Question

what is the net present value of a three year $3000 annuity if it currently costs 7200? the discount rate is 5%. A) would you recommend this annuity? briefly explain why or why not. B) How would your answer change if the annuity is paid semiannually $1500 every six months instead? No further calculation required: Briefly explain.

Answer 1

1)

Present value of 3 years annuity

=

Annual Cash flows

*

Present value of annuity of 1

=

$         3,000

*

2.723248

=

$   8,169.74

Present value of 3 years annuity is $ 8,169.74.But, it currently costs $ 7,200.It means we have to pay less amount than its present value.

So, is better to invest in such annuity.

Working:

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.05)^-3)/0.05

i

5%

=

2.72324803

n

3

2)

Present value of 3 years annuity

=

Annual Cash flows

*

Present value of annuity of 1

=

$         1,500

*

5.508125

=

$   8,262.19

My answer will remain same because even in this case, present value of annuity is more than its current cost.

So, is better to invest in such annuity.

Working:

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.025)^-6)/0.025

i

2.5%

=

5.50812536

n

6