This document discusses key concepts in discounted cash flow analysis including net present value (NPV) and internal rate of return (IRR). It provides examples of how to calculate NPV and IRR for investment projects and explains how to use NPV and IRR to evaluate whether projects will benefit shareholders. It also discusses limitations of IRR for ranking mutually exclusive projects and introduces the concept of portfolio return measurement using holding period return and money-weighted rate of return.

1. DISCOUNTED CASHFLOW
APPLICATIONS
By Yinka Daramola

2. •As analysts, much of our work involves evaluating transactions
involving present and future cash flows to predict return
possibilities
•In our line of work, It is pertinent that we specifically master the
TVM approaches to Discounted Cash Flow Analysis in equity, fixed
income, and derivatives
•In this module, we will learn about NET PRESENT VALUE and
INTERNAL RATE OF RETURN as important TVM tools for evaluating
cash flow streams, portfolio return measurement, and the
calculation of money market yields
Introduction

3. Net Present Value (NPV)
• The NPV rule Is a method of choosing amongst alternative
investments
• It is defined conceptually as “the present value of all cash inflows
that can be associated with an investment minus the present value
of all cash outflows of the same investment”
• The word “net” refers to this subtraction of the present value of
the investment’s cash outflows (costs) from the present value of its
cash inflows (or benefits) to arrive at the net benefit attributable to
the investment

4. Analysts use the NPV (and the IRR) as important prequalification criteria in
evaluating capital investments. These 2 Concepts are the most
comprehensive measures of whether or not, a project/investment is
profitable
n
NPV = ∑ CFt Outlay
t= 1
(1 + r)t
CFt= after tax cash flow at time t
r = required rate of return for the
investment
Outlay = investment cash flow at time zero
Net Present Value (NPV)

5. 1. Identify all cash flows associated with the investment-all inflows and outflows
2. Determine the appropriate discount rate or opportunity cost, r, for the
investment project
3. Using that discount rate, find the present value of each cash flow (inflows
have a positive sign and increase NPV; outflows have a negative sign and
decrease NPV)
4. Sum all present values. The sum of the present values of all cash flows
(inflows and outflows) is the investment’s Net Present Value
5. Apply the NPV rule. If the investment’s NPV is positive, an investor should
undertake it, and vice versa
6. If an investor has a 2 investment choices but can only undertake one, the
investor should choose the project with the higher positive NPV
Net Present Value (NPV) and the Net Present Value Rule

6. In calculating the NPV of an investment proposal, we use
an estimate of the opportunity cost of capital as the
discount rate
The opportunity cost of capital is the alternative return
that investors forgo to undertake an investment
When NPV is positive, the investment adds value because
it more than covers the opportunity of capital needed to
undertake it
What is the meaning of the NPV rule?

7. •Assume that Cornerstone Insurance is considering an investment of
N 500 million in GT Bank Plc which is estimated, based on current
dividend yield, to return after tax cash flows in dividend income of
N 160 million per year for the next four years and a further N 200
million in year 5. Their required rate of return is 10%
•What is the Net Present Value of this planned investment?
•Should Cornerstone Insurance go ahead with this investment ?
An Illustration

8. Interswitch Limited has been spending a lot of money on its
Research and Development Program for the current year. Its
Management has just announced that it intends to invest N 500
million in R & D. Incremental net cash flows are forecasted to be N 75
million per year in perpetuity. Interswitch’s cost of capital is 10%.
1. State whether Interswitch’s R & D program will benefit shareholders,
as judged by the NPV rule
2. Evaluate whether your answer to the above changes if Interswitch’s
cost of capital was 15% rather than 10%
Another Illustration

9. Internal Rate of Return (IRR)
Financial Managers want a single number that represents the rate of return
generated by an investment. The most frequently used measure is the IRR.
The IRR is the discount rate that makes the net present value equal to zero.
It equates the present value of all investment’s costs (outflows) to the
present value of the investment’s benefits (inflows)
The rate is internal because it depends only on the cash flows of the
investment, using no external data. As a result we can apply the IRR
concept to any investment that can be represented as a series of cash flows
The IRR rule uses the opportunity cost of capital as a hurdle rate and states
that “Accept Projects or Investments for which the IRR is greater than the
opportunity cost of capital”

