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A stock pays annually an amount of ` 10 from 6th year onwards. What is the
present value of perpetuity, if the rate of return is 20%
(a) 20.1
(b) 19.1
(c) 21.1
(d) 22.1?
present value of perpetuity, if the rate of return is 20%
(a) 20.1
(b) 19.1
(c) 21.1
(d) 22.1?
Most Upvoted Answer
A stock pays annually an amount of ` 10 from 6th year onwards. What is...
Understanding Present Value of Perpetuity
To calculate the present value of a perpetuity that starts paying out from the 6th year onwards, we need to consider the future cash flows and discount them back to the present value at the given rate of return.
Key Information
- Cash Flow = `10 (from year 6 onwards)
- Rate of Return (r) = 20% or 0.20
- Perpetuity starts in year 6
Calculating Present Value of Perpetuity
1. Present Value Formula for Perpetuity:
The present value of a perpetuity can be calculated using the formula:
\[
PV = \frac{C}{r}
\]
where:
- \(C\) = Cash flow per period (`10)
- \(r\) = Rate of return (0.20)
2. Calculate the Perpetuity Value:
Substituting the values into the formula:
\[
PV_{\text{year 6}} = \frac{10}{0.20} = 50
\]
3. Discounting to Present Value:
Since this cash flow starts from year 6, we need to discount it back to the present value (year 0) using the formula:
\[
PV = \frac{FV}{(1 + r)^n}
\]
where:
- \(FV\) = Future value (50)
- \(n\) = Number of years until cash flow starts (5 years)
4. Present Value Calculation:
\[
PV = \frac{50}{(1 + 0.20)^5} = \frac{50}{2.48832} \approx 20.1
\]
Conclusion
The present value of the perpetuity is approximately `20.1. Therefore, the correct answer is (a) 20.1.
To calculate the present value of a perpetuity that starts paying out from the 6th year onwards, we need to consider the future cash flows and discount them back to the present value at the given rate of return.
Key Information
- Cash Flow = `10 (from year 6 onwards)
- Rate of Return (r) = 20% or 0.20
- Perpetuity starts in year 6
Calculating Present Value of Perpetuity
1. Present Value Formula for Perpetuity:
The present value of a perpetuity can be calculated using the formula:
\[
PV = \frac{C}{r}
\]
where:
- \(C\) = Cash flow per period (`10)
- \(r\) = Rate of return (0.20)
2. Calculate the Perpetuity Value:
Substituting the values into the formula:
\[
PV_{\text{year 6}} = \frac{10}{0.20} = 50
\]
3. Discounting to Present Value:
Since this cash flow starts from year 6, we need to discount it back to the present value (year 0) using the formula:
\[
PV = \frac{FV}{(1 + r)^n}
\]
where:
- \(FV\) = Future value (50)
- \(n\) = Number of years until cash flow starts (5 years)
4. Present Value Calculation:
\[
PV = \frac{50}{(1 + 0.20)^5} = \frac{50}{2.48832} \approx 20.1
\]
Conclusion
The present value of the perpetuity is approximately `20.1. Therefore, the correct answer is (a) 20.1.
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A stock pays annually an amount of ` 10 from 6th year onwards. What is the present value of perpetuity, if the rate of return is 20% (a) 20.1 (b) 19.1 (c) 21.1 (d) 22.1?
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A stock pays annually an amount of ` 10 from 6th year onwards. What is the present value of perpetuity, if the rate of return is 20% (a) 20.1 (b) 19.1 (c) 21.1 (d) 22.1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A stock pays annually an amount of ` 10 from 6th year onwards. What is the present value of perpetuity, if the rate of return is 20% (a) 20.1 (b) 19.1 (c) 21.1 (d) 22.1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stock pays annually an amount of ` 10 from 6th year onwards. What is the present value of perpetuity, if the rate of return is 20% (a) 20.1 (b) 19.1 (c) 21.1 (d) 22.1?.
A stock pays annually an amount of ` 10 from 6th year onwards. What is the present value of perpetuity, if the rate of return is 20% (a) 20.1 (b) 19.1 (c) 21.1 (d) 22.1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A stock pays annually an amount of ` 10 from 6th year onwards. What is the present value of perpetuity, if the rate of return is 20% (a) 20.1 (b) 19.1 (c) 21.1 (d) 22.1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stock pays annually an amount of ` 10 from 6th year onwards. What is the present value of perpetuity, if the rate of return is 20% (a) 20.1 (b) 19.1 (c) 21.1 (d) 22.1?.
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