Question

If the interest rate is 6%, which of these investments would you prefer?

A single payment of $500 in year 3

A payment of $40 a year for 20 years starting in one year's time

A perpetuity of $30 a year starting in one year's time

A payment of $342.17 today

Answer 1

i)

Present Value of a single payment of $ 500 in year 3:

PV = FV/ (1+r)ⁿ

r = 6 % or 0.06

n = No. of periods = 3     

= $ 500/ (1+0.06)³

= $ 500/ (1.06)³

= $ 500/1.191016

= $ 419.80964 or $ 419.81

ii)

Present Value of $ 40 annual annuity for 20 years:

PV = C x [1-(1+r)^-n/r]      

C = Cash flow per period = $ 40

r = Rate per period = 6 % or 0.6

n = Numbers of periods = 20

PV = $ 40 x [1- (1 + 0.06)^-20 /0.06]

      = $ 40 x [1- (1.06)^-20 /0.06]

      = $ 40 x [(1- 0.311805)/0.06]

     = $ 40 x (0.688195/0.06)

     = $ 40 x 11.46992

     = $ 458.7968 or $ 458.80

iii)

Present Value of perpetuity of $ 30:

PV = C/r

C = Cash flow per period = $ 30

r = Discount rate = 6 % or 0.06

PV = $ 30/0.06 = $ 500

iv)

Today payment = $ 342.17

$ 30 perpetuity is preferable as PV of perpetuity is more than other options.