Investment appraisal & NPV

Chapter 8

Capital budgeting decision

investment into non-current assets that are long-lived and not easily reversed once made, some options for the firm and others arent

Net present value (NPV)

The difference between an investments market value and its initial cost of the investment. Identifying in advance whether investing is a good idea, determine whether its worth more than it costs.

• CFt​ = cash flow in year t

• r = discount rate (required rate of return)

• C0= initial investment cost

E.g. compare what renovated properties are selling for in the market, then estimate cost of buying a property and bringing it to market. Estimated total cost and estimated market value, if difference is positive then its worth undertaking.

• ✅ Accept if NPV > 0 (adds value)

• ❌ Reject if NPV < 0 (destroys value)

• ⚖ Indifferent if NPV = 0

Discounted cashflow valuation (DCF)

The process of valuing an investment by discounting its future cashflows. 

Hard to estimate market value when its not routinely bought and sold, so we use this to calculate the present value of the cashflows. With the estimate we then estimate NPV as difference between present value of future cashflows and cost of investment. 

• NPV directly measures the value created or destroyed by a project.

• It accounts for both timing and risk (via discount rate).

• The most reliable capital budgeting tool — other methods (like payback or IRR) are useful but have limitations.

NPV worked example

• Annual revenue = £20,000

• Annual costs = £14,000

• Net annual cash flow = £6,000

• Project life = 8 years

• Salvage value = £2,000 (at end of year 8)

• Initial cost = £30,000

• Discount rate = 15%

Identify cashflows: Year 0 (30,000)    Years 1-8 +6,000 each yr       8 +2,000 (salvage value)

Calculate PV annuity of annual cash inflows:

£6,000 per yr x (1 - (1 + 0.15)^-8 (yrs)/ 0.15 = 26,922

Add PV to the £2,000 salvage value: 2,000/ (1.5)^8 = 654 + 26,922 = £27,576 total PV inflows

Subtract initial investment: 27,576 - 30,000 = -£2,424 NPV

• The NPV is negative, meaning the project reduces firm value by £2,424.

• If there are 1,000 shares, each share’s value would drop by £2.42.

Payback Period (PB)

The payback period is the time it takes to recover the initial investment from the project’s cash inflows.

Payback Period = Years before recovery + Remaining amount to recover​ / Cash flow in following year

• Accept if PB ≤ target cutoff (e.g. 2 years).

• Reject otherwise.

Advantages:

• Simple and intuitive.

• Favours liquidity (quick cash recovery).

Limitations:

• Ignores time value of money.

• Ignores cash flows after cutoff.

• Cutoff period is arbitrary.

Payback period example

Investment = £60,000
Year 1 inflow = £20,000
Year 2 inflow = £90,000

After 1 year → £20,000 recovered; £40,000 left.
In Year 2, recover £40,000 out of £90,000 → 40,000/90,000 =0.44 of the year.
➡ Payback = 1.44 years

Discounted Payback Period

The time it takes for the discounted cash inflows to equal the investment cost — adjusts for time value of money.

DPB = Year before DPB occurs + (Cumulative Discounted Cash flow in year before recovery ÷ Discounted cash flow in year after recovery).

Discounted Payback Period Example

• Cost = €300

• Cash inflow = €100 per year for 5 years

• Discount rate = 12.5%

Year	Cash Flow (€)	Discount Factor (12.5%)	PV (€)	Cumulative PV (€)

1

100

0.889

88.9

88.9

2

100

0.790

79.0

167.9

3

100

0.702

70.2

238.1

4

100

0.624

62.4

300.5

5

100

0.555

55.5

356.0

✅ Discounted Payback = 4 years

• The project “pays back” in 4 years when time value is included.

• NPV = €55, meaning this is a good investment.

• If discounted payback occurs → NPV must be ≥ 0.

Average Accounting Return (AAR)

Measures profitability using accounting data, not cash flows.

AAR = Average Net income/ Average Book value

Example:

• Investment = £500,000 (depreciated straight-line over 5 years)

• Book value averages (£500,000 + 0)/2 = £250,000

• Average Net Income = £50,000 per year

AAR = 50,000/250,000 = 20%

✅ Rule: Accept if AAR > target rate (e.g. 20%).

Limitations:

• Ignores time value of money.

• Based on accounting profits, not cash flows.

• Arbitrary target cutoff.

Internal Rate of Return (IRR)

The discount rate that makes NPV = 0.

Example:
Investment = €100 → Cash inflows = €60/year for 2 years.
Find IRR such that NPV = 0:

At 10% → NPV = €9.1
At 15% → NPV = –€2.5
➡ IRR ≈ 13.1%

✅ Rule: Accept if IRR > required return.

Advantages:

• Easy to understand (“return” language).

• Does not require knowing discount rate.

Limitations:

• Multiple IRRs possible with non-conventional cash flows.

• Can conflict with NPV for mutually exclusive projects.

Modified Internal Rate of Return (MIRR)

Purpose:
Solves the multiple IRR problem by modifying cash flows before calculating return.

Approaches:

1. Discounting Approach: Discount all negative CFs to time 0.

2. Reinvestment Approach: Compound positive CFs to the end.

3. Combination Approach: Discount negatives + compound positives.

Produces a single MIRR value.

Profitability Index (PI)

PI = Present Value of future cash inflows / initial investment

Example:
PV of cash inflows = €220, Cost = €200

PI=220/200=1.1PI = 220 / 200 = 1.1PI=220/200=1.1

✅ Rule: Accept if PI > 1.

Interpretation:
For every €1 invested, €1.10 of value is created (i.e. €0.10 NPV per euro).

Capital Budgeting in Practice

• NPV and IRR are most used in real-world corporate finance.

• Payback and AAR often used for small or quick decisions.

• Firms combine methods: e.g. Require both NPV > 0 and Payback < 3 years.

• Industry matters:

  • Predictable cash flows → use NPV (e.g. oil & gas).

  • Uncertain cash flows → avoid NPV (e.g. film industry).