Question

Question 4 Draw the cashflow profile (aka the total cashflow at each time period) for the following present value expression (t = 0); 1207-20137 - 2007 i- e where all factors use i, except where j is stated.j = and e = 5% pa (1+e)

Can someone show me how to draw these cash flow profiles please?!

Answer 1

Symbol  a_6| represents the present value of six payments each of 1 at times 1, 2, 3, 4, 5, 6.

$\therefore$ 12 a_6| is the PV of six payments each of 12 at times 1, 2, 3, 4, 5, 6.

Symbol (Iä)_3| represents PV of three payments of 1, 2, 3 at times 0, 1, 2 respectively.

$\therefore$ -2(Iä)_3| is the PV of three payments of -2, -4, -6 at times 0, 1, 2 respectively.

v⁶ is the PV of a payment of 1 at time 6

$\therefore$ -2v⁶a_2| is the PV of a payment of -2a_2| at time 6, but a payment of -2a_2| at time 6 is the PV(at time 6) of two payments each of -2 at times 7, 8.

$\therefore$ -2v⁶a_2| is the PV(at time 0) of two payments each of -2 at times 7, 8.   

The following time line shows these three payment streams

12 12 12 12 12 12    12 a_6|

-2 -4 -6                  -2(Iä)_3|

-2 -2    -2v⁶a_2|

|_________|_________|_________|_________|_________|_________|__________|__________|_________|____________

0 1 2 3 4 5 6 7 8 9

Summing up we have

-2 8 6 12 12 12 12 -2 -2

|__________|_________|__________|__________|__________|__________|__________|__________|__________|______

0 1 2 3 4 5 6 7 8 9