Lecture 7 - NPV and PI Flashcards
(22 cards)
- What is NPV?
- First, let’s recall present value (PV) and future value
(FV)
Present value (PV): the value of the assets (cash flows) now.
Future value (FV): the value of the assets (cash flows)
on a specific date in the future.
PV = FV/(1+R)T and FV = PV * (1+R)T
where R is the discount rate, T is the number of period,
PV is the present value of the cash flow and FV is the
future value of the cash flow.
- Then, what is the present value of a series of cash
flows?
- In this case, you can take this series of cash flows as a
special case of an annuity. - For a conventional annuity, we start receiving annual
payments in one year and the annual payments are
identical. - For this special case, there is a cash flow occurs at the
beginning (time point 0), and the annual cash flows
may not be identical. - The present value of this special case is called the net
present value (NPV)
Net present value (NPV)
- An example of NPV
Given required rate of return is 10%, what is the NPV of
following cash flows?
Points in time
(Yearly intervals)
Cash flows (£)
0 -10
1 10
2 8
3 10
4 8
5 10
- Example Illustration (breakdown to each year)
Year/Cash flow(FV)/PV
0 -10 -10
1 10 10/(1+10%)
2 8 8/(1+10%)2
3 10 10/(1+10%)3
4 8 8/(1+10%)4
5 10 10/(1+10%)5
- Example Illustration
- The NPV of these cash flows is the present values of all individual cash flows.
- NPV = -10 + 10/(1+10%) + 8/(1+10%)2 +
10/(1+10%)3 + 8/(1+10%)4 +10/(1+10%)5
= £24.89
Net present value (NPV)
- Net present value (NPV) is simply the sum of
present values of all cash flows (including the
one occurring at time 0). - The general formula of NPV
Where CFt is the cash flow occurring at time
point t and R is the required rate of return (or
interest rate or cost of capital or discount rate…).
NPV and investment decision
- For a business project, normally, there is an initial
cost (cash outflow) at the beginning of the
project. And then, the project will generate gross
profits (cash inflows) in the future during the life
of the project. - Should we invest in this project? (Are those
future cash inflows enough to cover the initial
cash outflow? ) - The NPV approach can be applied on project
appraisal to make investment decisions.
NPV and investment decision 2
- The NPV of a project is the sum of present
values of all future cash flows and deduct the
initial outlay. - The NPV rule in investment decision
- If NPV ≥ 0, the project should be accepted.
- If NPV< 0, the project should be rejected.
- The NPV approach
- It takes time value of money (we calculate PV
of each cash flow!) into consideration. - If NPV ≥ 0, it indicates the future gross profits
are enough to offset the initial cash outlay,
and the project will make a profit. - If NPV< 0, it indicates the future gross profits
are not enough to cover the initial cash outlay,
the project will suffer a loss.
- Example
A company is examining two projects, A and B, the
cash flows are as follows:
Points in time
Cash flows (£)
(Yearly intervals)
A B
0 (cash outlay)
1
2 250,000 250,000
3 200,000 20,000
100,000 120,000
20,000 220,000
- Example
Using required rate of return (discount rate) of 8%, and then 16%, calculate the NPVs and state which project is superior.
NPV and investment decision
* Example illustration
When R = 8%
NPVA = -250,000+200,000/(1+8%)+100,000/(1+8%)2
+20,000/(1+8%)3 = 36,796
NPVB = -250,000+20,000/(1+8%)+120,000/(1+8%)2
+220,000/(1+8%)3= 46,043
- Example illustration
Using an 8% discount rate, both projects produce
positive NPVs, according to the NPV rule, If NPV ≥ 0,
the project should be accepted, so both projects
should be accepted (if they are not mutually
exclusive). Between two projects, B is superior
because it creates more value (higher positive NPV)
than project A. If projects are mutually exclusive,
only up to one project can be accepted.
* What if the discount rate is 16%?
- Example illustration
When R = 16%
NPVA :
-250,000+200,000/(1+16%)+100,000/(1+16%)2
+20,000/(1+16%)3 = 9,543
NPVB :
-250,000+20,000/(1+16%)+120,000/(1+16%)2
+220,000/(1+16%)3= -2,634
- Example illustration
- According to the NPV rule, project A should be
accepted as it generates a positive NPV, it
implies the company will make a profit from
project A. - While project B should be rejected as it
generates a negative NPV, it implies the
company will suffer a loss from project B.
- Example illustration
Tired of calculation? We can use present value
table (Table A-3) to get the same result!
Take project A with a discount rate of 8% for
example.
NPVA = -250,000 + 200,0000.9259 +
100,0000.8573 + 20,000*0.7938
= 36,796 (same as our previous calculation)
* Have a try on the discount rate of 16%
- The NPV approach (Pros)
- It takes into account the time value of money
- It is easy to apply
- It takes into account investment size (absolute
amount) - It can handle non-conventional cash flows
- The NPV approach (Cons)
- Prediction on future cash flows could be
inaccurate. - It assumes the predicted future cash flows are
not subject to change. - Prediction on future discount rate could be
inaccurate. - The result of the NPV approach could be
contradictory to other approaches.
Profitability index (PI)
- A method to make project investment decision
- It is the ratio of sum of PVs of all future cash flows divided by the absolute value of initial cash outlay
PI = PV of all future cash flows/inital cash outlay
- Example (assuming discount rate is 8%)
Points in time
Cash flows (₤)
(Yearly intervals)
A B
0 (250,000) (250,000)
1 200,000 20,000
2 100,000 120,000
3 20,000 220,000
Profitability index (PI)
* Example illustration
PIA =[200,000/(1+8%)+100,000/(1+8%)2
+20,000/(1+8%)3]/250,000 = 1.15
PIB = [20,000/(1+8%)+120,000/(1+8%)2
+220,000/(1+8%)3]/250,000= 1.18
Profitability index (PI) rules in investment
decision making
- To independent projects
- Accept the project if PI>1
- Reject otherwise
- To mutually exclusive projects
- Accept the project has the highest PI given PI>1
- Reject remaining projects
- We follow the NPV rule if it is contradictory to the
PI results.
