Question

XKL Co. plans a new project that will generate $129,709 of continuous cash flow each year for 9 years and additionally $82,286 at the end of the project. If the continuously compounded rate of interest is 3.45%, estimate the present value of the cash flows. (Please use formulas and step-by-step, NOT EXCEL)

Answer 1

For calculating the present value of cash flows, we need to calculate the present value of annuity of $129709 and present value of cash flow of $82286,at the end of of the project.We will use the following formula for continous compounding for annuity:

First we calculate the present value of annuity of $129709 at continous compounding at 3.45%

PV = (Cash flows / e^r-1) * (1 - e^-rn)

where, PV = Present value of annuity, e = Value of e is 2.7183, r = rate of interest, t = time period

Cash flows = $129709, t = 9 years , r = 3.45 %.

Now, putting these values in the above formula:

PV = ($129709 / e^{3.45% -1}) * (1 - e^{-3.45% * 9})

PV = ($129709 / 2.7183^{0.0345 -1}) * ( 1 - 2.7183^{-0.0345 * 9})

PV = ($129709 / 0.38079029801 ) * ( 1 - 0.73307880278)

PV = $49391.92876457909 * 0.26692119722

PV = $13183.75275884641

Now, we will calculate the present value of cash flow after 9 years at continous compounding of 3.45% is given by the following formula:

PV = Cash flow / e^rt

Now, putting the values in the above formula, we get,

PV = $82286 / e^{3.45% * 9}

PV = $82286 / 2.7183^0.3105

PV = $82286 / 1.36410982858

PV = 460322.12236580497

Now, Present value of the cash flows = Present value of annuity of $129709 + Present value of $82286

Present value of the cash flows = $13183.75275884641 + 460322.12236580497

Present value of the cash flows = = $473505.875