Question

Q5) A real estate corporation is planning on spending $40,000 on maintenance now, and $28,000 four years from now, using a real interest rate of 15% per year and inflation of 4% per year. What is the equivalent annual worth of the cost over a period starting year 1 through year 6?

Answer 1

As per the information provided in the question

The Initial spending on maintenance (I) =$40000

Spending on maintenance for four year (A) =$28000

Period of maintenance spending (N)=4 years

Real Interest rate (i’) = 15% = 0.15 per year     

Inflation rate (f) =4% = 0.04    per year

The market interest rate (i) = i’ + f + i’f = 0.15 +0.04 + (0.15)(0.04) =0.19 +0.006 =0.196=19.6%

Present worth (PW) of Spending on maintenance for four year = $28000(P/A, 19.6%,4)

(P/A,i,N)= A[{(1+i)^N-1}/{i(1+i)^N}]

=$28000[{(1+0.196)⁴-1}/{0.196(1+0.196)⁴}]

=$28000[{(1.196)⁴-1}/{0.196(1.196)⁴}]

=$28000(2.608484334)

=$73037.5613

Present worth of Maintenance cost (P) = Initial spending on maintenance+ Present worth (PW) of Spending on maintenance for four year

Present worth of Maintenance cost (P) = $40000 + $73037.5613= $113037.5613

As per the question the annual equivalent annual worth (EAW) of cost over a period of 6 year =?

So P=$113037.5613   i=19.6%   and N=6 year

EAW= $113037.5613(A/P,19.6%,6)

EAW= $113037.5613[{i(1+i)^N}/{(1+i)^N-1}]

EAW= $113037.5613[{0.196(1+0.196)⁶}/{(1+0.196)⁶-1}]

EAW= $113037.5613[{0.196(1.196)⁶}/{(1.196)⁶-1}]

EAW= $113037.5613(0.2977251876)= $33654.1292   

The annual equivalent annual worth (EAW) of cost over a period of 6 year = $33654.1292