A new chemical production facility that is under construction is expected to be

Question

A new chemical production facility that is under construction is expected to be in full commercial operation one year from now. Once in full operation, the facility will generate $95,000 cash profit daily over the plant's service life of 10 years. Determine the equivalent present worth of the future cash flows generated by the facility at the beginning of commercial operation, assuming:

(a) 10% interest compounded daily, with the daily flows.

(b) 10% interest compounded continuously, with the daily flow series approximated by a uniform continuous cash flow function.

Also, compare the difference between part (a) discrete (daily) and part (b) continuous compounding.

Explanation / Answer

given i = 10%, N = 10 years, A = 95000 * 360 = 34200000

a) P = A(P/A, 10%/365, 4380,)

= 95000 * ( P/A, 10%, 4380)

b) P = 34200000 * (e^ (0.10 *10) -1)/(0.10 * e^ (0.10 *10))

= 216185231

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