Rate of Return Analysis - Worked Examples

Rate of Return Analysis - Worked Examples

0 of 2 Steps Completed

0 of 2 Steps Completed

0 of 2 Steps Completed

0 of 2 Steps Completed

0 of 2 Steps Completed

0 of 2 Steps Completed

0 of 2 Steps Completed

0 of 3 Steps Completed

0 of 2 Steps Completed

0 of 2 Steps Completed

0 of 3 Steps Completed

0 of 2 Steps Completed

0 of 4 Steps Completed

Rate of Return Analysis - Worked Examples

Example 1 — Find the IRR of PHP -1.0M now followed by PHP 300k/year for 5 years.

Step-by-Step Solution

Example 2 — Apply the MARR rule to Example 1 if MARR is 12%.

Step-by-Step Solution

Example 3 — The same project has MARR 18%. What is the decision?

Step-by-Step Solution

Example 4 — Estimate IRR from NPV values +PHP 80k at 10% and -PHP 20k at 14% using linear interpolation.

Step-by-Step Solution

Example 5 — Identify multiple-root risk for cash flows -100, +230, -132.

Step-by-Step Solution

Example 6 — Why is no IRR percentage needed when all project cash flows are nonnegative?

Step-by-Step Solution

Example 7 — Two mutually exclusive alternatives have stand-alone IRRs 30% and 22%. Can the 30% alternative be selected immediately?

Step-by-Step Solution

Example 8 — Incremental decision: B costs PHP 500k more than A and produces PHP 140k/year additional net cash flow for 5 years. MARR is 10%.

Step-by-Step Solution

Example 9 — Incremental ROR is 8% while MARR is 11%. Which alternative survives?

Step-by-Step Solution

Example 10 — An NPV profile has roots at 5% and 25%, while MARR is 12%. Why is saying IRR = 25% insufficient?

Step-by-Step Solution

Example 11 — Modified rate: negative-flow PW magnitude is PHP 1.2M, positive-flow FW at the chosen reinvestment rate is PHP 2.1M at year 6.

Step-by-Step Solution

Example 12 — Cross-check: a conventional project has IRR 14% and MARR 10%, but a spreadsheet reports negative NPV at 10%. What should you do?

Step-by-Step Solution

Example 13 — Repeated-root case: cash flows are +PHP 0.25M at t=0, -PHP 1.00M at year 1, and +PHP 1.00M at year 2. Show why an IRR can exist without an NPV sign crossing.

Step-by-Step Solution

$Example 1 — Find the IRR of PHP -1.0M now followed by PHP 300k/year for 5 years.$

$Example 2 — Apply the MARR rule to Example 1 if MARR is 12%.$

$Example 3 — The same project has MARR 18%. What is the decision?$

$Example 4 — Estimate IRR from NPV values +PHP 80k at 10% and -PHP 20k at 14% using linear interpolation.$

$Example 5 — Identify multiple-root risk for cash flows -100, +230, -132.$

$Example 6 — Why is no IRR percentage needed when all project cash flows are nonnegative?$

$Example 7 — Two mutually exclusive alternatives have stand-alone IRRs 30% and 22%. Can the 30% alternative be selected immediately?$

$Example 8 — Incremental decision: B costs PHP 500k more than A and produces PHP 140k/year additional net cash flow for 5 years. MARR is 10%.$

$Example 9 — Incremental ROR is 8% while MARR is 11%. Which alternative survives?$

$Example 10 — An NPV profile has roots at 5% and 25%, while MARR is 12%. Why is saying IRR = 25% insufficient?$

$Example 11 — Modified rate: negative-flow PW magnitude is PHP 1.2M, positive-flow FW at the chosen reinvestment rate is PHP 2.1M at year 6.$

$Example 12 — Cross-check: a conventional project has IRR 14% and MARR 10%, but a spreadsheet reports negative NPV at 10%. What should you do?$

$Example 13 — Repeated-root case: cash flows are +PHP 0.25M at t=0, -PHP 1.00M at year 1, and +PHP 1.00M at year 2. Show why an IRR can exist without an NPV sign crossing.$