Question

To maintain a structure with a life of 20 yrs, it is necessary to provide the following for repairs. 20,000 at the end of 5th year, 30,000 at the end of 10th year, 40,000 at the end of 15th yr. If money is worth 10% compounded annually, determine the equivalent uniform annual maintenance cost for the 20yr period.

3608/yr

3542/yr

3142/yr

3942/yr

Answer 1

Solution

Here maintenance outflows are given for 3 years i.e 5,10,15

First, we will find out the Present Value of each outflow and sum them to find present value of total costs

PV = Cashflow/(1+r)^n

here r=10%

Therefore PV are given below

Excel formula

Therefore the total PV of outflows= 33560.40712

Now equivalent uniform annual maintenance cost will the the annuity amount which will give a present value of 33560.40712 @ 10% in 20 years

Formula for PV of annuity is

Here Present value of annuity=33560.40712

rate= 10%

t= 20 years

33560.40712= Annual payment/.1*(1-1/1.1^20)

3356.041= Annual payment*0.851356

Solving the equation we get

Annual payment=equivalent uniform annual maintenance cost=3942/year