What discount rate would make you indifferent between receiving $3,401.00 per year forever and $5,060.00 per year for 29.00 years? Assume the first payment of both cash flow streams occurs in one year.
Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate
=$5060[1-(1+discount rate)^-29]/discount rate
Present value of perpetuity=Annual cash flows/discount rate
=$3401/discount rate
$5060[1-(1+discount rate)^-29]/discount rate =$3401/discount rate
$5060[1-(1+discount rate)^-29] =$3401
[1-(1+discount rate)^-29]=(3401/5060)
1-(3401/5060)=(1+discount rate)^-29
1/(1+discount rate)^29=0.327865612
(1+discount rate)^29=1/0.327865612
(1+discount rate)=(1/0.327865612)^(1/29)
1+Discount rate=1.0392
Discount rate=(1.0392-1)
=3.92%(Approx).
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