Question

An investment will pay $32,000 per year forever beginning 10 years from today. If the relevant...

An investment will pay $32,000 per year forever beginning 10 years from today.

If the relevant rate is 8% compounded monthly, the investment is worth $______ today.

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Answer #1

Annual Payment = $32,000

Annual Interest Rate = 8.00%
Monthly Interest Rate = 8.00% / 12
Monthly Interest Rate = 0.66667%

Effective Annual Rate = (1 + Monthly Interest Rate)^12 -1
Effective Annual Rate = (1 + 0.0066667)^12 - 1
Effective Annual Rate = 1.083 - 1
Effective Annual Rate = 0.0830 or 8.30%

First payment is made in 10 years

Value of Perpetuity 9 years from now = Annual Payment / Effective Annual Rate
Value of Perpetuity 9 years from now = $32,000 / 0.0830
Value of Perpetuity 9 years from now = $385,542.16867

Value of Perpetuity now = Value of Perpetuity 9 years from now / (1 + Effective Annual Rate)^9
Value of Perpetuity now = $385,542.16867 / (1 + 0.0830)^9
Value of Perpetuity now = $188,111.69

The investment is worth $188,111.69 today

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