Present Value and Discounted Cash Flows

Present Value Formula

• For a fixed market interest rate $r$, the present value of a single cash flow $C$ that is discounted $n$ periods backwards is:

$PV = \frac{C}{(1 + r)^n}$

Interest Rate and Present Value

Example

• If you want to get £1,000 in three years with an annual interest rate of 6%, compounded semi-annually:-

  • The interest rate is applied twice a year.

  • Semi-annual interest rate: $6\%/2 = 3\%$

  • Number of compounding periods in three years: 6 times

    $PV = \frac{£1000}{(1 + 3\%)^6} = £837.48$

Discounted Cash Flow - Investment Decision Making

• Investment involves an outlay of economic value (usually cash) at one point in time, which is expected to yield economic benefits at some other point in time.

• The outlay usually precedes the benefits.

• The outlay is typically a single large amount, while the benefits arrive as a series of smaller amounts over a protracted period.

Importance of Investment Decisions

• Large amounts of resources are often involved.

• It is often difficult and/or expensive to bail out of an investment once it has been undertaken.

Investment Appraisal Methods

• Discounted cash flow methods

  • Net Present Value (NPV)

  • Internal Rate of Return (IRR)

• Non-discounted cash flow methods

  • Accounting Rate of Return

  • Payback Period

Net Present Value (NPV)

• The NPV method considers all costs and benefits of each investment opportunity and makes a logical allowance for the timing of those costs and benefits.

• Time is important because people do not normally see an amount paid out now as equivalent in value to the same amount being received in a year’s time.

Reasons why £100 received in a year’s time is not equal in value to £100 paid immediately:

• Interest lost

• Risk

• Inflation

Application of the NPV Method

• Compare the investment with an alternative investment with similar risk.

• Calculate the present value of cash inflows and outflows.

$NPV = PV(Cash Inflows) - PV(Cash Outflows)$

Example

• Initial costs: £100,000

• Cash flows:

  • CF1: £20,000

  • CF2: £40,000

  • CF3: £60,000

  • CF4: £60,000

  • CF5: £40,000

• Discount rate: $r = 20\%$

• Calculations:

  • $PV(£20,000) = \frac{£20,000}{(1 + 20\%)^1} = £16,667$

  • $PV(£40,000) = \frac{£40,000}{(1 + 20\%)^2} = £27,778$

  • $PV(£60,000) = \frac{£60,000}{(1 + 20\%)^3} = £34,722$

  • $PV(£60,000) = \frac{£60,000}{(1 + 20\%)^4} = £28,935$

  • $PV(£40,000) = \frac{£40,000}{(1 + 20\%)^5} = £16,075$

• Total PV (Cash Inflows) = £124,177

• Total PV (Cash Outflows) = -£100,000

• $NPV = -£100,000 + £124,177 = £24,177$

NPV Rules - Project

• A positive net present value means that undertaking this project can add value to the company, while a negative net present value indicates a loss in value.

• Therefore, there is no reason for a fashion brand to accept a project with a negative NPV.

Why the NPV Method is better

• The timing of the cash flows: NPV takes account of the time value of money by discounting the various cash flows.

• The whole of the relevant cash flows: NPV includes all of the relevant cash flows.

• The objectives of the business: NPV is the only method of appraisal in which the output of the analysis has a direct bearing on the wealth of the owners of the business.

• Positive NPVs enhance wealth; negative ones reduce it.

NPV Rules

• If the NPV is positive, the project should be accepted; if it is negative, the project should be rejected.

• If there are two (or more) competing projects that have positive NPVs, the project with the higher NPV should be selected.

NPV Rules - What else?

• Why is a fashion company undertaking a project? Either to get ahead of its competitors or to catch up with them.

• Projects also need to consider budget and how to finance them.

• Risks and time of the project.

• Net present value is the primary financial investment indicator, while other key performance indicators may focus on other aspects such as sustainability.