CURRENT THEN-CURRENT

INCOME $ COST $ $

0$270,000.00 -$270,000.00

1$120,000.00 $40,000.00 $80,000.00

2$120,000.00 $44,400.00 $75,600.00

3$120,000.00 $49,284.00 $70,716.00

4$120,000.00 $54,705.24 $65,294.76

5$120,000.00 $60,722.82 $59,277.18

7$120,000.00 $74,816.58 $45,183.42

8$120,000.00 $83,046.41 $36,953.59

9$120,000.00 $92,181.51 $27,818.49

3$105,155.59 $43,187.40 $61,968.19

4$100,627.36 $45,873.70 $54,753.66

5$96,294.13 $48,727.09 $47,567.04

6$92,147.49 $51,757.96 $40,389.53

7$88,179.41 $54,977.35 $33,202.06

8$84,382.22 $58,397.00 $25,985.22

PROBLEM 10.37

RATE OF DECREASE IN REAL UNIT PRICE = 10%

GROWTH RATE IN # UNITS PURCHASED/YEAR = 30%

INFLATION RATE = 3.7%

REAL INTEREST RATE = 8%

UNIT PRICE IN YEAR 0 = $2,000

# UNITS PURCHASED IN YEAR 0 = 100

YEAR

0$200,000.00

1$260,000.00

2$338,000.00

3$439,400.00

4$571,220.00

5$742,586.00

YEAR

0$200,000.00

1$269,620.00

2$363,474.72

3$490,000.27

4$660,569.37

5$890,513.56

c) PW = $1,804,586.46 EXCLUDING YEAR 0

d) PW = $1,804,586.46 EXCLUDING YEAR 0

THEN-CURRENT

EXPENDITURE

CONSTANT DOLLAR

EXPENDITURE

PROBLEM 10.38

INITIAL INVESTMENT = $90,000

REDUCED MATERIAL REQUIREMENT = 10,000 POUNDS

PRESENT UNIT COST OF MATERIAL = $2 PER POUND

INFLATION RATE = 4.20% PER YEAR

COMBINED INTEREST RATE = 7.97% SOLVER CHANGE CELL

EOY CASH FLOW

0 -$90,000.00

1$20,840.00

2$21,715.28

3$22,627.32

4$23,577.67

5$24,567.93

PW = $0.00 SOLVER TARGET CELL

REAL INTEREST RATE = 3.618%

PROBLEM 10.39

AVERAGE RENTAL PRICE $45 /DAY

# CARS OWNED IN 2010 = 150

# DAYS RENTED PER CAR IN 2010 = 200

GROWTH RATE IN # CARS OWNED = 10%

ANNUAL INFLATION RATE = 5%

REAL MARR = 10%

Number of cars in 2015 = 150*1.105 = 241.5765

$C revenue in 2015 = 241.5765*$45*200 = $2,174,188.50

PW = $2,174,188.50 (P|F 10%,5) = $2,174,188.50(0.62092) = $1,349,997.12

YEAR # OWNED PW

2010 150 30,000.00 $45.00 $1,350,000.00 $1,350,000.00

2011 165 33,000.00 $45.00 $1,485,000.00 $1,350,000.00

2012 181.5 36,300.00 $45.00 $1,633,500.00 $1,350,000.00

2013 199.65 39,930.00 $45.00 $1,796,850.00 $1,350,000.00

2014 219.615 43,923.00 $45.00 $1,976,535.00 $1,350,000.00

2015 241.5765 48,315.30 $45.00 $2,174,188.50 $1,350,000.00

$C REVENUE

# DAYS

RENTED

$C REVENUE

PER CAR

NOTE: THE REAL MARR EQUALS THE GROWTH RATE IN # CARS OWNED. SINCE THE REVENUE

PER CAR PER DAY IS CONSTANT OVER THE 5-YEAR PERIOD, THE PRESENT WORTH OF

CONSTANT DOLLAR REVENUE IS THE SAME FOR EVERY YEAR.

