The Time Value of Money Money NOW is worth more than money LATER!

What is The Time Value of Money? A dollar received today is worth more than a dollar received tomorrow –This is because a dollar received today can be invested to earn interest –The amount of interest earned depends on the rate of return that can be earned on the investment Time value of money quantifies the value of a dollar through time

Uses of Time Value of Money Time Value of Money, or TVM, is a concept that is used in all aspects of finance including: –Bond valuation –Stock valuation –Accept/reject decisions for project management –Financial analysis of firms –And many others!

$10,000 today Obviously, $10,000 today. TIME VALUE TO MONEY You already recognize that there is TIME VALUE TO MONEY!! The Interest Rate $10,000 today $10,000 in 5 years Which would you prefer -- $10,000 today or $10,000 in 5 years?

TIME INTEREST TIME allows you the opportunity to postpone consumption and earn INTEREST. Why TIME? TIME Why is TIME such an important element in your decision?

Formulas Common formulas that are used in TVM calculations: * –Present value of a lump sum: PV = CF t / (1+r) t OR PV = FV t / (1+r) t –Future value of a lump sum: FV t = CF 0 * (1+r) t OR FV t = PV * (1+r) t –Present value of a cash flow stream: n PV =  [CF t / (1+r) t ] t=0

Variables where –r = rate of return –t = time period –n = number of time periods –PMT = payment –CF = Cash flow (the subscripts t and 0 mean at time t and at time zero, respectively) –PV = present value (PVA = present value of an annuity) –FV = future value (FVA = future value of an annuity)

Present Value of a Cash Flow Stream A cash flow stream is a finite set of payments that an investor will receive or invest over time. The PV of the cash flow stream is equal to the sum of the present value of each of the individual cash flows in the stream. The PV of a cash flow stream can also be found by taking the FV of the cash flow stream and discounting the lump sum at the appropriate discount rate for the appropriate number of periods.

Example of PV of a Cash Flow Stream Joe made an investment that will pay $100 the first year, $300 the second year, $500 the third year and $1000 the fourth year. If the interest rate is 10 percent, what is the present value of this cash flow stream? 1.Draw a timeline: ? $100$300$500$1000 ? ? ? i = 10%

Example of PV of a Cash Flow Stream 2.Write out the formula using symbols: n PV =  [CF t / (1+r) t ] t=0 OR PV = [CF 1 /(1+r) 1 ]+[CF 2 /(1+r) 2 ]+[CF 3 /(1+r) 3 ]+[CF 4 /(1+r) 4 ] 3.Substitute the appropriate numbers: PV = [100/(1+.1) 1 ]+[$300/(1+.1) 2 ]+[500/(1+.1) 3 ]+[1000/(1.1) 4 ]

Example of PV of a Cash Flow Stream 4.Solve for the present value: PV = $ $ $ $ PV = $

Effect of discounting Net value of 100 kr in 10 years

Chinese for risk In most language risk means something dangerous will happen, in finance the definition for risk is both an opportunity and dangerous!

Risk Risk vs. uncertainty

Cost of capital There are two capital interests: debt equity

Discounted cash-flow

Cost of capital We got 3 firms A, B and C. All firms do have exactly the same cash-flows.

CAPM r f = Risk Free rate r m = Stockmarket return β= Beta value (risk)

The argument Risk free rate – the least in all investment Risk premium, the extra risk taken when investing at the stock market Beta value, the relative risk by investing in one individual stock.

Risk Free Rate Represents return an investor can achieve on the least risky asset in the market Generally based on current yield to maturity on Government bond What bond? –Use YTM on local government bond; or –a global bond (e.g. Germany) and adjust for country risk (Global CAPM) What term? … rule of thumb is to match to the term to explicit period in the projections

Development of Bond market

Beta “What Is Beta and How Is It Calculated?” or….

