Question

all true/false

3. when solving for the present value of annuity, all cash flows are discounted t/f

5. other things equal, the pv of an annuity due,> of perpetuity t/f

6. the payment on a discount loan is simply the future value of a loan t/f

9. If you save $100 annually for 30 years and earn 4% your future value < $6000 t/f

10. Take a lottery's cash option is the lottery's indifference point > the rate you could earn t/f

13. If r=12% and n = 12 the PVIFA > 6 t/f

Answer 1

Solution

3. True. The annuity itself is made up of cash flows of equal amount and they are discounted to get the present value.

5. False. The present value of an annuity due is always less than or equal to that of a perpetuity. Since a perpetuity is an infinite annuity its present value is always greater or where the annuity due is over a very large period its present value would get near to that of the perpetuity but never greater than its present value.

6. True. The discount loan given by a bank is nothing but the amount agreed to be paid in future (or its future value) at the end of its tenure minus the interest.

9. True. The future value is $5,608.49 which is < $6,000

Calculation as below:

FV_A = A x [(1+r)ⁿ - 1 ] / r

where annuity, A = $100, number of periods, n = 30 years and rate, r = 4% or 0.04

FV_A =100 x [(1+0.04)³⁰ - 1 ] / 0.04

FV_A =100 x [(1.04)³⁰ - 1 ] / 0.04

FV_A =100 x [(3.2433975 - 1 ] / 0.04

FV_A =100 x 2.2433975 / 0.04

FV_A = $5,608.49

10. False. The indifference point of the lottery is the rate of return at which the present value of the annuity payouts from making investments of the lumpsum cash prize equals the lumpsum cash prize. In other words, it is the interest / return earned by the prize winner on opting for the annuity payout option offered by the lottery. If this is greater than the rate you could earn by investing the lumpsum cash payout yourself, it makes sense to opt for the annuity payout and NOT take the cash option (or lumpsum payout)

13. False. If r = 12% and n = 12 the PVIFA < 6 since the PVIFA is 6.19 calculated below:

Formula for present value of annuity factor (assuming that it is an annuity of $1)

PVIFA = A x [(1+r)ⁿ - 1] / [r x (1+r)ⁿ]

= 1 x [(1+0.12)¹² - 1] / [0.12 x (1+0.12)¹²]

= [(1.12)¹² - 1] / [0.12 x (1.12)¹²]

= [3.89597599 - 1] / [0.12 x 3.89597599]

= 2.89597599 / [0.12 x 3.89597599]

= 6.1944 or 6.19 approx.