Question

Given the following alternatives and cash flows:

Alternative #1 has an investment of $25,000 and an annual income of
$6,000/year for eight years.

Alternative #2 has an investment of $35,000 and an annual income of
$12,500/year for four years

If MARR = 12% What is the the difference in present worth
AW_{2} - AW_{1} assuming repeatability?

-$1,631 |
||

$9 |
||

$1,631 |
||

-$1,839 |

Answer #1

**NPV of Alternative #1**

Net Present Value = Present Value of annual cash inflows – Initial Investment

= $6,000[PVIFA 12%, 8 Years] - $25,000

= [$6,000 x 4.96764] - $25,000

= $29,806 – 25,000

= $4,806

Annual Worth = Net Present Value / [PVIFA 12%, 8 Years]

= $4,806 / 4.96764

= $968

**NPV of Alternative #2**

Net Present Value = Present Value of annual cash inflows – Initial Investment

= $12,500[PVIFA 12%, 5 Years] - $35,000

= [$12,500 x 3.03735] - $35,000

= $37,967 - $35,000

= $2,967

Annual Worth = Net Present Value / [PVIFA 12%, 5 Years]

= $2,967 / 3.03735

= 977

**The difference in present worth AW2 - AW1**

The difference in present worth AW2 - AW1 = AW - Alternative #2 - AW - Alternative #1

= $977 – 968

= $9

**“The difference in present worth AW2 - AW1 =
$9”**

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