Find the present value of an income stream which has a negative flow of $100 per year for 3 years, a positive flow o $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 of the income stream, we need to discount each cash flow back to time 0 using the appropriate discount rate for each year. 
The present value of the negative flow of $100 at 4% for three years is: 
PV = -100/(1 + 0.04) + -100/(1 + 0.04)² + -100/(1 + 0.04)³ = -$285.07 
The present value of the positive flow of $200 at 5% in year 4 is: 
PV = 200/(1 + 0.05)³ = $161.16 
The present value of each of the positive flows of $300 at 5% in years 5 through 8 is: 
PV = 300/(1 + 0.05)⁴ + 300/(1 + 0.05)⁵ + 300/(1 + 0.05)⁶ + 300/(1 + 0.05)⁷ = $1,076.40

Therefore, the total present value is: 
PV = -$285.07 + $161.16 + $1,076.40 = $952.49

Therefore, the best choice is C) $792.49, as it is the closest value to $952.49.

Find the Present Value of an Income Stream Which Has