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##### More About Present Values

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**More AboutPresent Values**Applications: Concept of Net Present Values Fußzeile**Valuing an Office Building**Step 1: Forecast cash flows Cost of building = C0 = 350 Sale price in Year 1 = C1 = 400 Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 7%, then Cost of capital = r = 7% Fußzeile**Valuing an Office Building**Step 3: Discount future cash flows Step 4: Go ahead if PV of payoff exceeds investment Fußzeile**The Concept of Net Present Value**Fußzeile**Risk and Present Value**• Higher risk projects require a higher rate of return • Higher required rates of return cause lower PVs Fußzeile**Risk and Present Value**The Higher the Risk, the Higher The Opportunity Cost of Capital i.e. The Higher The Requested Return Fußzeile**Net Present Value Rule**• Accept investments that have positive net present value: • If there are competing investment opportunities, select the one that offers the highest net present value: Fußzeile**Example**Suppose we can invest $50 today and receive $60 in one year. Should we accept the project given a 10% expected return? Net Present Value Rule • Accept investments that have positive net present value Fußzeile**The Rate of Return Concept**• Calculate the rate of return of your investment and check, if it exceeds the “required” return • Example • In the project listed below, the foregone investment opportunity is 12%. Should we do the project? Fußzeile**Rate of Return Rule**• Accept investments that offer rates of return in excess of their opportunity cost of capital r: • If there are competing investment opportunities, select the one that offers the highest rate of return: Fußzeile**Market Values with Project A**FIXED ASSETS 12.000 EQUITY 11.000 LIQUIDITY 1.000 DEBT 5.000 PV(CF)Proj.A 3.000 NPV Meets Value Maximization Market Values without Project A Project A offers a perpetual future Cash Flow of 300 p.a. The initial Investment would be 2.000. The interest rate is at 10%. FIXED ASSETS 12.000 EQUITY 10.000 DEBT 5.000 LIQUIDITY 3.000 The PV of future Cash Flows is at 3.000. The NPV at 1.000. The NPV reflects the increasing market value of equity. Fußzeile**Opportunity Cost of Capital**Example You may invest $100,000 today. Depending on the state of the economy, you may get one of three possible cash payoffs: Fußzeile**Opportunity Cost of Capital**Example - continued You know, the expected cash flow of 110.000 ist uncertain. To calculate the NPV of your project you need the appropriate (risk adjusted) discount rate. How to get it ? You look at the market for risky investments – for example the stock market – and find a stock, trading for $95.65. Next year’s stock price, given a normal economy, is forecasted at $110 Fußzeile**Opportunity Cost of Capital**Example – continued The stocks expected payoff leads to the “expected return”. Fußzeile**Opportunity Cost of Capital**Example - continued Discounting the expected payoff at the expected rate of return of a comparable risky financial asset investment leads to the PV of the project Fußzeile