## Special Case 2: Interest Rate Not Given – Use IRR

### When does this arise?

The question gives Fair Value, annual lease rentals, lease term, and UGRY/GRV — but does not give the interest rate or discount rate.

### Concept

The interest rate implicit in the lease is defined in AS 19 as the rate that equates the present value of future cash flows to the Fair Value (cost) of the asset on Day 1:

> `Fair Value = PV of (Lease Rentals) + PV of UGRY`

> Find r such that this equation holds → that r is the IRR

This is identical to the Internal Rate of Return (IRR) used in financial mathematics.

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### Method to Find IRR (Trial & Error / Interpolation)

Step 1 – Pick two trial rates (one giving PV > Fair Value, one giving PV < Fair Value)

Step 2 – Compute PV at each trial rate

Step 3 – Interpolate

```

IRR = Lower Rate + [ (PV at Lower Rate − Fair Value) / (PV at Lower Rate − PV at Higher Rate) ] × (Higher Rate − Lower Rate)

```

Step 4 – Once IRR is known, proceed normally:

Net Investment = Fair Value
Build the finance charge schedule using IRR as the interest rate

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### Key Point

Once you have the IRR, the rest of the lessor accounting is identical to the standard finance lease procedure — the IRR simply replaces the given interest rate.

Worked example

### Example 1

Conceptual illustration (detail to be covered in FM subject)

Given: Fair Value = ₹X | Annual LR = ₹Y p.a. | Term = n years | UGRY = ₹Z

Find r (IRR) such that:

`Y × PVAF(n, r) + Z × PVF(n, r) = X`

Try r₁ → PV₁; Try r₂ → PV₂

If PV₁ > X > PV₂:

`IRR = r₁ + [(PV₁ − X) / (PV₁ − PV₂)] × (r₂ − r₁)`

Once IRR is found:

Net Investment = Fair Value
Build schedule: Interest each year = Opening Balance × IRR
GI, NI, UFI computed as normal

⚠️ Common exam mistakes

Attempting to solve the IRR equation algebraically instead of using trial-and-error interpolation.
Using an arbitrary rate (e.g., 10%) as a default when the rate is not given instead of solving for IRR.
Applying interpolation with PV values that are both above or both below Fair Value (must straddle the target).
Forgetting that once IRR is established, Net Investment still equals Fair Value of the asset (not a separately calculated PV).
Mixing up IRR calculation (lessor perspective) with lessee's implicit rate calculation – the concept is the same but the inputs may differ slightly.

Bare-Act text Para 3 – Definitions · AS 19 – Leases (ICAI) · click to expand

The interest rate implicit in the lease is the discount rate that, at the inception of the lease, causes the aggregate present value of (a) the minimum lease payments under a finance lease from the standpoint of the lessor; and (b) the unguaranteed residual value accruing to the lessor, to be equal to the fair value of the leased asset.

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AS 19 Leases – Special Case 2: Interest Rate Not Given (Find IRR)

Worked example

⚠️ Common exam mistakes