Question

What is the equivalent annual worth of a 20 year project that has a $2 million initial cost, annual operating costs of $75,000 and annual benefits of $250,000? Assume a discount rate of 7.3%.

options:

-$188,501

-$18,210

$18,210

$188,501

None of the above

Answer 1

Initial Cost = $2,000,000

Annual Operating Cost = $75,000

Annual Benefits = $250,000

Project Life = 20 years

Discount Rate = 7.3%

Calculate the Equivalent Annual Worth

Step – 1

Calculate the Net Annual Cash Flow

NACF = Annual Benefits – Annual Operating Cost

NACF = $250,000 – $75,000 = $175,000

Step – 2

Calculate the EAW

EAW = -$2,000,000 (A/P, 7.3%, 20) + $175,000

EAW = -$2,000,000 (0.0966049) + $175,000

EAW = -$193,210 + $175,000

EAW = -$18,210

Answer = -$18,210

Note –

To calculate the value of (A/P, 7.3%, 20), use the alternative formula of (A/P)

Formula = 0.073 (1+0.073) ²⁰ ÷ (1+0.073) ²⁰ – 1