Concept explainers
Present Value and Multiple Cash Flows. Investment X offers to pay you $3,400 per year for nine years, whereas Investment Y offers to pay you $5,200 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 6 percent? If the discount rate is 22 percent?
To calculate: The investment of cash flow that gives the higher present value @6% and 22% rate of discount.
Introduction:
The present value of future cash flows that is discounted at a particular rate of discount is called the present value.
Answer to Problem 2QP
The cash flow X at 6% and 22% is $23,125.75 and $12,873.37 respectively and the cash flow Y at 6% and 22% is $21,904.29 and $14,890.93 respectively. Note that the present value cash flow is greater than at 6% in both the investment. At 6% rate of interest, Investment X is more valuable since it has the highest present value and at 22% interest, Investment Y has the highest present value.
Explanation of Solution
Given information:
Investment X provides Person X $3,400 in a year for nine years, whereas Investment Y provides $5,200 in a year for five years. The rate of discount is given.
Time line for Investment X:
Time line for Investment Y:
Formula to calculate the present value annuity:
Note: C denotes the annuity payment or annual cash flow, r denotes the rate of exchange, and t denotes the period.
Compute the present value annuity for Investment X at 6%:
Hence, the present value annuity for Investment X at 6% is $23,125.75.
Compute the present value annuity for Investment Y at 6%:
Hence, the present value annuity for Investment Y at 6% is $21,904.29.
Compute the present value annuity for Investment X at 22%:
Hence, the present value annuity for Investment X at 22% is $12,873.37.
Compute the present value annuity for Investment Y at 22%:
Hence, the present value annuity for Investment Y at 22% is $14,890.93.
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