Video summary

ACCA FM SEP 2026 | Lecture 7 | Perpetuity Cash Flows & NPV Explained | Chinmay Shah

Main summary

Key takeaways

Educational

Main ideas / lessons conveyed

  • Perpetuity cash flows (present value) depend on whether payments start immediately or start later.
  • Key exam skill: identify the type of perpetuity cash flow:
    • Perpetuity starting now (first payment at year 0)
    • Perpetuity starting later (first payment at some later year; e.g., “starting from year 4”)
    • Perpetuity with growth (payments grow each year by a constant rate)
  • Logical valuation method: the lecturer emphasizes the “why” behind shifting cash flows to the correct time point (often one year before the perpetuity begins), rather than memorizing blindly.
  • NPV assembly:
    • NPV = (initial investment, negative) + PV of the perpetuity component
  • Constraints for perpetuity with growth:
    • Growth rate must be lower than the discount rate (otherwise the formula breaks / becomes invalid).
  • Next chapter direction: after perpetuity and NPV logic, the lecture moves toward IRR and contrasts it with other appraisal measures.

Methodologies / formulas / step-by-step instructions

A) PV of a perpetuity starting later (payments begin after year 1)

Core logic taught:

  • If perpetuity payments begin at the end of year (k), compute PV as of:
    • the year just before perpetuity begins (i.e., one year before the first perpetuity payment),
    • then discount back to the valuation base (often year 0).

Why “one year before”?

  • The lecturer repeatedly asks: “Why take one year before perpetuity starts?”

Generic structure (conceptual):

  1. Determine the level payment (C), discount rate (r), and the timing of the first perpetuity payment.

  2. Convert the perpetuity into a PV at the “one year before it starts” point:

    • [ PV = \frac{C}{r} ]

  3. Discount that PV back to year 0 using the appropriate discount factor.

Then compute NPV:

  • [ NPV = -\text{Initial investment} + PV(\text{perpetuity starting later}) ]

B) PV of a perpetuity starting now

Core logic taught:

  • Payments start at year 0 and continue forever at constant amount (C).
  • Because there is a cash flow immediately at year 0, PV is simpler and requires handling the immediate year-0 payment effect (often via an “add 1”-type expression in the lecturer’s approach).

Conceptual computation:

  • If the PV of an ordinary perpetuity is ( \frac{C}{r} ) at year 1, then starting now adds the immediate payment and effectively shifts timing.

NPV:

  • [ NPV = -\text{Initial investment} + PV(\text{perpetuity starting now}) ]

C) Using a “logical method” / flagging method for timing

The lecture uses a timing intuition:

  • Mark where perpetuity begins.
  • Conceptually “wait” until the first payment time.
  • Apply a method that:
    • treats the last cash flow period correctly,
    • then pulls the perpetuity PV to the correct earlier point (often one year before the start).

D) NPV shortcut used in worked examples (perpetuity starting later)

The lecturer’s repeated workflow:

  • Identify the cash flows and timing.
  • Use perpetuity PV as of the correct reference time.
  • Discount back to year 0.
  • Add to initial investment to get NPV.

Exam warning (timing/assumptions):

  • Be careful about whether you discount using a table vs direct calculator discounting.

E) PV of perpetuity with growth

Given:

  • First cash flow (C_1) at the end of year 1 (as framed in the formula)
  • Growth rate (g)
  • Discount rate (r)

Logic emphasized:

  • Growth can be handled by using an adjusted rate:
    • if cash flows grow at (g), effective discounting behaves like (r - g).
  • The lecturer frames it as:

    instead of growing the cash flow, we are reducing the discounting cost.

Final formula:

  • [ PV = \frac{C_1}{r-g} ]

NPV with perpetuity with growth:

  • [ NPV = -\text{Initial investment} + \frac{C_1}{r-g} ]

Important condition:

  • Must have (g < r), otherwise the denominator becomes invalid and the formula fails.

F) Worked structure for an uneven cash flows + perpetuity with growth problem

For complex problems (uneven cash flows early, then growth perpetuity later), the lecture suggests:

  1. Step 1 (uneven cash flows):

    • Compute PV of irregular cash flows for years 1–3 using standard discounting at rate (r).

  2. Step 2 (perpetuity with growth starting later):

    • Compute PV of the growing perpetuity beginning after year 3 (e.g., from year 4 onward).

    • Use: [ PV_{\text{at reference}}=\frac{C_{\text{first}}}{r-g} ]

    • Discount that PV back to the appropriate earlier year (often year 3 or year 0 depending on the reference used).

  3. Step 3 (combine):

    • Add PV from Step 1 and Step 2.
    • Subtract initial investment to get NPV.

Timing warning (first-payment timing):

  • If growth perpetuity begins “from year 4,” the first growing-perpetuity cash flow occurs at the end of that first year of the perpetuity stream.
  • The lecturer highlights common “year 4 vs year 5” timing mistakes.

G) IRR introduction and contrast request (wrap-up)

Definition:

  • IRR = internal rate of return of the project.

Method taught (high level):

  • Use NPV logic and compute NPV at trial discount rates (trial-and-error).
  • IRR is the rate that makes:
    • NPV = 0

Homework mentioned:

  • Compute NPV at 5%, 10%, 15%, 20%, then proceed to IRR later.

Comparison mentioned:

  • IRR uses discounting
  • ROCE / return on capital employed uses profits (not discounting) (The comparison is referenced but not fully completed in the provided subtitles.)

Speakers / sources featured (all identified)

  • Chinmay Shah (lecturer; addressed repeatedly as “sir,” and credited in video title)
  • Students / participants (responding with short answers like “Yes sir,” “Positive,” and numeric inputs)
  • Examiner (referenced as a source of exam assumptions, including discounting-table usage)

Original video