Question

1-4 $25,000 per year (payments at the end of the year)

5-9 $20,000 per year (payments at the end of the year)

Assume an interest rate of 6% compounded annually. Calculate the present value of the stream of cash flows above.

Answer 1

Solution:

Present value of the Cash flow will be computed as below:

Year end Cash flow($)* Present Value fector*** Present Value ($)**

1 25000 .943 23,575

2 25000 .890 22,250  

3 25000 .840 21,000

4 25000 .792 19,800

5 20000 .747 14,940

6 20000 .705 14,100

7 20000 .665 13,300

8 20000 .627 12,540

9 20000 .592 11,840

Present Value   1,53,345

Working Note:

* Cash flow as mentioned in Question

** Present Value (PV)= Cash Flow ($) multiplied by Present Value Fector (PVF)

*** Computation of Present Value Fector (PVF)

Formula: 1/(1+r)ⁿ  (i.e. 1 divide by (1+r) power n)

where, r = Rate of return (given in Question i.e. 6%)

n = Number of period ( as in Question year 1 to Year 9)

so, Year end PVF

1 1/(1+6%)¹

2 1/(1+6%)²

³ 1/(1+6%)³

The same is continued till year 9

so mathematically if we compute, it comes as

Year end PVF

1 1/(1.06)¹   = 0.943

2 1/(1.06)² or we can say 1/(1.06)*1/(1.06) = 0.890

3 1/(1.06)³ or multiply 1/(1.06) three times = 0.840

The same is contued till Year 9

9 1/(1.06)⁹ = 0.592