2 . Uneven cash flows A series of cash flows may not always necessarily be an annuity. Cash flows can also be uneven and variable in amount, but the concept of the time value of money will continue to apply. Consider the following case: The Purple Lion Beverage Company expects the following cash flows from its manufacturing plant in Palau over the next five years: Annual Cash Flows Year 1 Year 2 Year 3 Year 4 Year 5 $250,000 $20,000 $180,000 $450,000 $550,000 The CFO of the company believes that an appropriate annual interest rate on this investment is 4%. What is the present value of this uneven cash flow stream, rounded to the nearest whole dollar

$1,255,617

Explanation:

Although the cash flows are occurring at equal intervals, we cannot use the annuity formula because each cash flow is a different amount. Annuity formula can only be used when the same amount of cash flows are occurring at equal intervals!

We need to compute the present value of the cash flows separately for each amount

The first cash flow is occurring at the end of the first year

We use the formula PV = FV/(1+i)^n  

Where PV = Present Value, FV = Future value, i = Interest rate, which is the rate at which the cash flows are to be discounted,  and n = the year in which the cash flow occurs

Plugging the values in the formula, we get the present value for the first year

PV = 250,000/(1+0.04)^1 = 250,000/1.04 = 240,384.62 = $240,385

The present values for the successive years are provided as under

PV = 20,000/(1+0.04)^2 = 20,000/1.0816 = 18,491.12= $18,491

PV = 180,000/(1+0.04)^3 =180,000/1.124864 = 160,019.34= $160,019

PV = 450,000/(1+0.04)^4 =450,000/1.169859 = 384,661.89= $384,662

PV = 550,000/(1+0.04)^5 =550,000/1.041.121665 = 452,059.91= $452,060

Adding up the present values for each of the years, we obtain the present value of the cash flow stream

240,385+18,491+160,019+384,662+452,060 = $1,255,617 approximately (since all the figures are rounded to the nearest whole dollar)

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