Question

A company with a MARR = 10% is considering the two options shown

Each will produce annual benefits for 5 years and have no salvage value. The company is uncertain about the uniform annual benefits of the second option

Option #1: First Cost = $45,000, Uniform Annual Benefits each year for 5 years = $18,500

Option #2: First Cost = $62,000, Uniform Annual Benefits each year for 5 years = ???????

What is the breakeven point in terms of the Annual Benefits of option #2?

Answer 1

Step 1 : Identification of Alternatives

Option #1: First Cost = $45,000, Uniform Annual Benefits each year for 5 years = $18,500

Option #2: First Cost = $62,000, Uniform Annual Benefits each year for 5 years = ???????

MARR = 10%

Step 2 : Calculation of NPV in Option 1

Net Present Value = Present Value of Cash Inflows - Present Value of Cash Outflows

Particulars	Period	Amount	PVF @ 10%	Present Value
Cash Outflows:
First Cost	0	($45,000.00)	1	($45,000.00)
Cash Inflows:
Annual Benefit	1-5	$18,500.00	3.790786769	$70,129.56
Net Present Value				$25,129.56

NPV in Option 1 = $25,129.56

Step 3 : Calculation of breakeven point in terms of the Annual Benefits of option #2

In order to break even the NPV of Option should be equal to NPV of Option 2
Therefore, Required NPV of Option 2 = $25,129.56

Net Present Value = Present Value of Cash Inflows - Present Value of Cash Outflows
$25,129.56 = Present Value of Cash Inflows - $62,000
Present Value of Cash Inflows = $87,129.55

Annual Benefits per year of option 2 = Total of Present Value of Cash Inflows for 5 years / PVAF(10%,5)
Annual Benefits per year of option 2 = $87,129.55 / 3.790786769
Annual Benefits per year of option 2 = $22,984.56

Breakeven point in terms of the Annual Benefits of option #2 = $22,984.56

Note :
PVF(r,t) = (1/(1+r))^n
PVAF = (1/(1+r))^1 + (1/(1+r))^2 +...+(1/(1+r))^n