A machine costs $260,000 to purchase and will provide $60,000 a year in benefits. The company plans to use the machine for 12 years and then will sell the machine for scrap, receiving $15,000. The company interest rate is 11%. What is the present value of buying the machine, receiving annual benefits, and then selling the machine

$133,828.98  

Explanation:

The computation of the net present value is shown below:

YearCash flowsDiscount factorPresent value

0$260,000.00               1                         $260,000.00 (A)

1$60,000.00         0.9009009009$54,054.05

2$60,000.00        0.8116224332            $48,697.35

3$60,000.00        0.7311913813            $43,871.48

4$60,000.00        0.6587309741          $39,523.86

5$60,000.00        0.5934513281          $35,607.08

6$60,000.00        0.5346408361       $32,078.45

7$60,000.00         0.4816584109        $28,899.50

8$60,000.00         0.4339264963        $26,035.59

9$60,000.00         0.3909247714        $23,455.49

10$60,000.00         0.3521844788        $21,131.07

11$60,000.00         0.3172833142          $19,037.00

12$75,000.00         0.2858408236        $21,438.06

Total present value                                     $393,828.98  (B)

Net present value                                   $133,828.98     (B - A)

The discount is come from

= 1 ÷ (1 + rate) ^ years  

i guess you could put raise the economic balance

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20