Fi8000 Valuation of Financial Assets Milind Shrikhande Associate Professor of Finance

Today ☺ Syllabus ☺ Course overview ☺ Lecture Sequence: Options…

Syllabus ☺ Expectations ☺ Be here ☺ Ask questions ☺ Work practice problems ☺ Required skills ☺ Spreadsheet (Excel) and Internet ☺ Required materials ☺ Text: Bodie, Kane and Marcus 6 th edition ☺ Solutions manual

Syllabus ☺ Grading ☺ 3 20% each Similar to or related to practice problems and examples No make-ups ☺ Final exam 30% ☺ Stock-Trak 10% ☺ Make-up Policy ☺ No make-up quizzes ☺ Everyone must take the final exam

Syllabus ☺ Grading – Typical Department Policy ☺ No more than 35% A ☺ Majority (approximately 50%) B ☺ Lagging performance earns a C or lower ☺ Administrative – Withdrawal with a WF ☺ Beyond 3 absences from class ☺ Withdrawal after the semester midpoint ☺ Withdrawal while doing failing work

Syllabus ☺ Materials ☺ (Financial) Calculator – bring every day ☺ Text – leave it where you read it ☺ Lecture notes, handouts – provided ☺ Office Hours ☺ Drop-in, phone, and by appointment

Approaches to Valuation ☺ Discounted cash flows The value of an asset is related to the stream of expected cash flows that it generates, and should reflect compensation for time and risk. ☺ Arbitrage pricing When two assets have exactly the same stream of cash flows (magnitude, date, state) their prices should be identical.

Valuation of Financial Assets BondsStocksDerivative CF stream coupons and face-valuedividends contingent on contract and underlying asset Time line fixed maturity no maturity fixed expiration Risk default risk systematic risk contingent on contract and underlying asset

Discounted Cash Flows (DCF) Valuation The Idea The value of an asset is the present value of its expected cash flows. The Philosophical Basis Every asset has an intrinsic value that can be estimated, based upon the characteristics of the stream of cash flows that the asset generates. Every asset has an intrinsic value that can be estimated, based upon the characteristics of the stream of cash flows that the asset generates.

Inputs for DCF Valuation ☺ The magnitude of the expected CFs ☺ The timing of the expected CFs ☺ The risk level of the expected CFs

Assumptions Underlying DCF Valuation ☺ Magnitude: investors prefer to have more rather than less. ☺ Timing: investors prefer a dollar today rather than a dollar some time in the future. ☺ Risk: investors would rather get a certain CF of $1 than get a lottery ticket with an expected (average) CF of $1.

The Mechanics of DCF CF 1 CF 2 CF 3 CF 4 CF T CF 1 CF 2 CF 3 CF 4 CF T | | | | | |---> t … T

Notation PV = Present Value FV = Future Value CF t = Cash Flow on date t t is the time (date) index (t = 1, 2, …, T) k = risk-adjusted discount rate (risk-adjusted / opportunity cost of capital) (risk-adjusted / opportunity cost of capital) rf = risk-free discount rate (use as the discount rate if the probability of default is zero) (use as the discount rate if the probability of default is zero) g = growth rate

The Mechanics of Time Value Compounding Converts present cash flows into future cash flows. Discounting Converts future cash flows into present cash flows. The Additivity Principal Cash flows at different points in time cannot be compared or aggregated. All cash flows have to be brought to the same point in time before comparisons or aggregations can be made.

Compounding a Cash Flow $100 FV | |-----> t k = 5% | |-----> t k = 5% $100 FV | | |---> t k = 5% | | |---> t k = 5% PV FV | | | |---> t | | | |---> t … T … T

Example In a study of returns on stocks and bonds between 1926 and 1997, Ibbotson and Sinquefield found that on average stocks made 12.4% annual return, treasury bonds made 5.2% and treasury bills made 3.6%. Assuming that these returns continue into the future, what will be the value of $100 invested in each category for 1year, 5 years, 10 years?

Solution Holding Period StocksT.BondsT.Bills 1$112.40$105.20$ $179.40$128.85$ $321.86$166.02$142.43

Discounting a Cash Flow PV $100 | |-----> t k = 5% | |-----> t k = 5% 0 1 PV $100 | | |-----> t k = 5% | | |-----> t k = 5% PV FV | | | |---> t | | | |---> t … T

The Present Value of a Stream of Cash Flows CF 1 CF 2 CF 3 CF 4 CF T CF 1 CF 2 CF 3 CF 4 CF T | | | | | |---> t | | | | | |---> t … T … T

Examples 1. How much will you pay today for a project that is expected to pay a dividend of $500,000 three year from now, if the appropriate (risk- adjusted) annual discount rate for this project is 10%? 2. What is the value of a project that is expected to pay $150,000 one year from now and $500,000 three years from now, if the appropriate (risk-adjusted) annual discount rate for this project is 10%?

Solutions 1. PV = $500,000/(1+0.1) 3 = $375, PV = $150,000/(1+0.1) 1 + $500,000/(1+0.1) 3 = $136, $375, = $136, $375, = $512, = $512,021.04

Cash Flow Streams – special cases A growing perpetuity: CF CF(1+g) … CF(1+g) (t-1) … CF CF(1+g) … CF(1+g) (t-1) … | | | | > time | | | | > time … t … … t …

Example In 1992, Southwestern Bell paid dividends per share of $2.73. It’s earnings and dividends had grown at 6% a year between 1988 and 1992 and were expected to grow at the same rate in the long term. The rate of return required by investors on stocks of equivalent risk was 12.23%. What should be the value of the stock?

Solution Current dividend per share = $2.73 Expected growth rate g = 6% = 0.06 CF 1 = $2.73 ·(1+0.06) = $ Discount rate k = 12.23% =

Example - continued In fact, the stock was actually trading at $70 per share. This price could be justified by using a higher expected growth rate.

Cash Flow Streams – special cases A growing annuity: CF CF(1+g) … CF(1+g) (T-1) CF CF(1+g) … CF(1+g) (T-1) | | | | > time | | | | > time … T … T

Example Suppose you are trying to borrow $200,000 to buy a house on a conventional 30-year mortgage with monthly payments. The monthly interest rate on this loan is 0.7%. What is the monthly payment on this loan?

Solution PV = $200,000 T = 30·12 = 360 k = 0.7% = g = 0

The Frequency of Compounding The frequency of compounding affects both the future and present values of cash flows. The quoted annual interest rate may be compounded more frequently than once a year. This will affect the effective annual interest rate which is determined by the specified frequency of compounding.

Example A government note pays a coupon (interest) of 4.75% of par value. This means that a $1,000 face-value note pays $47.50 in annual interest in two semiannual installments of $23.75 each. The quoted annual interest rate is 4.75%, but it is compounded semiannually. What is the effective annual interest rate?

Solution

The Frequency of Compounding Frequency Quoted Rate m Effective Rate annual10%110.00% Semi-annual10%210.25% monthly10% % weekly10% % continuous10%∞10.52%

Continuous Compounding

The Frequency of Compounding - continued

Terminology and Notation The quoted annual rate is also called the APR (Annual Percentage Rate) The Effective Annual Rate is the EAR We will use the notation r q,annual = quoted annual rate r eff,annual = effective annual rate r annual = annual rate (when r q,annual = r eff,annual )

Example The quoted annual rate of return is 10%, compounded semiannually. Calculate the following rates: a. Effective rate for 1 year (10.25%) b. Effective rate for 2 years (21.55%) c. Effective rate for 18 months (15.76%) d. Effective rate for 6 months (5%) e. Effective rate for 2 months (1.64%)