problem 1 - 4 please show work and no messy hand writing 1. Industrial Electric

Question

problem 1 - 4
please show work and no messy hand writing

1. Industrial Electric Services has a contract with an embassy in Mexico to provide maintenance for scanners and other devices in the building. What is the present worth of the contract (in year 0) if the company will receive a total of nine $13,000 payments beginning in year 2 and ending in year 10 and the interest rate is 14% per year. The present worth of the contract for the company is $ 2. Find the present worth in year 0 for the cash flows shown. Leti 17% per year. 0 12 3 45 678 Year 50 V 70 90 110 130 150 170 200 The present worth is determined to be $ 3. How much money would be accumulated 18 years from now from deposits of $11,000 per year for 5 consecutive years, starting 2 years from now, if the interest rate is 9% per year The amount that would be accumulated is determined to beS 4. A recently hired chief executive officer wants to reduce future production costs to improve the company's earnings, thereby increasing the value of the company's stock. The plan is to invest $86,000 now and $68,000 in each of the next 4 years to improve productivity. By how much must annual costs decrease in years 5 through 13 to recover the investment plus a retum of 9% per year? The annual cost decreases by $

Explanation / Answer

1.

Year

Cash Flow (C)

PV Factor Calculation

PV Factor @ 14 % (F)

PV(=C x F)

0

$0

1/(1+0.14)^0

1

$0.00

1

$0

1/(1+0.14)^1

0.877192982

$0.00

2

$13,000

1/(1+0.14)^2

0.769467528

$10,003.08

3

$13,000

1/(1+0.14)^3

0.674971516

$8,774.63

4

$13,000

1/(1+0.14)^4

0.592080277

$7,697.04

5

$13,000

1/(1+0.14)^5

0.519368664

$6,751.79

6

$13,000

1/(1+0.14)^6

0.455586548

$5,922.63

7

$13,000

1/(1+0.14)^7

0.399637323

$5,195.29

8

$13,000

1/(1+0.14)^8

0.350559055

$4,557.27

9

$13,000

1/(1+0.14)^9

0.307507943

$3,997.60

10

$13,000

1/(1+0.14)^10

0.26974381

$3,506.67

Total PV

$56,405.99

Present worth is $ 56,405.99

2.

Year

Cash Flow (C)

PV Factor Calculation

PV Factor @ 17 % (F)

PV(=C x F)

0

$0

1/(1+0.17)^0

1

$0.00

1

$200

1/(1+0.17)^1

0.854700855

$170.94

2

$50

1/(1+0.17)^2

0.730513551

$36.53

3

$70

1/(1+0.17)^3

0.624370556

$43.71

4

$90

1/(1+0.17)^4

0.533650048

$48.03

5

$110

1/(1+0.17)^5

0.456111152

$50.17

6

$130

1/(1+0.17)^6

0.389838592

$50.68

7

$150

1/(1+0.17)^7

0.333195378

$49.98

8

$170

1/(1+0.17)^8

0.284782374

$48.41

Total PV

$ 498.44

Present worth is - $ 498.44 (as these are cash outflows).

3.

Year

Cash Flow (C)

FV Factor Calculation

FV Factor @ 9 % (F)

FV(=C x F)

1

$0

(1+0.09)^17

4.32763341

$0.00

2

$11,000

(1+0.09)^16

3.970305881

$43,673.36

3

$11,000

(1+0.09)^15

3.64248246

$40,067.31

4

$11,000

(1+0.09)^14

3.341727027

$36,759.00

5

$11,000

(1+0.09)^13

3.065804612

$33,723.85

6

$11,000

(1+0.09)^12

2.812664782

$30,939.31

7

$0

(1+0.09)^11

2.580426405

$0.00

8

$0

(1+0.09)^10

2.367363675

$0.00

9

$0

(1+0.09)^9

2.171893279

$0.00

10

$0

(1+0.09)^8

1.992562642

$0.00

11

$0

(1+0.09)^7

1.828039121

$0.00

12

$0

(1+0.09)^6

1.677100111

$0.00

13

$0

(1+0.09)^5

1.538623955

$0.00

14

$0

(1+0.09)^4

1.41158161

$0.00

15

$0

(1+0.09)^3

1.295029

$0.00

16

$0

(1+0.09)^2

1.1881

$0.00

17

$0

(1+0.09)^1

1.09

$0.00

18

$0

(1+0.09)^0

1

$0.00

Total FV

$ 185,162.83

Accumulated amount is $ 185,162.83.

   4.

Computation of FV of expenses:

Year

Cash Flow (C)

FV Factor Calculation

FV Factor @ 9 % (F)

FV(=C x F)

0

$86,000

(1+0.09)^4

1.41158161

$121,396.02

1

$68,000

(1+0.09)^3

1.295029

$88,061.97

2

$68,000

(1+0.09)^2

1.1881

$80,790.80

3

$68,000

(1+0.09)^1

1.09

$74,120.00

4

$68,000

(1+0.09)^0

1

$68,000.00

Total FV

$ 432,368.79

Total FV of $ 432,368.79 is the PV (in year 4) of cash inflows in the year 5 through 13, which can be computed as:

PV = C x PVIFA (i, n)

I = Rate of interest = 9 %

n = No. of periods = 0

C = cash inflow per year

$ 432,368.79 = C x PVIFA (9%, 9)

$ 432,368.79 = C x 5.9952

C = $ 432,368.79/5.9952 = $ 72,119.16

The annual cost decreases by $ 72,119

Year

Cash Flow (C)

PV Factor Calculation

PV Factor @ 14 % (F)

PV(=C x F)

0

$0

1/(1+0.14)^0

1

$0.00

1

$0

1/(1+0.14)^1

0.877192982

$0.00

2

$13,000

1/(1+0.14)^2

0.769467528

$10,003.08

3

$13,000

1/(1+0.14)^3

0.674971516

$8,774.63

4

$13,000

1/(1+0.14)^4

0.592080277

$7,697.04

5

$13,000

1/(1+0.14)^5

0.519368664

$6,751.79

6

$13,000

1/(1+0.14)^6

0.455586548

$5,922.63

7

$13,000

1/(1+0.14)^7

0.399637323

$5,195.29

8

$13,000

1/(1+0.14)^8

0.350559055

$4,557.27

9

$13,000

1/(1+0.14)^9

0.307507943

$3,997.60

10

$13,000

1/(1+0.14)^10

0.26974381

$3,506.67

Total PV

$56,405.99

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