# Discounting Uneven Cash Flows

P. Peterson Drake
```Problem CF1        CF2       CF3           Discount      PV at the end
rate per      of period 0
period

1       \$5,000     \$5,000    \$3,000        5%

2       \$3,000     0         \$3,000        4%

3       \$0         \$1,000    \$1,000        5%

4       \$10,000    0         \$10,000       2%

5       \$100       \$100      \$200          4%

```

CFt = Cash flow at the end of period t

## Present Value of a Deferred Annuity

```Problem Cash flow  Number    Discount      First cash    Present value
per        of cash   rate per      flow at the
period     flows     period        end of
period:

1       \$1,000     4         5%            2

2       \$2,000     4         6%            10

3       \$3,000     5         4%            5

4       \$1,000     3         5%            3

5       \$5,000     4         5%            10

```

# Uneven Cash Flows and Deferred Annuities

## Discounting Uneven Cash Flows

```Problem CF1        CF2       CF3           Discount      PV at the end
rate per      of period 0
period

1       \$5,000     \$5,000    \$3,000        5%            \$11,888.56

2       \$3,000     0         \$3,000        4%            \$5,551.60

3       \$0         \$1,000    \$1,000        5%            \$1,770.87

4       \$10,000    0         \$10,000       2%            \$19,227.14

5       \$100       \$100      \$200          4%            \$366.41

```

CFt = Cash flow at the end of period t

## Present Value of a Deferred Annuity

```Problem  Cash      Number    Discount      First cash    Present value
flow per  of cash   rate per      flow at the
period    flows     period        end of
period:

1        \$1,000    4         5%            2             \$3,377.10

2        \$2,000    4         6%            10            \$4,101.98

3        \$3,000    5         4%            5             \$11,416.31

4        \$1,000    3         5%            3             \$2,470.07

5        \$5,000    4         5%            10            \$11,428.75

```