Question

Find the equivalent uniform annual worth of the following cash flow. Assume the interest rate of 7.78% per year compounded quarterly.

	Project A
First cost	$1,000,000
Annual operating cost	$100,000
Annual income	$150,000
Overhaul cost every 5 years	$200,000
Salvage value	$400,000
Life in years	40 years

Answer 1

Effective interest rate = (1+0.0778/4)^4 -1

= (1+0.01945)^4 -1

= 1.080099 - 1

= 8.0%

NPW of the project = -1000000 + (150000 -100000)*(P/A,8%,40) - 200000 * ((P/F,8%,5) + (P/F,8%,10) + (P/F,8%,15) + (P/F,8%,20) + (P/F,8%,25) + (P/F,8%,30) + (P/F,8%,35)) + 400000 * (P/F,8%,40)

= -1000000 + 50000*11.924613 - 200000 * (0.680583 + 0.463193 +0.315242 +0.214548 + 0.146018 +0.099377 + 0.067635) + 400000 *0.046031

= -782676.15

Equivalent annual worth = -782676.15 * (A/P,8%,40) = -782676.15 * 0.083860 = -65635.35