You are offered a 16-year annuity of $10,000 annual payments.However, the annuity begins in 9...

You are offered a 16-year annuity of $10,000 annual payments. However, the annuity begins in 9 years (you will not receive any payments for 9 years, but will then receive $10,000 at the end of each year for 16 years. If the discount rate is 7% per year (compounded annually), what is the current value of the annuity?

Solutions

Expert Solution

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

PV of annuity after 8 years:

Assuming first payment received at the end of Year 9.

Particulars	Amount
Cash Flow	$ 10,000.00
Int Rate	7.0000%
Periods	16

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 10000 * [ 1 - [(1+0.07)^-16]] /0.07
= $ 10000 * [ 1 - [(1.07)^-16]] /0.07
= $ 10000 * [ 1 - [0.3387]] /0.07
= $ 10000 * [0.6613]] /0.07
= $ 94466.49

PV of ANnuity Today:

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Future Value	$ 94,466.49
Int Rate	7.0000%
Periods	8

Present Value = Future Value / ( 1 + r )^n
= $ 94466.49 / ( 1 + 0.07 ) ^ 8
= $ 94466.49 / ( 1.07 ) ^ 8
= $ 94466.49 / 1.7182
= $ 54980.36

Present Value of Anuuity today is $ 54980.36

jeff jeffy answered 2 years ago

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