Discounting Future Cash Flows

HL Investment AppraisalP190-192 (Stimpson & Smith, 2012, Business &

Management for the IB Diploma Program)

Discounting Future Cash Flows

• When calculating the Average Rate of Return for project (ARR) it is important to discount future cash flows.

• This additional calculation considers the impact of inflation on the future returns from a project.

Future Cash Flows & Inflation(Example)

• If you were offered a $1000, today or in one years time, most people would take the money today. The pay today is preferred for these reasons:

It can be spent immediately and the benefits of this expenditure can be obtained immediately. This is not waiting.

The $1000 could be saved at the current rate of interest. The total cash plus interest will be greater than the offer of $1000 in one year’s time.

The cash today is certain , but the future cash offer is always open to uncertainty.

The Time Value of Money

• When we calculate how much money will be worth in the future, we are taking the “time value of money” into consideration.

• Discounting is the process of reducing the value of future cash flows to give then their value in today’s terms.

• How much less is future cash worth compared to today’s money?

• The answer depends on the rate of interest.

The Time Value of Money

• If $1000 received today can be saved at 10%, then it will growth to $1100 in one years time.

• Therefore $1100 in one years time has the same value as $1000 today at 10% interest.

• The value of $1000 is called the present value of $1100 received in one years time.

• Discounting calculates the present value of future cash flows so that investment projects can be compared with each other by considering the today’s value of their returns.

Discounting – How does it work?

The present value of a future sum of money depends on two factors:• The higher the interest rate, the less value

future cash has in today’s money. • The longer into the future cash is received, the

less value it has today

Two Variables: Interest Rates & Times

• The two variables – interest and time are used to calculate discount factors

• You do not have to calculate these percentages – they are given in an IB table, which can be used in exams.

Discount Table - ExampleYear 6% 8% 10% 12% 16% 20%

1 .94 .93 .91 .89 .86 .832 .89 .86 .83 .79 .74 .693 .84 .79 .75 .71 .64 .584 .79 .74 .68 .64 .55 .485 .75 .68 .62 .57 .48 .406 .72 .63 .56 .51 .41 .33

How to use this table: ExampleA company anticipates that a project will generate a return of $3000 in 3 years time. The current interest rate is 10%. The discount factor to be used is .75. This means that $1 received in 3 years time is worth 75 cents today. The discount factor is multiplied by $3000 and the present value is $2250.

Net Present Value (NPV)

Net Present Value (NPV)• Today’s value of the estimated cash flows

resulting from an investment.• It requires you to calculate the discount rate in

various years to get the total discounted cash flows and subtract the initial investment.

How to calculate Net Present Value (NPV) of a Project over several years: (example)

Year Cash Flow Discount Factors @ 8%

Discounted Cash Flows (DCF)

0 ($10,000) Initial Investment

Not Applicable

1 $5000 .93 $4650

2 $4000 .86 $3440

3 $3000 .79 $2370

4 $2000 .74 $1480

Net Present Value is now calculated:

Total Discounted Cash Flows = $ 11,940 (4560+3440+2370+1480)Subtract Original Investment = - $(10,000)NPV (Net Present Value) $1940

Analysis of NPV Example

• In the previous example, the project earns $1940 in today’s money value.

• So if the finance can be borrowed at an interest rate of less than 8% the investment will be profitable.

• What would happen to the NPV if the discount rate was raised, perhaps because interest rates have increased?

• This would reduce NPV as future cash flows are worth even less when they are discounted at a higher rate.

What discount rate will a business use?

• Usually a business will choose a rate of discount that reflects the interest cost of borrowing the capital to finance the investment.

• Even if the finance is raised internally, the rate of interest should still be used to discount future returns.

• This is because the opportunity cost of internal finance – it could be left on deposit in the bank to earn interest.

What discount rate will a business use?

• An alternative approach to selecting the discount rate to be used is for a business to adopt a cut-off or criterion rate.

• The business would use this to discount the returns on the project and, if the net present value is positive, the investment could go ahead.

Advantages & Disadvantages of NPVAdvantages of Net Present Value (NPV) Disadvantages of Net Present Value (NPV)I

* It considers both the timing of cash flows and the size of them in arriving at an appraisal.

* It is reasonably complex to calculate and to explain to non-numerate managers!

* The rate of discount can be varied to allow for different economic circumstances. For instance, it could be increased if there is a general expectation that interest rates were about to rise.

* The final result depends greatly on the rate of discount used, and expectations about interest rates may be inaccurate.

* It considers the time value of money and takes the opportunity cost of money into account.

* Net present value can only be compared with other projects, but only if the initial capital cost is the same. This is because the method does not provide a percentage rate of return on investment.

Exercises – Discounting Future Cash Flows

• A company spends a $855,000 on a new fleet of five trucks.

• It is anticipated that the trucks will generate the following new revenue each year:

• Year 1: $275,000• Year 2: $305,000• Year 3: $310,000• Year 4: $299,000• The discount rate is 20%.• Calculate the discounted cash flow for each year and the

Net Present Value (NPV) at the end of the 4 year period.