Q:
A:
For $800,000 invested today, an insurance company promises to start making perpetual payments to you beginningÂ seven years from now. What must these perpetual payments be if the longterm savings rate is expected to remain constant at 5.5%?
A) $60,669
B) $64,006
C) $166,249
D) Present value is infinite because payments continue into infinity.
A) $60,669
B) $64,006
C) $166,249
D) Present value is infinite because payments continue into infinity.
The correct answer is: A)
We must first link the $800,000 today to the period when the perpetuity payments will begin. In this case: PV=800,000; I=5.5; N=6; thus, FV=1,103,074. Note that the $1,103,074 is the value of the perpetuity by the end of the sixth year. We also know that:
Present Value of a Perpetuity @ period t = [cash flow for period t+1]
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â [Period interest rate]
Therefore:
Present value of $1,103,074 @ period 6 = [Cash flow beginning period 7]
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.055
Therefore, the cash flow beginning in period 7 and continuing indefinitely is ($1,103,074)*(0.055) = $60,669.08.
We must first link the $800,000 today to the period when the perpetuity payments will begin. In this case: PV=800,000; I=5.5; N=6; thus, FV=1,103,074. Note that the $1,103,074 is the value of the perpetuity by the end of the sixth year. We also know that:
Present Value of a Perpetuity @ period t = [cash flow for period t+1]
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â [Period interest rate]
Therefore:
Present value of $1,103,074 @ period 6 = [Cash flow beginning period 7]
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 0.055
Therefore, the cash flow beginning in period 7 and continuing indefinitely is ($1,103,074)*(0.055) = $60,669.08.
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