Question

Billy Anderson wishes to choose the better of two equally costly cash flow streams: annuity X and annuity Y.
X is an annuity due with a cash inflow of $9,000 for each of 6 years. Y is an ordinary annuity with a cash inflow of $10,000 for each of six years.
Assume that Billy can earn 15% on his investments.

1) On a purely subjective basis, which annuity do you think is more attractive? Why?
2) Find the future value at the end of year 6 for both annuities.
3) Use your findings in Question 2 to indicate which annuity is more attractive. Why? Compare your finding to your subjective response in Question 1.

Answer 1

1) on a purely subjective basis, annuity Y is more attracted as the amount of cash inflow is more.

2) future value of annuity X, ie, annuity due is,

= P*(1+r)*((1+r)^n -1)/r

= 9000*(1+0.15)*((1+0.15)^6 -1)/0.15

= $ 90601.19

Future value of annuity Y, ie, ordinary annuity is,

= P*((1+r)^n -1)/r

= 10000*((1+0.15)^6 -1)/0.15

= $ 87537.38

3)Since, the future value of annuity X is more than the future value of annuity Y, it is more attractive.

But as stated in part 1 annuity Y was more attractive because of more periodic amount.

Please note: In annuity due, payment occurs at the beginning of the year. Whereas in case of an ordinary annuity, payments occur at the end of the year.