From by Engineering Economics class: A person signs an agreement to offer person

Question

From by Engineering Economics class:

A person signs an agreement to offer personal services over a period of five years. The company that hires him, offered to pay him an advance of $30,000 for his professional services at the moment of signing the contract and five additional payments to be made at the end of each of the five years of the contract, for a total of six payments. The first of these five payments will be for $45,000 and each subsequent payment will be $20,000 higher than the previous payment (year). The person to be hired prefers that the six payments are made on those dates (one payment at the moment of signing the contract, and the other payments made at the end of each year, for the five years of contract) but that all payments be made for the same amount of money.

a) Determine the amount that each of those uniform payments (annuities) must be, considering an annual interest rate of 10%.

b) Determine the cumulative value of the six annual payments at the end of the third year as of the date of signing the contract.

Explanation / Answer

Answer Part a.

Let the uniform payment be of amount X. To find the value of X we need to equate the present value of the amount from 2 payment schemes.

Present Value from payment scheme where payment increases by 20000 is given by:

(45000)+(65000/1.1)+(85000/(1.1)^2)+(105000/(1.1)^3)+(125000/(1.1)^4)+(145000/(1.1)^5)

=428637.1708

Present Value from payment scheme where we have uniform payment of X:

= X+(X/1.1)+(X/(1.1)^2)+(X/(1.1)^3)+(X/(1.1)^4)+(X/(1.1)^5)

=4.790786X

Equating the two present values, we get:

4.790786X= 428637.1708

X= 89471.15

Part B.

We need to find the cumulative value of the payment scheme at the end of the 3rd year. At the end of 3rd year, 4 payments have been paid out already and 2 are due in the 4th and 5th year. Thus the cumulative value of 6 payments is:

45000(1.1)^3+65000(1.1)^2+85000(1.1)+105000+(125000/1.1)+(145000/(1.1)^2)

= 570516.0744

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