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TitleYield Curve
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Table of Contents
                            Yield Curve
	DEFINITION of 'Yield Curve'
	BREAKING DOWN 'Yield Curve'
	Quantitative Methods - Introduction
	Quantitative Methods - What Is The Time Value Of Money?
	Quantitative Methods - The Five Components Of Interest Rates
	Quantitative Methods - Time Value Of Money Calculations
	Quantitative Methods - Time Value Of Money Applications
	Quantitative Methods - Net Present Value and the Internal Rate of Return
	Quantitative Methods - Money Vs. Time-Weighted Return
	Quantitative Methods - Calculating Yield
	Understanding the Yield Curve
Document Text Contents
Page 1

Yield Curve

DEFINITION of 'Yield Curve'
A line that plots the interest rates, at a set point in time, of bonds having
equal credit quality, but differing maturity dates. The most frequently reported
yield curve compares the three-month, two-year, five-year and 30-year U.S.
Treasury debt. This yield curve is used as a benchmark for other debt in the
market, such as mortgage rates or bank lending rates. The curve is also used to
predict changes in economic output and growth.

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The shape of the yield curve is closely scrutinized because it helps to give an
idea of future interest rate change and economic activity. There are three main
types of yield curve shapes: normal, inverted and flat (or humped). A normal yield
curve(pictured here) is one in which longer maturity bonds have a higher yield
compared to shorter-term bonds due to the risks associated with time.

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An inverted yield curve is one in which the shorter-term yields are higher than the
longer-term yields, which can be a sign of upcoming recession. A flat (or
humped) yield curve is one in which the shorter- and longer-term yields are very
close to each other, which is also a predictor of an economic transition. The slope
of the yield curve is also seen as important: the greater the slope, the greater the
gap between short- and long-term rates.

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Page 20

Quantitative Methods - Net Present
Value and the Internal Rate of Return
This section applies the techniques and formulas first presented in the time value of money
material toward real-world situations faced by financial analysts. Three topics are
emphasized: (1) capital budgeting decisions, (2) performance measurement and
(3) U.S. Treasury-bill yields.

Net Preset Value
NPV and IRR are two methods for making capital-budget decisions, or choosing between
alternate projects and investments when the goal is to increase the value of the enterprise
and maximize shareholder wealth. Defining the NPV method is simple: the present value of
cash inflows minus the present value of cash outflows, which arrives at a dollar amount that
is the net benefit to the organization.

To compute NPV and apply the NPV rule, the authors of the reference textbook define a
five-step process to be used in solving problems:

1.Identify all cash inflows and cash outflows.
2.Determine an appropriate discount rate (r).
3.Use the discount rate to find the present value of all cash inflows and outflows.
4.Add together all present values. (From the section on cash flow additivity, we know that
this action is appropriate since the cash flows have been indexed to t = 0.)
5.Make a decision on the project or investment using the NPV rule: Say yes to a project if
the NPV is positive; say no if NPV is negative. As a tool for choosing among alternates, the
NPV rule would prefer the investment with the higher positive NPV.

Companies often use the weighted average cost of capital, or WACC, as the appropriate
discount rate for capital projects. The WACC is a function of a firm's capital structure
(common and preferred stock and long-term debt) and the required rates of return for these
securities. CFA exam problems will either give the discount rate, or they may give a WACC.

To illustrate, assume we are asked to use the NPV approach to choose between two
projects, and our company's weighted average cost of capital (WACC) is 8%. Project A
costs $7 million in upfront costs, and will generate $3 million in annual income starting three

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years from now and continuing for a five-year period (i.e. years 3 to 7). Project B costs $2.5
million upfront and $2 million in each of the next three years (years 1 to 3). It generates no
annual income but will be sold six years from now for a sales price of $16 million.

For each project, find NPV = (PV inflows) - (PV outflows).

Project A: The present value of the outflows is equal to the current cost of $7 million. The
inflows can be viewed as an annuity with the first payment in three years, or an ordinary
annuity at t = 2 since ordinary annuities always start the first cash flow one period away.

PV annuity factor for r = .08, N = 5: (1 - (1/(1 + r)N)/r = (1 - (1/(1.08)5)/.08 = (1 - (1/
(1.469328)/.08 = (1 - (1/(1.469328)/.08 = (0.319417)/.08 = 3.99271

Multiplying by the annuity payment of $3 million, the value of the inflows at t = 2 is ($3
million)*(3.99271) = $11.978 million.

Discounting back two periods, PV inflows = ($11.978)/(1.08)2 = $10.269 million.

NPV (Project A) = ($10.269 million) - ($7 million) = $3.269 million.

Project B: The inflow is the present value of a lump sum, the sales price in six years
discounted to the present: $16 million/(1.08)6 = $10.083 million.

Cash outflow is the sum of the upfront cost and the discounted costs from years 1 to 3. We
first solve for the costs in years 1 to 3, which fit the definition of an annuity.

PV annuity factor for r = .08, N = 3: (1 - (1/(1.08)3)/.08 = (1 - (1/(1.259712)/.08 =
(0.206168)/.08 = 2.577097. PV of the annuity = ($2 million)*(2.577097) = $5.154 million.

PV of outflows = ($2.5 million) + ($5.154 million) = $7.654 million.

NPV of Project B = ($10.083 million) - ($7.654 million) = $2.429 million.

Applying the NPV rule, we choose Project A, which has the larger NPV: $3.269 million
versus $2.429 million.

Problems on the CFA exam are frequently set up so that it is tempting to pick a choice that seems intuitively better (i.e. by people who are guessing), but this is wrong by NPV rules. In the case we used, Project B had
lower costs upfront ($2.5 million versus $7 million) with a payoff of $16 million, which is more than the combined $15 million payoff of Project A. Don\'t rely on what feels better; use the process to make the decision!

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