PROBLEM 10.40

INITIAL UNIT PRICE FOR PHONE = $250

INITIAL UNIT COST FOR PHONE = $50

# PHONES SOLD IN 2005 = 5,000,000

ANNUAL GROWTH RATE FOR PHONES SOLD THRU 2009 = 10%

REDUCTION IN DEMAND IN 2010 = 50%

RATE OF DECREASE IN THEN-CURRENT UNIT PRICE FOR PHONE = 20%

RATE OF DECREASE IN CONSTANT DOLLAR UNIT COST FOR PHONE = 25%

ANNUAL INFLATION RATE = 2%

REAL MARR = 10%

# Phones

Sales

Price ($T)

Unit Cost

($C)

Unit Cost

($T)

Profit ($T) PW

2005

5,000,000 $250.00 $50.00 $50.00 $1,000,000,000 $1,000,000,000

2006

5,500,000 $200.00 $37.50 $38.25 $889,625,000 $792,892,156.86

2007

6,050,000 $160.00 $28.13 $29.26 $790,969,438 $628,310,024.99

2008

6,655,000 $128.00 $21.09 $22.38 $702,868,782 $497,617,544.11

2009

7,320,500 $102.40 $15.82 $17.12 $624,259,920 $393,907,295.63

2010

3,660,250 $81.92 $11.87 $13.10 $251,897,755 $141,664,167.20

PW =

$3,454,391,189

PROBLEM 10.41

TRUE

INFLATION RATE = (10% – 6%)/(1 + 6%) =

3.7736%

PROBLEM 10.42

FALSE

THE COMBINED EXTERNAL RATE OF RETURN EQUALS 9% + 3% + 9%(3%), OR 12.27%,

WHICH IS GREATER THAN THE COMBINED MARR OF 12%.

PROBLEM 10.43

TRUE

THE COMBINED MARR IS 10% + 4% + 10%(4%), OR 14.4%, WHICH IS GREATER THAN THE COMBINED

EXTERNAL RATE OR RETURN OF 13.5%.

PROBLEM 10.44

INFLATION RATE 4.00%

COMBINED MARR 10.00%

REAL MARR 5.77%

FIRST COST $10,000.00

EOY THEN-CURRENT REAL MACRS(3)

$ $

1$3,333.00 $3,204.81 33.33%

2$4,445.00 $4,109.65 44.45%

3$1,481.00 $1,316.60 14.81%

4$741.00 $633.41 7.41%

SUM

100.00%

d3 IN REAL $= $1,316.60

PROBLEM 10.45

BASIS $9,000,000.00 REAL BTCF $6,000,000.00 INFL RATE= 4.00%

EST SALV $700,000.00 BTCF INCR –$1,000,000.00 TAX RATE 40.00%

RCVD SALV $700,000.00 USEFUL LIFE 6

MARRr=18.00%

PERIODS 6

MARRc=22.72%

EOY ACTUAL BTCF DWO TI T ACTUAL ATCF MACRS(5)

