Question

If you are willing to pay $46,850.00 today to receive $4,341.00 per year forever then your required rate of return must be ____%. Assume the first payment is received one year from today.

If you are willing to pay $20,509.00 today to receive a perpetuity with the first payment occurring next year then the payment must be $______. Assume a 7.00% discount rate.

What discount rate would make you indifferent between receiving $3,727.00 per year forever and $5,271.00 per year for 27.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer 1

a.Required rate of return=Annual inflows/Current value

=(4341/46850)

=9.27%(Approx).

b.Current value of perpetuity=Annual payments/discount rate

Annual payments=(20509*7%)

=$1435.63

c.Present value of perpetuity=3727/discount rate

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

=$5271[1-(1+discount rate)^-27]/discount rate

3727/discount rate=$5271[1-(1+discount rate)^-27]/discount rate

3727=$5271[1-(1+discount rate)^-27]

(3727/$5271)=1-(1+discount rate)^-27

1-(3727/5271)=(1+discount rate)^-27

(1+discount rate)^-27=0.292923543

[1/(1+discount rate)]^27=0.292923543

1/(1+discount rate)=(0.292923543)^(1/27)

1/(1+discount rate)=0.955542831

1/0.955542831=(1+discount rate)

(1+discount rate)=1.0465

Discount rate=1.0465-1

=4.65%(Approx).