Question

A company is considering buying a CNC machine. In today's dollars, it is estimated that the maintenance costs for the machine (paid at the end of each year) will be $33,000, $35,000, $38,000, $39,000, and $42,000 for years 1 to 5, respectively. The general inflation rate (T) is estimated to be 6% per year, and the company will receive 14% return (interest) per year on its invested funds during the inflationary period. The company wants to pay for maintenance expenses in equivalent equal payments (in actual dollars) at the end of each of the five years. Find the amount of the company's payments The amount of the company's payments is thousand. (Round to the nearest thousand.)

Answer 1

Solution :

i = ( i - f' ) / ( 1 + f ) = ( 0.14 - 0.06 ) / ( 1 + 0.06 ) = 0.0754716 = 7.55%

Now Constant Value of Dollar =  $33,000 * PVF (7.55% , 1) + $35,000 * PVF (7.55% , 2) + $38,000 * PVF (7.55% , 3) + $39,000 * PVF (7.55% , 4) + $42,000 * PVF (7.55% , 5)

= $33,000 * 0.92980 + $35,000 * 0.86453 + $38,000 * 0.80384 + $39,000 *0.74741 + $42,000 * 0.69494

= $30,683.4 + $30,258.55 + $30,545.92 + $29,148.99 + $29,187.48

= $149,824.34

Now the present value of $149,824.34 to determine equal amounts in actual dollars made at the end of each five years.

A = $149,824.34 * ( A/P , 14% , 5 )

A = $149,824.34 * 0.29128

A = $43,641.37

The amount of the company's payments is $44 thousand. (Round to the nearest thousand.)