QUESTION 1 Consider the ollowing cash ow diagrams In these d

QUESTION 1 Consider the ollowing cash ow diagrams. In these diagrams the present value the value of P larger than F,equal to F, or less than F? and the future value F are economically equivalent to the uniform series o payments A at a discount rate o 8% per period. Is P is larger than F P equals F is less than F

Solution

Future value is always larger than present value as interest is added in future value.

Let’s consider the cash flow as $ 1,000 per year and calculate PV and FV of annuities.

Calculation of PV:

PV = C x [1-(1+r)^-n/r]      

C = Cash flow per period = $ 1,000

r = Rate per period = 8 % = 0.08

n = Numbers of periods = 7

PV = $ 1,000 x [1- (1 + 0.08)^-7 /0.08]

      = $ 1,000 x [1- (1.08)^-7 /0.08]

      = $ 1,000 x [(1- 0.58349) /0.08]

      = $ 1,000 x (0.41651 /0.08)

      = $ 1,000 x 5.20637

     = $ 5,206.37

Calculation of FV:

FV = C x [(1+r)ⁿ - 1 /r]

Putting the same values as above, we get

FV = $ 1,000 x [(1+0.08)⁷ – 1/0.08]

     = $ 1,000 x [(1.08)⁷ – 1/0.08]

    = $ 1,000 x [(1.713824 – 1/0.08]

    = $ 1,000 x (0.713824/0.08)

    = $ 1,000 x 8.922803

    = $ 8,922.80

We also observed from the above calculation that FV of annuity is greater than PV of annuity.

Hence option “P is less than F” is correct answer.