Calculate the Equivalent Uniform Annual Benefit (EUAB) for the cash flow below for interest rate of 10%

The Equivalent Uniform Annual Benefit (EUAB) is 2,220.52.

Explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.

The explanation to the answer is now given as follows:

Note: See the attached excel file for the calculation of the total present values of cash flow (in bold red color).

Equivalent Uniform Annual Benefit (EUAB) refers to an annual benefit or cash flow that is obtained by converting any cash flow to an equivalent uniform cash flow.

From the question, the diagram indicates that the amount of the annual cash flows from year 1 to year 80 is $2,000, except for years 10 and 40 which are 7,000 and 15,000 respectively (in bold blue color in the attached excel file).

Because of years 10 and 40 which are 7,000 and 15,000, we first calculate the present value of all the annual cash flows from year 1 to 80 (in bold red color in the attached excel file).

From the attached excel file, we have:

Total present value of cash flows = 22,205.19

The annuity factor is calculated using the annuity formula as follows:

Annuity factor = ((1-(1/(1 + r))^n)/r) …………… (1)

Where;

r = interest rate = 10%, or 0.10

n = number of years = 80

Substituting the values into equation (1), we have:

Annuity factor = ((1-(1/(1 + 0.10))^80) / 0.10)

Annuity factor = 9.9951181414995

Approximating to 2 decimal places, we have:

Annuity factor = 10.00

The Equivalent Uniform Annual Benefit (EUAB) can therefore now be calculate using the formula for calculating the Equivalent Uniform Annual Benefit (EUAB) as follows:

EUAB = Total present value of cash flows / Annuity factor ……………. (2)

Substituting the values into equation (2), we have:

EUAB = 22,205.19 / 10.00

EUAB = 2,220.52

Therefore, the Equivalent Uniform Annual Benefit (EUAB) is 2,220.52.

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