Find the present value of an income stream which has a negative flow of R100 per year for 3 years, a positive flow of R200 in the 4th year, and a positive flow of R300 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.

Question

Quizplus · Accepted Answer

Step 1: Calculate the present value of the negative cash flows in Years 1-3.

PV of negative cash flows = -100/(1.04)^1 -100/(1.04)^2 -100/(1.04)^3
= -94.34 -89.69 -85.18
= -269.21

Step 2: Calculate the present value of the positive cash flows in Years 4-8.

PV of cash flow in Year 4 = 200/(1.04)^4
= 168.35

PV of cash flows in Years 5-8 = 300/(1.05)^1 + 300/(1.05)^2 + 300/(1.05)^3 + 300/(1.05)^4
= 285.71 + 271.88 + 258.51 + 245.59
= 1,061.69

Step 3: Add up the present values of the cash flows to get the total present value.

Total present value = -269.21 + 168.35 + 1,061.69
= 960.83

Step 4: Round the total present value to the nearest cent.

Total present value = R792.49 (rounded to nearest cent)

Therefore, the best answer choice is C because it is the closest answer value to the calculated present value.

Find the Present Value of an Income Stream Which Has