Case Study

A.

1.

Lump Sum

I%

Time

0

1

2

FV

 

 

100

2.

Annuity

I%

Time period

0

1

2

FV at year end

100

100

100

3.

Uneven cash flow stream.

I%

Time period

0

1

2

3

FV at year end

-50

100

75

50

B.

1.

Interest Rate: 10%

Cash Flow: 100

Time

0

1

2

3

FV

100

110.00

121

133.10

The results in the table above are calculated as:

After 1 year:

FV1 = PV + I1 = PV + PV (I) = PV (1 + I) = $100(1.10) = $ 110.00

Similarly, we calculate for the coming years:

FV2 = FV1 + I2 = FV1 + FV1 (I) = FV1 (1 + I) = $110(1.10) = $121.00

= PV(1 + I)(1 + I) = PV(1 + I)2.

FV3 = FV2 + I3 = FV2 + FV2 (I)

= FV2 (1 + I) = $121(1.10) = $133.10

= PV(1 + I)2(1 + I) = PV(1 + I)3.

B.

2.

Interest Rate: 10%

Cash Flow: 100

Here we have discounted back to the number of years, as shown in the table below:

Time

0

1

2

3

PV

$75.13

82.64

90.91

100.00

Calculated as:

C.

0

1

2

3

-100.00

 

 

125.97

The answer above is calculated as:

$100(1 + I) $100(1 + I)2 $100(1 + I)3

FV = $100(1 + I)3 = $125.97

D.

Interest Rate: 20 %

Time

0

1

2

?

PV

$1.00

 

 

2.00

The value of N can be computed by the following formula:

FVN = $2 = $1 (1 + I)N = $1 (1.20)N.

This can also be calculated by excel function “NPER”, the value of N comes out to be 3.8

E.

The series shown in the give question is an ordinary annuity. This is mainly because the payments are occurring at the end of each year and the first pay is settled at the end of first period.

Ordinary Annuity

Ordinary annuity is one in which equal payments are made ??at the end of each period. For example, the payment of wages to employees, the work in this case is performed first and payment is made afterwards.

Annuity Due

In the case of annuity due, the payments are made ??at the beginning of the period. For example, monthly lease of a house; it is paid first and then the service is availed.

Conversion

To convert ordinary annuity to annuity due, each payment has to be shifted to left so that you end with payments under the year zero and none at the last year (i.e. 3rd year).

F.

1.

N: 3

Interest Rate: 10 %

Payment: 100

Time

0

1

2

3

CFn

0

100

100

100

FV3

0

121

110

100

The future value of the annuity is calculated as:

FVAN = $100 (1) + $ 100 (1.10) + $100 (1.10)2

= $100 [1 + (1.10) + (1.10)2 ] = $ 100 (3.3100) = $ 331

2.

N: 3

Interest Rate: 10 %

Payment: 100

Time

0

1

2

3

CFn

0

100

100

100

PV3

0

90.91

82.64

75.13

The present value of the annuity comes out to be $248.69.

3.

N: 3

Interest Rate: 10 %

Payment: 100

In this case, the future value of the annuity due can be calculated as:

Time

0

1

2

3

CFn

100

100

100

0

FV3

133.1

121

110

0

We calculate the results by using the time line given above:

$ 133.10 + $ 121.00 + $ 110.00 = $ 364.1

Similarly, the present value of the annuity due can be calculated as:

Time

0

1

2

3

CFn

100

100

100

0

PV3

100.00

90.91

82.64

0.00

We calculate the results by using the time line given above:

$ 100 + $ 90.91 + $ 82.64 = $ 273.5

G.

1.

Time

0

1

2

3

4

5

CF

100

100

100

100

100

PV

90.91

82.64

75.13

68.3

62.09

The present value of the annuity comes out to be $ 379.08.

2.

We calculate the present value of the 10 year annuity by financial calculator.

It comes out to be $ 614.46.

3.

We calculate the present value of the 25 year annuity by financial ...