Question

What discount rate would make you indifferent between receiving $3,566.00 per year forever and $5,964.00 per year for 28.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer 1

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=$5964[1-(1+interest rate)^-28]/interest rate

Present value of perpetuity=Annual inflows/interest rate

=$3566/interest rate

$3566/interest rate=$5964[1-(1+interest rate)^-28]/interest rate

$3566=$5964[1-(1+interest rate)^-28]

($3566/$5964)=1-(1+interest rate)^-28

1-($3566/$5964)=(1+interest rate)^-28

[1/(1+interest rate)]^28=(0.402079141)

1+interest rate=[1/(0.402079141)]^(1/28)

1+interest rate=1.0331

interest rate=(1.0331-1)

=3.31%(Approx).