CASH FLOW ANALYSIS

Cash Flow Analysis and Time Value of Money Problem

Cash Flow Analysis and Time Value of Money

Question 1 Solution

Timeline:

Timeline represent the cash flow timing in graphical form. Timeline presented below shows the accrual of 100 dollars as total amount that will accumulate at the end of year 2.

Year 0 @ i%

Year 1 @ i%

Year 2 @ i%

 

 

$100

Timeline presented below shows the accrual of 100 dollars ordinary annuity for three years duration.

Year 0 @ i%

Year 1 @ i%

Year 2 @ i%

Year 3 @ i%

 

$100

$100

$100

Timeline presented below shows the accrual of uneven cash flows.

Year 0 @ i%

Year 1 @ i%

Year 2 @ i%

Year 3 @ i%

($50)

$100

$275

$50

Calculations

Suppose $100 are invested for 3 years, determine its future value using interest rate of 10%

Future Value = Present Value (1 + interest rate) years

FV = PV (1+ i)t

As we know that,

PV = 100 dollars

i = 10%

t = 3 years

By putting these values in the formula, we get:

FV = 100 (1+ 0.10)3

FV = 100 (1.10)3

FV = 133.10 dollars

If 100 dollars are invested for 3 years, its future value using interest rate of 10% would be 133.10 dollars.

Determine the present value of 100 dollars that will be received after three years assuming interest rate of 10%.

Future Value = Present Value (1 + interest rate) years

FV = PV (1+ i)t

As we know that,

FV = 100 dollars

i = 10%

t = 3 years

By putting these values in the formula, we get:

100 = PV x (1+ 0.10)3

100 = PV x (1.10)3

PV = 100 / (1.3310)3

PV = 75.13 dollars

Determine the duration required in order to double the sales volume of a company, it is increasing at 20% annual rate.

For this example, present sales value has been assumed as 1 dollar; however, future value of the sales has been assumed as 2 dollars. Using the below mentioned formula, duration of investment has been determined.

Future Value = Present Value (1 + interest rate) years

FV = PV (1+ i)t

As we know that,

FV = 2 dollars

PV = 1 dollar

i = 20%

By putting these values in the formula, we get:

2 = 1 x (1+ 0.20)t

2 = (1+ 0.20)t

Using exponential log (ln) function, we get:

ln 2 =

t ln (1.20)

ln 2 =

0.693

ln 1.2 =

0.182

t =

ln 2 / ln 1.2

t =

0.693 / 0.182

t =

3.808

This shows that it would take 3.81 years in order to double the sales volume in dollars.

Determine the interest rate required for doubling of investment amount. Timeline for this question is as follows.

Year 0 @ i%

Year 1 @ i%

Year 2 @ i%

Year 3 @ i%

1

 

 

$1

As we know that,

FV = 2 dollars

PV = 1 dollar

t = 3 years

By putting these values in the formula, we get:

2 = 1 x (1+ i)3

2 = (1+ i)3

Taking cube root on both sides, we get:

1 + i = 2(1/3)

1 + i = 1.2599

i = 1.2599 - 1

i = 0.2599

i = 25.99%

25.99% annual interest rate is required for doubling the investment amount in three years.

References

Using a timeline, show examples of an ordinary annuity and an annuity ...