0 -$9,000,000.00 -$9,000,000.00

1 $6,240,000.00 $1,800,000.00 $4,440,000.00 $1,776,000.00 $4,464,000.00 20.00%

2 $5,408,000.00 $2,880,000.00 $2,528,000.00 $1,011,200.00 $4,396,800.00 32.00%

3 $4,499,456.00 $1,728,000.00 $2,771,456.00 $1,108,582.40 $3,390,873.60 19.20%

4 $3,509,575.68 $1,036,800.00 $2,472,775.68 $989,110.27 $2,520,465.41 11.52%

5 $2,433,305.80 $1,036,800.00 $1,396,505.80 $558,602.32 $1,874,703.48 11.52%

6 $2,151,042.33 $518,400.00 $1,632,642.33 $653,056.93 $1,497,985.40 5.76%

SUM DEPR

MARRc=22.72%

$9,000,000.00

PW$T = $1,615,078.51

BOOK VALUE

FW$T = $5,516,780.68

$0.00

AW$T = $518,840.14

IRRc=31.74%

ERRc=26.14% ERRc=26.14%

IRRr=26.68%

ERRr=21.29%

a AS SHOWN

b PW$T = $1,615,078.51

c AW$T = $518,840.14

d FW$T = $5,516,780.68

IRRc=31.74%

ERRc=26.14%

IRRr=26.68%

ERRr=21.29%

PROBLEM 10.46

BASIS $9,000,000.00 REAL BTCF $6,000,000.00 INFL RATE= 4.00%

EST SALV $700,000.00 BTCF INCR -$1,000,000.00 TAX RATE 40.00%

RCVD SALV $700,000.00 USEFUL LIFE 6

MARRr=18.00%

PERIODS 6

MARRc=22.72%

EOY REAL BTCF REAL DWO TI T REAL ATCF MACRS(5)

0 -$9,000,000.00 -$9,000,000.00

1 $6,000,000.00 $1,730,769.23 $4,269,230.77 $1,707,692.31 $4,292,307.69 20.00%

2 $5,000,000.00 $2,662,721.89 $2,337,278.11 $934,911.24 $4,065,088.76 32.00%

3 $4,000,000.00 $1,536,185.71 $2,463,814.29 $985,525.72 $3,014,474.28 19.20%

4 $3,000,000.00 $886,260.99 $2,113,739.01 $845,495.61 $2,154,504.39 11.52%

5 $2,000,000.00 $852,174.02 $1,147,825.98 $459,130.39 $1,540,869.61 11.52%

6 $1,700,000.00 $409,699.05 $1,290,300.95 $516,120.38 $1,183,879.62 5.76%

SUM DEPR

MARRr=18.00% SUM MACRS

$8,077,810.89

PW$C = $1,615,078.51 100.00%

BOOK VALUE

FW$C = $4,359,991.90

$0.00

AW$C = $461,767.31

IRRr = 26.68%

ERRr = 21.29% ERRr = 21.29%

IRRc = 31.74%

ERRc = 26.14%

a AS SHOWN

PW$C = $1,615,078.51

AW$C = $461,767.31

FW$C = $4,359,991.90

PROBLEM 10.47

BASIS $190,000.00 REAL BTCF $45,000.00 INFL RATE= 3.90%

EST SALV $5,000.00 BTCF INCR $0.00 TAX RATE 40.00%

RCVD SALV $5,000.00 USEFUL LIFE 12

MARRr=10.00%

PERIODS 12

MARRc=14.29%

EOY ACTUAL BTCF DWO TI T ACTUAL ATCF MACRS(7)

