Answer:
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
