The document outlines key financial concepts, including present value, future value, and net present value (NPV), explaining how to calculate the present value of cash flows and the significance of the discount rate. It discusses investment criteria such as payback period, accounting rate of return, and internal rate of return (IRR), emphasizing that positive NPV projects should be accepted to enhance shareholder value. The document also highlights the importance of risk in investment decisions and the necessity of comparing IRR to the opportunity cost of capital.

1. 1
Present Value and
Investment Criteria

2. 2
Future Value
A rupee today is worth more than a rupee tomorrow
Value of investment after 1 year = present value x (1 + r), where “r” is the rate of
return
In general,
Future value = present value x (1 + r)t
Source: Brealey et al (2024), Chapter 2

3. 3
Present Value
If you receive a cash flow of Ct rupees at the end of year t, the present value of this
future payment is:
Present value, PV = Ct
(1 + r)t
where, r is is called the discount rate, and the present value is the discounted value
of the cash flow
Source: Brealey et al (2024), Chapter 2

4. 4
Net Present Value
Net present value (NPV) equals present value minus the required investment,
NPV = PV - investment
Or, NPV = C0 + C1 / (1 + r), for a project that has cash flows only at the end of first
year; cash flow (mostly, negative) now is the investment made on the project
If NPV > 0, the investment is worth more than its costs; the proposed project makes
a net contribution to shareholder value, and increases shareholders’ wealth
Source: Brealey et al (2024), Chapter 2

5. 5
Risk and Present Value
A safe rupee is worth more than a risky rupee
Most investors dislike risky ventures and won’t invest in them unless they see the
prospect of a higher return. The riskier the venture, the less they will be prepared
to pay and the higher the return that they will demand.
For risky investments, we discount the expected cash flows using the opportunity
cost of capital, which is the rate of return available in financial markets on
investments of similar risk to the project under consideration.
Source: Brealey et al (2024), Chapter 2

6. 6
Discounted Cash Flow
Calculating present values when there are multiple cash flows:
All present values are expressed in current rupees, so they can be added; the
present value of (A+B) is equal to present value of cash flow A plus the present
value of cash flow B
For valuing a stream of cash flows extending over a number of years, we use the
discounted cash flow (DCF) formula,
PV = DCF = , i.e., summation (represented by the sigma notation) of cash flows
expected at different times suitably discounted over the time elapsed
Source: Brealey et al (2024), Chapter 2

7. 7
Investment Criteria
Net Present Value, NPV
Payback and Accounting Rate of Return
Internal Rate of Return, IRR
Source: Brealey et al (2024), Chapter 5

8. 8
NPV Rule
• Accept all projects with a positive NPV and reject all projects with a negative NPV
• NPV depends on all the forecast cash flows from the project
• NPV rule recognizes that a rupee today is worth more than a rupee tomorrow
because the rupee today can be invested to earn interest immediately
• NPV depends solely on the forecast cash flows from the project and the
opportunity cost of capital. It is not affected by the profitability of the company’s
existing business, or of its other independent projects. Nor is it affected by a
company’s choice of accounting method.
Source: Brealey et al (2024), Chapter 5

9. 9
Payback Rule
A project’s payback period is found by counting the number of years it takes before
the cumulative cash flow equals the initial investment.
The payback rule states that a project should be accepted if its payback period is
less than some specified cutoff period.
Even though discounted payback rule uses NPV calculations, it takes no account of
cash flows after the cutoff date, so good long-term projects risk rejection
Source: Brealey et al (2024), Chapter 5

10. 10
Accounting Rate of Return Rule
• Accounting rate of return is calculated as a ratio of the project’s expected average
profits and the project’s average assets:
Accounting rate of return = (average profits) / (average assets)
• As per this rule, a project should be accepted if its accounting rate of return is
greater than the return the company generates on its existing assets
• It depends of accounting profits, which are different from cash flows; it also
depends on the average profits over the life time of the project and doesn’t take
into account when these profits are received.
Source: Brealey et al (2024), Chapter 5

11. 11
Internal Rate of Return
The Internal Rate of Return (IRR) is defined as the rate of discount that makes
NPV = 0
The LHS in this equation is 0. RHS is the NPV of cash flows over T years, discounted
at the internal rate of return, IRR.
IRR and opportunity cost of capital are not same. IRR is a profitability measure and
depends solely on the amount and timing of projected cash flows; opportunity cost
of capital is a benchmark against which we compare the profitability measure.
Source: Brealey et al (2024), Chapter 5

12. 12
IRR Rule
Firms should accept a project/an investment proposal if the IRR is greater than the
opportunity cost of capital
Whenever, the NPV of a project is a continuously declining function of the discount
rate, the IRR rule is same as the NPV rule.
However, concerns with the IRR rule are related to possibility of multiple IRRs or
when there are multiple opportunity costs of capital (different for short and long-
terms, for example)
Source: Brealey et al (2024), Chapter 5