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3 Net Present Value

A particular rate of interest is used to discount future flows of cash to present values. The discount rate used might reflect the cost of obtaining capital, or a target rate/cut-off rate,or a risk-adjusted rate. Once the future cash flows are discounted to present-day values they are totalled and compared with the cost of the project. If the discounted cash flows exceed the cost the difference is the net cash flow. In general, if the NPV is positive the project is worth considering.

Example:

A company wishes to evaluate a capital project based on the following information. The initial outlay is £100,000 and the project has an economic life of 5 years and realises £5,000 when it is sold at the end of year 5. The profits after depreciation have been estimated as year 1-3 £10,000 and £15,000 in the final two years. The rate of interest is 10%.

Year

Cash flow

Discount factor

Present value

Cumulative PV

£

£

£

0

(100,000)

1

(100,000)

1

29,000

0.909

26,361

26,361

2

29,000

0.826

23,954

50,315

3

29,000

0.751

22,939

73,254

4

34,000

0.683

23,222

94,476

5

34,000

0.621

21,114

117,590

6

5,000

0.564

2,820

120,410

---------

NPV =20,410

--------

Since theNPV is +£20,410, the project is worthwhile.

4 Discounted payback

In the calculation of the NPV in the previous example a column records the cumulative present value of the cash flows. Since the payback method is criticised for ignoring the time value of money it is possible to remedy this shortcoming by using the discounted cash flows to ascertain the payback period.

In this example, the payback period is just over 4years. There is a shortfall of £5,524 which has to be generated in year 5.

£5,524 365 days

--------- x = 17 days

£117,590

The discounted payback period is 4yrs. 17 days.

5 Internal Rate of Return

Sometimes the company wishes to know the internal rate of return (IRR) ie. the yield of a capital project. The company may operate a cut-off point in respect to projects and should a project’s yield be below this target or threshold it will be rejected. The method is to discount cash flows using different discount rates until the NPV = 0. At that point the total present value of the cash flows is equal to the outlay on the project. The discount rate which produces a NPV = 0 is the internal rate of return of the project. In effect, the company could borrow money at a rate of interest equal to the internal rate of return to finance the project and the returns from the project would allow the company to break even. If the company’s target rate of return for capital projects is less than a project’s yield (IRR) the project is worth consideration.

Example:

Using the data from the previous NPV example work out the projects IRR.

At a discount rate of 10% the NPV = +£20,410. To produce a negative NPV a higher discount rate needs to be chosen. The method proceeds on a trial and error basis. What is the result if a discount rate of 20% is used.

Year

Cash flow (£)

Discount factor 20%

Present Value (£)

0

(100,000)

0

(100,000)

1

29,000

0.833

24,157

2

29,000

0.694

20,126

3

29,000

0.579

16,791

4

34,000

0.482

16,388

5

34,000

0.402

13,668

6

5,000

0.335

1675

--------

NPV= - 7,245

-------

To determine the discount rate which produces NPV = 0 a process of interpolation is used. Alternatively, it may be solved graphically.

The formula for interpolation is:

IRR = A + [ a / a -b ] x ( A - B )

10% + £20,410

---------------- X 20% - 10% = 17%

(£20,410 + £7,245)

The yield or IRR of the project is 17%. If this is higher than the company’s target rate for projects it is worth consideration.

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