Find the present value of an income stream which has a negative flow of $100 per year for 3 years,a positive flow of $200 in the 4th year,and a positive flow of $300 per year in Years 5 through 8.The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years.Thus,a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years.All payments occur at year-end.
A) $528.21
B) $1,329.00
C) $792.49
D) $1,046.41
E) $875.18

Question

Quizplus · Accepted Answer

To calculate the present value, we need to discount each payment to its present value and then sum up all the present values. 
Year 1: -$100, discounted at 4% = -$96.15 
Year 2: -$100, discounted at 4% = -$92.59 
Year 3: -$100, discounted at 4% = -$89.26 
Year 4: $200, discounted at 4% = $170.17 
Year 5: $300, discounted at 5% = $260.67 
Year 6: $300, discounted at 5% = $248.21 
Year 7: $300, discounted at 5% = $236.39 
Year 8: $300, discounted at 5% for 4 years and then at 4% for 3 years = $235.26

Summing up all these present values, we get:
PV = -$96.15 - $92.59 - $89.26 + $170.17 + $260.67 + $248.21 + $236.39 + $235.26
    = $792.49

Therefore, the best choice is C, $792.49.

Find the Present Value of an Income Stream Which Has