Present Worth Analysis - Worked Examples

Example 1 — Project PW: first cost PHP 2.0M, annual net inflow PHP 600k for 5 years, salvage PHP 300k, MARR 10%.

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Example 2 — Cost-only comparison over 6 years at 8%: A costs PHP 3.0M + 400k/year with 500k salvage; B costs PHP 3.6M + 280k/year with 650k salvage.

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Example 3 — Discount a PHP 900k rehabilitation cost occurring at year 4 using 7%.

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Example 4 — Present worth of a PHP 250k/year maintenance cost forever at 5%, plus PHP 4M initial cost.

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Example 5 — Determine the maximum first cost for a project yielding PHP 350k/year for 6 years plus PHP 200k salvage at a 9% MARR.

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Example 6 — Compare two mutually exclusive revenue alternatives with PW values PHP 420k and PHP 510k at the same MARR and study basis.

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Example 7 — Disposal cost: an asset requires PHP 600k environmental cleanup at year 12. Find its PW at 6%.

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Example 8 — A project has PHP -1.5M at t=0, +500k at year 2, +700k at year 4, and +800k at year 6. Find PW at 8%.

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Example 9 — Explain why a 4-year machine and an 8-year machine should not be compared using one-cycle PW if service is required for 8 years.

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Example 10 — Sensitivity: a project PW is PHP 120k at 8% and PHP -40k at 12%. What can be concluded without calculating IRR?

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Example 11 — Bond valuation: face value PHP 1.0M, 8% annual coupon paid semiannually, 5 years remaining, and market yield 10% nominal compounded semiannually. Find the bond value.

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Example 12 — Premium bond: face value PHP 1.0M, annual coupon PHP 120k, 5 annual payments remaining, market yield 9% effective annually. Find the bond value.

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Example 13 — A bond pays semiannual coupons but an analyst discounts them using a 10% annual effective rate as if each half-year were one full year. Identify the error.

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