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