Multiple Choice QuestionWhich of the following is the approximate internal rate of return for an investment that costs $12,680 and has net cash flows of $4,000 for 4 years?Present Value of 1RatePeriods8%10%12%40.73500.68300.6355Present Value of an Annuity of 1RatePeriod8%10%12%43.31213.16993.0373Multiple choice question.10%12%8%6%
Question
Multiple Choice QuestionWhich of the following is the approximate internal rate of return for an investment that costs 4,000 for 4 years?Present Value of 1RatePeriods8%10%12%40.73500.68300.6355Present Value of an Annuity of 1RatePeriod8%10%12%43.31213.16993.0373Multiple choice question.10%12%8%6%
Solution
To solve this problem, we need to calculate the present value of the cash flows and compare it to the initial investment.
The present value of the cash flows can be calculated using the formula for the present value of an annuity:
PV = C * (1 - (1 + r)^-n) / r
where:
- PV is the present value,
- C is the net cash flow per period,
- r is the rate of return, and
- n is the number of periods.
Given that the net cash flow is $4,000 for 4 years, we can use the present value of an annuity of 1 table to find the present value factor for each rate.
For 8%, the factor is 3.3121. For 10%, the factor is 3.1699. For 12%, the factor is 3.0373.
Multiplying these factors by the net cash flow gives us the present value of the cash flows for each rate:
For 8%, PV = 13,248.4. For 10%, PV = 12,679.6. For 12%, PV = 12,149.2.
Comparing these values to the initial investment of $12,680, we can see that the present value of the cash flows is closest to the initial investment at a rate of 10%.
Therefore, the approximate internal rate of return for the investment is 10%.
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