Pensions are retirement plans that provide income to individuals from the time that they retire until the time they die. Pensions are almost always established by large corporations and governments and are generally expressed in terms of an individual's salary at the time of retirement. There are two challenges to determining the cash value of a pension. The first involves not knowing when a person will die. The second involves choosing the right discount rate to use to value the pension.

## Estimate the Cash Flows

Pensions are expressed in terms of salary, so estimate salary at retirement age. For example, an individual who expects to be earning £65,000 per year at age 65 with a 50 per cent pension will receive .50 X 100,000 = £32,500 per year in retirement.

## Build a Table to Discount the Cash Flows

Write down a table with the headings: "Age" "Rate" "Factor" "Discount" "Pension" and "DCF." "DCF" means discounted cash flow.

Write down each age in retirement until death under the "Age" column. If the person expects to live until 80, then the column will look like this:

Age

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

Write down 1.05 in each row of the "Rate" column to represent a 5 per cent annual discount rate.

Write the number 1 through 15 under the "Factor" column.

Raise the rate to the power of the factor in each row of the "Discount" column. In other words, (1.05) ^x. The column should look like this:

Discount

1.05

1.10

1.16

1.22

1.28

1.34

1.41

1.48

1.55

1.63

1.71

1.80

1.89

1.98

2.08

Write down £32,500 in each row of the "Pension" column.

## Finish the Table

Multiply each £32,500 times the discount number to get the answer for the "DCF" column.

The table should look like this by column:

The Age column:

Age

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

The Rate column:

Rate

1.05

1.05

1.05

1.05

1.05

1.05

1.05

1.05

1.05

1.05

1.05

1.05

1.05

1.05

1.05

The Factor column:

Factor

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

The Discount column:

Discount

1.05

1.10

1.16

1.22

1.28

1.34

1.41

1.48

1.55

1.63

1.71

1.80

1.89

1.98

2.08

The Pension column:

Pension

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

£32,500

The DCF column:

DCF

£30,952

£29,478

£28,074

£26,737

£25,464

£24,252

£23,097

£21,997

£20,949

£19,952

£19,002

£18,097

£17,235

£16,414

£15,633

## Determine the Value at 65

Add up all of the numbers in the "DCF" column to get £337,338. This is the cash value of the pension at age 65.

## Discount to the Present Day

Calculate the cash value today by discounting £337,338 to the present day. For example, if the individual is 45 now, then the cash value has to be discounted by 65 minus 45, or 20 years.

Raise 1.05^20 to get 2.65.

Divide 2.65 into 518,983 to get £127,140. This is the cash value of the pension today.