10. Internal Rate of Return (IRR)
n
∑ CFt Outlay = 0
t= 1
(1 + IRR)t
For a project with one investment outlay, made initially, The IRR is
the discount rate that makes the net present value of the future
after tax cash flows equal to that investment outlay
CFt= after tax cash flow at time t
IRR = Internal Rate of Return
Outlay = investment cash flow at time zero

11. An Illustration
Cadbury Nigeria is considering whether or not to open a new plant in
Abuja to manufacture beverages. The factory will require an investment of
N 1,000 million. It is expected based on past experience to generate level
cash flows of N 294.8 million per year in each of the next 5 years following
its completion. According to information in its financial reports, Cadbury’s
typical cost of capital for this type of project is 11%.
1. Determine whether the project will benefit Cadbury’s shareholders using
the NPV rule
2. Determine whether the project will benefit Cadbury’s shareholders using
the IRR rule

12. Limitations of the IRR
The NPV and IRR rule usually give the same accept or reject decision when
projects are independent.
When an investor or company cannot finance all the projects it would like
to undertake (i.e. when projects/investments are mutually exclusive), it will
have to rank projects from the most profitable to the least. The NPV and
IRR will tend to rank projects differently when:
• The size or scale of the projects differs (size referring to the initial outlay
requirement)
• The timing of the project/investment’s cash flows differ
When they conflict in ranking. The analyst takes direction from the NPV rule

13. IRR and NPV for Mutually Exclusive Projects of
Different Size
Project A involves an immediate investment of N 10 million. This project will
make a single cash payment of N 15 million at t = 1
Project B involves an immediate outflow of N 30 million and is expected to
make a single cash payment of N 42 million at t = 1
Afromedia Limited has only N 30 million in investible funds and cannot
afford both projects. At an opportunity cost of capital of 8%, which should
it undertake? Rank them by preference for our next meeting with their
Chief Executive.
Our choice is expected to be the one that maximizes shareholder value

14. IRR and NPV for Mutually Exclusive Projects with
Different Timing of Cash Flows
Project A involves an immediate investment of N 10 million. This project will
make a single cash payment of N 15 million at t = 1
Project D involves an immediate outflow of N 10 million and is expected to
make a single cash payment of N 21.22 million at t = 3
Elekula Limited has only N 10 million in investible funds and cannot afford
both projects. At an opportunity cost of capital of 8%, which should it
undertake?
The NPV’s rule assumption about reinvestment rates is more realistic and
economically relevant because it incorporates the market-determined
opportunity cost of capital as a discount rate

15. Portfolio Return Measurement
As an Investment Manager, you are constantly faced with the responsibility of not
only adding value to your client’s seed investment, but also of measuring your
performance. You are constantly engaged in two related but distinct tasks:
PERFORMANCE MEASUREMENT and PERFORMANCE APPRAISAL
PERFORMANCE MEASUREMENT: Involves calculating returns in a logical and
consistent manner and is the foundation for further analysis. Accurate performance
measurement provides the basis for your performance appraisal
We will use the fundamental concept of HOLDING PERIOD RETURN (HPR), the
return an investor earns over a specified holding period in this discussion. For an
investment that makes one payment at the end of the holding period:
HPR = (P1 – P0 + D1)/ P0

16. Money-Weighted Rate of Return
This measure is an application of the IRR calculation. In investment
management applications, the IRR is called the money-weighted rate
of return because it accounts for the TIMING and AMOUNT of all Naira
flows into and out of the portfolio
As an illustration, we will consider an investment that covers a 2 year
horizon. At time t = 0, Alex Tarka bought 1 million units of Crusader
Insurance at a weighted average cost (W.A.C.) of N 2 per share. At time
t = 1 he bought an additional 1 million shares at N2.25/share. At the end
of year 2, t = 2, he sells both acquisitions at a W.A.C. of N2.35. During
both years, the Crusader paid dividends of N 0.05k per share. The t = 1
dividend is not reinvested (he spent this).

17. Money-Weighted Rate of Return
The MWRR puts a greater weight on the second year’s relatively poor
performance of 6.67% than the first year’s relatively good performance
of 15% , because more money was invested in the second year than the
first.
This is why we refer to this method of calculating HPR as “money-
weighted”.
This is a serious drawback for this approach as only clients can
influence when they will invest more money. There is therefore a need
for a method of measurement that evaluates investment performance
considering only actions of the investment manager

18. Next Week, we’ll discuss Time-Weighted Rates of Return and Money Market Yields
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