Question

Annuities

What is the present value of $1,000 contribution earned each year for years 1-10, when the required return on investment is 11%.?

How would the present value change if the cashflow started in year 0 or if the cashflow started in year 3?

Perpetuities

What is the present value of $600 per annum in perpetuity at a discount rate of 15%?

Answer 1

Annuity is the series of equal payment in a time period

Formulae for Present Value of Annuity

PVA = A + [1-(1+r)-n]/r or A+[1- 1/(1+r)n]/r

Where A is Annual payment /receipt

r is rate of interest

N is number of year

1)PVA = 1000 [1-1/(1+0.11)10]÷0.11

=1000[1-0.3855]/0.11

=1000*5.59091

=$5590.91

a)If above case is consider and cash flow start flow year 0 till year 10 there will be 11 cash flow and at 0 year cash flow is at present value pv for 10 year calcluate above will add up with the year 0 cash flow [Assuming cashflow continue till 10 year ]

If payment starts from year 0

Pv = Year 0 contribution + PV of future cash flow (1-10)

=$1000+ 5590.91

=$6590.91

If payment starts from year 3 PV upto the start point of year 3 will be bring . And then this year 3 pv will bring back to year 0 point ie discounted back to 2 year

As number of year payment is 10

PV (yr 3) = 1000(1-1/(1+0.11)10 /0.11

=5590.91

PV(point 0) = 5590.91/(1+0.11)3

=4200.53

2) Perpetuity means continous cash flow with which last forever

Formulae for perpetuity

PV=A/r

A is amount per annum / period

r rate of interest or discount

PV = 600/0.15

=$4000