Cheat Sheet Midterm V2.docx - Formula sheet Expected return...

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Formula sheet Present value: C t : Per period cash flow, r t : discount rate Present value of a perpetuity with cash flow c per period and discount rate r Present value of a growing perpetuity with cash flow c in the first period, discount rate r and growth rate g Present value of an annuity for T periods with cash flow c per period and discount rate r Present value of a growing annuity for T periods with cash flow c in the first period, discount rate r and growth rate g Future value T periods later, with the discount rate=r, an amount PV today When r is the annual percentage rate (APR), compounded m times in a year, the Effective Annual Rate is When r is the annual percentage rate (APR), the continuously compounded rate is When there are n periods in a year, and r is the (effective) annual rate NPV of a project that generates free cash flows = FCF, with appropriate discount rate r is Free cash flows: Net Working Capital (NWC): Terminal Value (TV) at time T of future cash flows, when the FCF T is the free cash flow in period T, which will grow at the rate g forever and discount rate is r Variance of a portfolio of two assets with weights summing to 1 (Var: Variance, Cov: Covariance) Expected return for asset X, based on probabilities p(s) Variance of return for asset X, based on probabilities p(s) Covariance between returns of assets A and B, based on probabilities p(s) Correlation between returns of assets A and B, Portfolio with many assets The CAPM equation: Levering and unlevering beta (Asset Beta = Unlevered Beta, Equity Beta = Levered Beta) Weighted average cost of capital Consider firm with 3 divisions, with assets values A 1 , A 2 , A 3 and each its own beta, the total assets for the firm and asset beta for the firm are
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(PSG) has a market capitalization (market value of equity) of INR 90 billion, INR 30 billion in debts debt beta is 0.2. PSG's equity beta is 1.2. You are planning to start a sporting risk‐free interest to be 7% and market risk premium to be 9%. 100% equity financed . estimated cost of capital Solution: First calculate asset beta for PSG. That would be asset beta for your business. Equity beta would be same as no debt financing, use this Asses Beta into CAPM. BA = (D/D+E)*BD +(E/E+D)*BE => BA= 0.95. COC = 7+0.95*9=15.55%. Beta differs from volatility: True. B) The risk premium investors can earn by holding the market portfolio is the difference between the market portfolio's expected return and the risk‐ free interest rate: True. C) Stocks in cyclical industries, in which revenues tend to vary greatly over the business cycle, are likely to be more sensitive to systematic risk and have higher betas than stocks in less sensitive industries: true. D) Returns to the market portfolio represent unsystematic shocks to the economy: False – Systematic shocks. Variance of Portfolio: Consider a portfolio that consists of an equal investment in 10 firms. Variance of return each of the firm is 0.01 and covariance for each pair is 0.005. What is the variance of this portfolio? Portfolio Variance = (1/N)*Var avg + (1-1/N)*Cov avg = 1/10*0.01 + (1‐1/10)*0.005 =0.0055.
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