Question

What discount rate would make you indifferent between receiving $3,853.00 per year forever and $5,817.00 per year for 27.00 years? Assume the first payment of both cash flow streams occurs in one year.

Derek will deposit $4,279.00 per year for 15.00 years into an account that earns 15.00%. Assuming the first deposit is made 4.00 years from today, how much will be in the account 40.00 years from today?

Answer 1

a.Present value of perpetuity=Annual cash flows/discount rate

=3853/discount rate

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

=5817[1-(1+discount rate)^-27]/discount rate

3853/discount rate=5817[1-(1+discount rate)^-27]/discount rate

3853=5817[1-(1+discount rate)^-27]

(3853/5817)=[1-(1+discount rate)^-27]

1-(3853/5817)=(1+discount rate)^-27

0.337631081=[1/(1+discount rate)]^27

(0.337631081)^(1/27)=[1/(1+discount rate)]

1/(1+discount rate)=0.960583018

1+discount rate=(1/0.960583018)

discount rate=(1/0.960583018)-1

=4.10%(Approx).

2.Present value=Cash flows*Present value of discounting factor(rate%,time period)

=4,279/1.15^4+4,279/1.15^5+..................+4,279/1.15^18

=4,279[1/1.15^4+1/1.15^5+.................+1/1.15^18]

=4279*3.844740757

=16451.6457

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=16451.6457*(1.15)^40

=$4406796.16(Approx).