Lecture notes Fundamentals of Finance (BS1612)

Week 3: Investment Appraisal 2: NPV and IRR
Discounted cash ow models
NPV
IRR

• Take account of all the relevant costs and bene ts and their timings
• Thus the time value of money
• Both are based in the entire life of project

NPV
Is the present value of cash in ows less the present value of cash out ows, discounted at the
company’s cost of capital.

Wealth maximisation:we must compensate nance providers for the risk that expected returns
might not materialise, the loss of purchasing power and time, The cost of capital would account
for these elements.

Decision rule:
NPV>0 (PV of in ows > PV of out ows, accept as the return is greater than the cost of capital.
NPV<0 (PV of in ows < PV of out ows), reject as the return is less than the cost of capital.

Competing projects:
The best project is the one with the highest NPV.




PV value of cash ows=
1818+2479+3757=8054

Less initial outlay of 10000

NPV=-1946

Decision Negative NPV, so reject the
project.

But when using the tables for nding
out the discount rate, what if the
Interest rates were 7.5% or 7.23%?




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, Annuities
A repetitive cash ow- where an investment pays out a constant sum for each year for a known
number of years.

Example:
A project gives cash in ows of £20000 at the end of
each year for 3 years. The cost of capital is 10%,
calculate the NPV.

(Keep discount rate at 10%)

Using annuity tables:
Annuity factor
(n=3, discount rate 10%) =2.4869

Multiply by constant cash ow
£20,000 x 2.4869 = 49,738

Perpetuities
An annuity that occurs in nitely.
Given by:
Example: An investment that pays out 2400 per
year inde nitely with a discount factor of 12%

PV= 2400/0.12
=20,000

(I=Rate of required return, in questions)




Di erentiating between project example:
A company has the funds to undertake one of the ooring 2 projects:

Project A:
Lasts 3 years-machine life 3 years
Machine cost- 90,000
Depreciated on straight line basis, no sv
Cost of capital 12%

Project B:
Lasts 3 yrs
Machine cost 80,000
Deprecitaed SLM, SV=15,000
Cost of capital 12%


Calculate the NPV of both projects and
advise which, if either should be
accepted.

Note for Project B: The SV is a relevant
cash ow and must be included.




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, Comparison:

Project A:NPV = 3423
Project B; 815

Decision: Accept project A, reject project
B.




Advantages of NPV
• Time value of money considered
• Consistent with principal with principal objective
• Uses cash ows
• Includes all relevant info
• Can deal with non-conventional cash ows (see IRR later)
• Additive- E.g Can add NPVs to show better information.

Disadvantages of NPV
• Can be di culty to understand
• Calculations can be complex
• Choosing the discount rate
• Cost of capital may change over the period
• No initial hep where capital is rationed- Output measure than input measure.

Internal Rate of Return

Similar to NPV method-involves
accounting cash ows

Gives the yield on an investment- the
discount rate that equates the present
value of cash in ows to the cash
out ows.

I.e the discount rate at which the NPV is
zero

Decision rule
If IRR>i, accept
If IRR<i, reject

(i=IRR set by management)

Steps for calculating for IRR
-Calculate the NPV of the project at the
given discount rate

-If the rst NPV is positive, calculate a new NPV at an estimated, but realistic, discount rate that s
higher that the rst. If the rst NPV is negative, caluctae a new NPV at an estimated, but realistic,
discount rate that is over than the rst.

The aim is to reach one positive and one negative NPV to locate the rate where NPV is 0.




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