Question

A new office building has been constructed at a cost of $3,000,000. It is estimated to have a life of 50 years with a value at that time of $200,000. It will have maintenance costs of $10,000 per year. It will also have major repairs costing $80,000 that occur at years 10, 20, 30 and 40. It will have additional repairs at the end of year 25 costing $250,000. Determine the equivalent uniform annual cost if the rate of interest of the firm is 7%

Answer 1

The question is a case of Time Value of Money.

We need to assume some points before we go forward.

1. All Costs are incurred at the beginning of the year.

2. Compounding is annual.

For solving the question we will not consider $3,000,000 as the amount has been already incurred and the construction is done. Only the upcoming costs will be considered to get an Equivalent Uniform Annual Cost.

For this we need to take out the Present Value of each and every costs that will be incurred in the upcoming years.

1. For $10,000 to be incurred every year for 50 years

PV = , where A is the annual amount, r is the rate and n is the no of years

     =

     = $ 138,007.46

2. For $80,000 at 10,20,30,40 years

Formula: PV for single Sum=    , where r is the rate and n is the number of years

At 10year =

                = $ 40,668

At 20year =   

                = $ 20,673.52

At 30year =   

= $ 10,509.37

At 40year =   

                = $ 5,342.43

3. For $250,000 at 25th Year

PV =   

      = $ 46,062.29  

   

Total Present value =   $ 138,007.46 + $ 40,668 + $ 20,673.52 + $ 10,509.37 + $ 5,342.43 + $ 46,062.29

                                 = $ 261,263.07

Equivalent Uniform Annual Cost = , (where A is Amount(Total PV), r is the rate and n is the number of years.)

                                                     =

                                                     = $19,568.60

                                                        (Answer)