## 5-minute Work-outs for

# 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

# Solutions to 5-minute Work-outs

# 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