Topic 1:

Introduction

Interest Rate• Interest rate (r) is rate of return that reflects the

relationship between differently dated cash flows.• Real risk-free interest rate is the single-period rate for a

completely risk-free security if no inflation were expected.

• Inflation premium compensates investors for the expected inflation.

• Nominal risk-free interest rate is the sum of the real risk-free interest rate and the inflation premium.

• Default risk premium compensates investors for the possibility that the borrower will fail to make a promised payment.

• Liquidity premium compensates investors for the risk of loss relative to an investment’s fair value if the investment needs to be converted to cash quickly.

• Maturity premium compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended.

Frequency of Compounding

monthlyfor 12 quarterly,for 4 ex.

year ain periods gcompoundin ofnumber m

rate annual stated r

m

r1PVFV

s

mN

sN

Example: Future Value with Quarterly Compounding

• Find the FV of $10,000 invested today at 8% if the interest is compounded quarterly.

$11,716.59

02)$10,000(1.

m

r1PVFV

2 N

4 m

8% r

$10,000 PV

8

nM

sN

s

Continuous Compounding

• Interest can be compounded in discrete intervals such as daily, monthly or quarterly, or it can compound continuously. For continuous compounding we use,

7182818.2e

PVeFV NrN

s

Example: Future Value with Continuous Compounding

• Use the same information before to find the FV with continuous compounding.

$11,735.11

$10,000e

PVeFV

2 N

8% r

$10,000 PV

.08(2)

NrN

s

s

Stated and Effective Rates

• Stated rates do not account for the number of compounding periods and so we need to compute the effective annual rate (EAR)

1rate)interest Periodic1(EAR m

Example

• Find the EAR if the stated interest rate is 8% and semiannual compounding is used.

0816.

12

08.1

1m

r1EAR

2

m

s

Stated and Effective Rates

• The effective annual rate with continuous compounding is

1eEAR sr

Discounted Cash Flow Applications

• Discounted cash flow has numerous applications including:– determining if an investment is desirable

(capital budgeting).– valuing securities

Net Present Value

• Net present value (NPV) compares the cash outlay to the present value of the cash flows from the project. If NPV ≥ 0 we accept the project. If NPV < 0, we reject the project.

N

0tt

t

)r1(

CFNPV

Example: Using NPV

• RAD Corporation intends to invest $1 million in R&D and expects incremental cash flows of $150,000 in perpetuity from this investment. If the opportunity cost of capital is 10%, compute NPV

accept ,0000,500$10.

000,150$000,000,1$

r

CFCFNPV 0

Internal Rate of Return

• The internal rate of return on a project is the interest rate that makes the NPV = 0. If IRR ≥ discount rate, we accept the project.

0)IRR1(

CF...

)IRR1(

CF

)IRR1(

CFCFNPV

NN

22

11

0

Example: Using IRR

• Use IRR rule to determine the desirability of the R&D given in the example before

15.000,000,1$

000,150$

Investment

CFIRR

0IRR

CFInvestmentNPV

Problems with IRR

• IRR has several problems that make it less desirable than NPV:– If we are comparing different size projects, the

one with the highest IRR may not add the greatest value to the firm.

– If the sign of the cash flows changes more than once, we may get more than one IRR.

Portfolio Return Measurement

• Suppose you want to assess the success of your investments.

• Need to consider two related but distinct tasks:– The first is performance measurement, which

involves calculating returns in a logical and consistent manner.

– The second is performance appraisal which is, the evaluation of risk adjusted performance.

Portfolio Return Measurement

• We will use the fundamental concept of holding period return (HPR), the return that an investor earns over a specified holding period in our discussion of portfolio return.

0

101

P

DPPHPR

Money-Weighted Rate of Return

• In investment management applications, the internal rate of return is called the money-weighted rate of return because it accounts for the timing and amount of all dollar flows into and out of the portfolio.– One drawback is that it is affected by the

amount of money given in by investors.• not under the control of the money manager.

Time-Weighted Rate of Return

• The time-weighted rate of return, is not sensitive to additions and withdrawals.– preferred performance measure in the

industry.– it measures the compound rate of growth of

$1 initially invested in the portfolio over a stated measurement period.

Time-Weighted Rate of Return

• To compute an exact time-weighted rate of return on a portfolio, take the following three steps:1. Price the portfolio immediately prior to any significant addition or withdrawal of funds. Break the overall evaluation period into subperiods based on the dates of cash inflows and outflows.

2. Calculate the holding period return on the portfolio for each subperiod.3. Link or compound holding period returns to obtain an annual rate of return for the year (the time-weighted rate of return for the year). If the investment is for more than one year, take the geometric mean of the annual returns to obtain the time-weighted rate of return over that measurement period.

Example Time-Weighted Rate of Return

• Suppose that the portfolio earned returns of 15 percent during the first year and 6.67 percent during the second year, what is the portfolio’s time-weighted rate of return over an evaluation period of two years?

%76.10

1)0667.1)(15.1(return weighted-

)0667.1)(15.1(return) weighted-1( 2

Time

Time

Time-Weighted Rate of Return• We can often obtain a reasonable approximation of the time-

weighted rate of return by valuing the portfolio at frequent, regular intervals.– The more frequent the valuation, the more accurate the

approximation.• To compute the time-weighted return for the year, we first

compute each day’s holding period return:

where,

MVBt is the market value at the beginning of the period.

MVEt is the market value at the end of the period.

• We calculate an annualized time-weighted return as the geometric mean of N annual returns, as follows:

t

ttt MVB

MVBMVEr

1)r1()r1()r1(r N/1N21TW