You are offered a 5 year contract for a position at a large factory. They offere

Question

You are offered a 5 year contract for a position at a large factory. They offered three different payment terms and asked you to decide your preferred option.

Option 1 (Fixed Salary): $75,000 per year with no annual raises

Option 2 (Increasing Salary): $65,000 for the first year with annual raises of 5% starting in year 2

Option 3 (Irregular Salary): Because of the irregular nature of the assignment, the company has offered to pay you a salary to reflect the intensity of the position. They will give you $2000 signing bonus today, $60,000 in the first year, $80,000 in the second year, $50,000 in the third year, and $70,000 in the last two years of the contract Assume, initially, that your salary is to be paid only at the end of each year and that the prevailing interest rate is 9% compounded annually.

(a) Draw a cash flow diagram that corresponds to each of the three salary options.

(b) Which of the three options should you choose?

(c) If each of these payment options are to be paid two times per month (bi-monthly) in equal installments, instead of the proposed one time per year, what would be the equivalent equal bi-monthly payments that you would receive under each salary option?

(d) You have estimated your living expenses (rent, food, gas, etc.) to be $3400 per bi-monthly pay period. What minimum annual salary would you need to receive (assume that you are paid in equal bi-monthly payments) to cover these expenses, assuming the interest rate stays the same?

Explanation / Answer

Option 1

Year

Salary

Amount at the end

Year 1

75000

105868.62

Year 2

75000

97127.18

Year 3

75000

89107.50

Year 4

75000

81750.00

Year 5

75000

75000.00

448853.30

Option 2

Year

Salary

Amount at the end

Year 1

65000.0

91752.80

Year 2

68250.0

88385.73

Year 3

71662.5

85142.22

Year 4

75245.6

82017.73

Year 5

79007.9

79007.91

426306.39

Option 3

Year

Salary

Amount at the end

Year 0

2000

3077.24791

Year 1

60000

84694.90

Year 2

80000

103602.32

Year 3

50000

59405.00

Year 4

70000

76300.00

Year 5

70000

70000.00

394002.22

Thus, the highest cash is accumulated in option 2 and thus we should choose the same.

Now, if each of these options were paid bimonthly:

Option 1:

(x*1.045)+x=75000

Thus x= 36675

Option 2:

(y1*1.045)+y1= 65000

Y1= 31785

Similarly, y2= 33375

Y3= 35043

Y4= 36795

Y5= 38635

Option 3:

Z1= 29340

Z2= 39120

Z3= 24450

Z4= 34230

Z5=34230

Now, for paying basic expenses of $3400 bi monthly,

The first bi monthly salary received is $3400 and thus the multiplier would be:

=1+(1.015)+(1.015^2)+(1.015^3)+(1.015^4)+(1.015^5)

=6.229

Thus, minimum salary would be= 3400*6.229= $21178.6

Option 1

Year

Salary

Amount at the end

Year 1

75000

105868.62

Year 2

75000

97127.18

Year 3

75000

89107.50

Year 4

75000

81750.00

Year 5

75000

75000.00

448853.30

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