0-$190,000.00 -$190,000.00

1$46,755.00 $27,151.00 $19,604.00 $7,841.60 $38,913.40 14.29%

2$48,578.45 $46,531.00 $2,047.44 $818.98 $47,759.47 24.49%

3$50,473.00 $33,231.00 $17,242.00 $6,896.80 $43,576.20 17.49%

4$52,441.45 $23,731.00 $28,710.45 $11,484.18 $40,957.27 12.49%

5$54,486.67 $16,967.00 $37,519.67 $15,007.87 $39,478.80 8.93%

6$56,611.65 $16,948.00 $39,663.65 $15,865.46 $40,746.19 8.92%

7$58,819.50 $16,967.00 $41,852.50 $16,741.00 $42,078.50 8.93%

8$61,113.46 $8,474.00 $52,639.46 $21,055.79 $40,057.68 4.46%

9$63,496.89 $0.00 $63,496.89 $25,398.76 $38,098.13

10 $65,973.27 $0.00 $65,973.27 $26,389.31 $39,583.96

11 $68,546.22 $0.00 $68,546.22 $27,418.49 $41,127.73

PW$T = $43,495.36

BOOK VALUE

FW$T = $216,043.77

$0.00

AW$T = $7,782.26

IRRc=19.40%

ERRc=16.27% ERRc=16.27%

a AS SHOWN

PW$T = $43,495.36

AW$T = $7,782.26

IRRc=19.40%

IRRr=14.92%

PROBLEM 10.48

BASIS $190,000.00 REAL BTCF $45,000.00 INFL RATE= 3.90%

EST SALV $5,000.00 BTCF INCR $0.00 TAX RATE 40.00%

RCVD SALV $5,000.00 USEFUL LIFE 12

MARRr=10.00%

PERIODS 12

MARRc=14.29%

EOY REAL BTCF REAL DWO TI T REAL ATCF MACRS(7)

0 -$190,000.00 -$190,000.00

1 $45,000.00 $26,131.86 $18,868.14 $7,547.26 $37,452.74 14.29%

2 $45,000.00 $43,103.38 $1,896.62 $758.65 $44,241.35 24.49%

3 $45,000.00 $29,627.62 $15,372.38 $6,148.95 $38,851.05 17.49%

4 $45,000.00 $20,363.57 $24,636.43 $9,854.57 $35,145.43 12.49%

5 $45,000.00 $14,012.88 $30,987.12 $12,394.85 $32,605.15 8.93%

6 $45,000.00 $13,471.79 $31,528.21 $12,611.29 $32,388.71 8.92%

7 $45,000.00 $12,980.64 $32,019.36 $12,807.74 $32,192.26 8.93%

8 $45,000.00 $6,239.71 $38,760.29 $15,504.12 $29,495.88 4.46%

9 $45,000.00 $0.00 $45,000.00 $18,000.00 $27,000.00

10 $45,000.00 $0.00 $45,000.00 $18,000.00 $27,000.00

11 $45,000.00 $0.00 $45,000.00 $18,000.00 $27,000.00

12 $50,000.00 $0.00 $50,000.00 $20,000.00 $30,000.00

SUM DEPR

MARRr=10.00% SUM MACRS

$165,931.43

PW$C = $43,495.36 100.00%

BOOK VALUE

FW$C = $136,507.08

AW$C = $6,383.52

IRRr = 14.92%

ERRr = 11.91% ERRr = 11.91%

PROBLEM 10.49

BASIS $1,400,000.00 REAL BTCF $400,000.00 INFL RATE= 4.20%

EST SALV $200,000.00 BTCF INCR $0.00 TAX RATE 40.00%

RCVD SALV $200,000.00 USEFUL LIFE 8

MARRr=10.00%

PERIODS 8

MARRc=14.62%

EOY ACTUAL BTCF DWO TI T ACTUAL ATCF MACRS(5)

0 -$1,400,000.00 -$1,400,000.00

1 $416,800.00 $280,000.00 $136,800.00 $54,720.00 $362,080.00 20.00%

2 $434,305.60 $448,000.00 -$13,694.40 -$5,477.76 $439,783.36 32.00%

3 $452,546.44 $268,800.00 $183,746.44 $73,498.57 $379,047.86 19.20%

4 $471,553.39 $161,280.00 $310,273.39 $124,109.35 $347,444.03 11.52%

5 $491,358.63 $161,280.00 $330,078.63 $132,031.45 $359,327.18 11.52%

6 $511,995.69 $80,640.00 $431,355.69 $172,542.28 $339,453.41 5.76%

7 $533,499.51 $0.00 $533,499.51 $213,399.80 $320,099.71

8 $833,859.73 $0.00 $833,859.73 $333,543.89 $500,315.84

SUM DEPR

MARRc=14.62%

$1,400,000.00

PW$T = $326,090.32

BOOK VALUE

FW$T = $971,451.55

$0.00

AW$T = $71,763.49

IRRc=21.38%

ERRc=17.66% ERRc=17.66%

IRRr=16.49%

a AS SHOWN

PW$T = $326,090.32

AW$T = $71,763.49

IRRc=21.38%

IRRr=16.49%