An investment offers $7,000 per year for 15 years, with the first payment occurring one year from...

Question:

An investment offers $7,000 per year for 15 years, with the first payment occurring one year from now.

If the required return is 8%, what is the value of the investment?

What would the value be if the payments occurred for 40 years? For 75 years? Forever?

Present Value Annuity:

Present Value Annuity is a concept which is used in determining the value of a constant stream periodic cash flows for a particular period. It is based on the concept of time value of money and hence one dollar amount is worth more today than in the future. When the payments are made at the end of each period then it is termed as present value of ordinary annuity whereas, when the payment is made at the beginning of each period it is called present value annuity due.

Answer and Explanation:

a ) Present Value of ordinary annuity (PVA) for 15 years is calculated as follows:

  • {eq}PVA = P * [ 1 - ( 1 / 1+r )^n ] / r {/eq}

where,

  • P = payment made = 7000
  • r = required return = 8%
  • n = number of periods = 15

Putting the values in the equation:

  • {eq}PVA = 7000 * [ 1 - (1 / 1 + 0.08 )^15 ] / 0.08 {/eq}
  • {eq}PVA = 7000 * [ 1 - 0.315242 ] / 0.08 {/eq}
  • {eq}PVA = 7000 * 0.684758 / 0.08 {/eq}
  • {eq}PVA = 59916.35 {/eq}

Answer: Value if the investment is for 15 years would be $59916.35

b) Present Value of ordinary annuity (PVA) for 40 years is calculated as follows:

  • {eq}PVA = P * [ 1 - ( 1 / 1+r )^n ] / r {/eq}

where,

  • P = payment made = 7000
  • r = required return = 8%
  • n = number of periods = 40

Putting the values in the equation:

  • {eq}PVA = 7000 * [ 1 - (1 / 1 + 0.08 )^40 ] / 0.08 {/eq}
  • {eq}PVA = 7000 * [ 1 - 0.046031 ] / 0.08 {/eq}
  • {eq}PVA = 7000 * 0.953969 / 0.08 {/eq}
  • {eq}PVA = 83472.29 {/eq}

Answer: Value if the investment is for 40 years would be $83472.29

c) Present Value of ordinary annuity (PVA) for 75 years is calculated as follows:

  • {eq}PVA = P * [ 1 - ( 1 / 1+r )^n ] / r {/eq}

where,

  • P = payment made = 7000
  • r = required return = 8%
  • n = number of periods = 75

Putting the values in the equation:

  • {eq}PVA = 7000 * [ 1 - (1 / 1 + 0.08 )^75 ] / 0.08 {/eq}
  • {eq}PVA = 7000 * [ 1 - 0.003113 ] / 0.08 {/eq}
  • {eq}PVA = 7000 * 0.996887 / 0.08 {/eq}
  • {eq}PVA = 87227.59 {/eq}

Answer: Value if the investment is for 75 years would be $87227.59

d) Present Value of ordinary annuity (PVA) for investment which is forever

  • {eq}PVA = P / r {/eq}

where,

  • P = payment made = 7000
  • r = required return = 8%

Putting the values in the equation:

  • {eq}PVA = 7000 / 0.08 {/eq}
  • {eq}PVA = 87500 {/eq}

Answer: Value if the investment is forever would be $87500


Learn more about this topic:

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How to Calculate the Present Value of an Annuity

from Business 110: Business Math

Chapter 8 / Lesson 3
11K

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