Consider the following uneven cash flow stream:
year cash flow 0 $2,000 1 2,500 2 0 3 1,500 4 3,000 5 4,500
a. what is the present (year 0) value of the cash flow steam if the opportunity cost rate is 10%?

The present (Year 0) value of the cash flow steam if the opportunity cost rate is 10% is $10742.50

Explanation:

For computing the present value, first we have to calculate the discounted factor. After that multiply the discounted factor with cash flows so that present value could be calculated.

So, the formula for computing discounted factor is

= 1/ (1+rate)^year

where,

rate is 10%

year = 0,1,2,3,4,5

So Discounted factor for:

Year 0 is 1

Year 1 is 0.909

Year 2 is 0.826

Year 3 is 0.751

Year 4 is 0.683

Year 5 is 0.621

Now, after getting discounted factor, the present value is

= Discounted factor of each year + Cash flow of each year

So,

For year 0 = 1 × $2,000 = $2,000

For year 1 =  0.909 × $2,500 = $2272.50

For year 2 =  0.826 × $0 = $0

For year 3 =  0.751 × $1,500 = $1,126.50

For year 4 =  0.683 × $3,000 = $2,049

For year 5 =  0.621 × $4,500 = $2794.50

Hence, the present value is = Present value of year 0 + Present value of year 1 + Present value of year 2 + Present value of year 3 + Present value of year 4 + Present value of year 5

= $2,000 + $2,772.50 + $0 + $1,126.50 + $2,049 + $2794.50

= $10742.50

Thus, the present (Year 0) value of the cash flow steam if the opportunity cost rate is 10% is $10742.50

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