Beta A “coefficient measuring a stock’s relative volatility” Beta measures a stock’s sensitivity to overall market movements Source:UBS Warburg Dictionary of Finance and Investment Terms

Beta – portfolio theory Specific Risk Systematic Risk Specific risk of investments can be eliminated, but systematic risk cannot be diversified away … Beta measures an equity’s exposure to systematic risk

In practice, Beta is measured by comparing changes in a stock price to changes in the value of the S&P 500 index over a given time period The S&P 500 index has a beta of 1

A Generic Example Stock XYZ has a beta of 2 The S&P 500 index increases in value by 10% The price of XYZ is expected to increase 20% over the same time period

Beta can be Negative Stock XYZ has a beta of –2 The S&P 500 index INCREASES in value by 10% The price of XYZ is expected to DECREASE 20% over the same time period

If the beta of XYZ is 1.5 … And the S&P increases in value by 10% The price of XYZ is expected to increase 15%

A beta of 0 indicates that changes in the market index cannot be used to predict changes in the price of the stock The company’s stock price has no correlation to movements in the market index

Beta What influences an equity’s beta? cyclicality of revenue streams (i.e. relationship to state of the economic cycle) level of operational leverage in a company’s cost structure level of financial leverage in a company’s capital structure

CompanyBeta AMGN0.82 BRK.B0.73 C1.37 XOM0.10 MSFT1.80 MWD2.19 NOK2.05 PXLW1.93 TXN1.70 VIA.B1.39 Source: taken from yahoo.finance.com, except PXLW from bloomberg.com

Beta and Risk Beta is a measure of volatility Volatility is associated with risk

Risk-Reward Curve Risk Expected Return

If beta is a measure of risk, then investors who hold stocks with higher betas should expect a higher return for taking on that risk

Beta and CAPM The capital asset pricing model: E(R) = Rf + B(Rm-Rf) where: E(R) or Re = Expected return Rf = risk free rate of return B = beta Rm = market return

WACC Weighted average cost of capital: WACC = (D/V)*Rd*(1-T) + (E/V)*Re where: D = market value of firm’s debt Rd = return on debt securities T = tax rate E = market value of firm’s equity securities Re = return on equity securities (from CAPM) V = total value of firm’s securities (D + V)

WACC and Beta WACC increases as the beta and the rate of return on the equity securities increases (all else constant) WACC is used as the discount rate in DCF models Therefore, increasing WACC reduces the firms valuation to reflect the increase in risk

How to Calculate Beta Beta = Covariance(stock price, market index) Variance(market index) **When calculating, you must compare the percent change in the stock price to the percent change in the market index**

How to Calculate Beta Easily calculated using Excel and Yahoo! Finance Use COVAR and VARP worksheet functions

Risk premium  Changes in the economy. Risk premium are higher for more volatile countries. Weaker economy – higher risk premium.  Political risk. Risk for more political instability – higher risk premium.  Structure of the stock market. Some markets are very risky as Sweden due to many and small firms. More volatile market – higher risk premium.

Risk premium EMRP = (Rm - Rf) EMRP reflects the premium investors require for investing in equities rather than risk-free securities There are two main approaches to calculate EMRP; these are: –historic averages - ; and –forward looking methods (surveys, dividend discount model)

Risk premium Source: Ibbotson Associates and Grabowski and King Current consensus EMRP range is 4%-8%

Historical risk premium Swedish market US market

CAPM Total Company Risk Specific Risk Systematic risk Litigation industry events Labour force strike New rival company Market events: interest rate GDP inflation Company size Number of Observations Statistical significance LocationGearing Comparators Asset Beta Cyclicality of revenues Operational leverage Company activities

Max and min cost of capital Sectra January 2003 Beta 0,99 vs. 2,70 Risk premium 3,10 vs. 6,97 Risk free rate 3,61 vs. 4,70 3,61 + 0,99 * 3,10 = 6,68 4,70 + 2,70 * 6,97 = 23,52 All other forecasts equal will give expected price per share 118 kr and 26 kr, the price was 44 kr.

WACC… summing up Risk Free Rate4.50% EMRP5.0% Beta (Equity) % Cost of Equity 10.75% Cost of Debt6.50% Tax 35%(2.28%)4.22% Gearing (Debt: Debt+ Equity)40% WACC8.14%