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Finance (Subject) / Capital Budgeting (Lesson)

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• NPV Pros The Net Present Value: Present value of inflows - present value of outflows (2) Recognizes time value of money: Investing a pound today, which will return more than a Pound tomorrow Compounding effect: you earn interest on interest (3) Recognizes risk of the project:  Discount rate is higher than the interest rate for a risk-less investment (4) Measure of wealth you created
• Payback Period Year it takes before cumulative forecasted cash flows equal the initial investment – Only accept projects which payback in less than T years– If projects are mutually exclusive projects, do the one with theshortest payback
• Pro & Con Payback Period • Advantages:– Easy, No need to compute the cost of capital– Some Managers have short horizons, because they move jobs and want to earn returns before they leave projects– Gives a feel for time investment is at risk Disadvantages:  - Does not give value to Cash inflows received after the payback time 
• Calculate the cash flows from selling the old equipment? When Loss: Selling price: 200,000Loss relative to book value = 50,000Tax effect of loss = 50,000*0.3 = 15,000Cash flow from selling equipment = Selling price + Tax effect = 200,000 + 15,000 = 215,000. When Gain: Selling price: 200,000Gain relative to book value = 50,000Tax effect of gain = 50,000*0.3 = 15,000Cash flow from selling equipment = Selling price - Tax effect = 200,000 - 15,000 = 215,000.
• What is the WACC of XY? As debt to equity has a ratio of 1 it must be that D=E D/D+E = D/D+D = D/2D = 0.5 as wD
• What are the cash flow effects from depreciations? (1) New equipment: Annual depreciations = 1,000,000/10 = 100,000PV gained Tax shield = 100,000*0.3* Ausing WACC = 219,241 + (2) Old equipment: PV of lost Tax shield = Old BV/Useful Life * A =68,607.98 (3) Total effect of depreciation = 219,241.89 - 68,607.98 = 150,633.92
• What is the NPV of buying the new machine? NPV= -investment + cash flow from sales + PV(cost savings) + PV(depreciation tax shield) OR 1.) Annuity Cf 3-10 (excluding Sale) = CF * Ausing WACC 2.) Sale of machinge Year 10 = CF from Sales / (1+WACC)10 NPV = -Capex - Excess Capacity + PV(inflows) + PV(CF from Sale)
• Find the market portfolio in the presence of risk-free investment opportunities. The PF with the highest Sharpe Ratio is the market portfolio ! Sharpe ratio maximizes slope of the efficient frontier, i.e. Market Porftolio (highest Return for a given Risk) 1) Calculate the Sharpe ratios: 0.8, 1.23, 1.40, 1.42, 1.40.2) The Portfolio with the highest Sharpe ratio, 25% A and 75% B, is the market portfolio.
• Replicating Strategies CALL + BOND investment at PV(K) = PUT + S Protective put = LONG stock + Long Put will deliver the exact payoff as Fiduciary call + LONG call and investing the present value (PV) of the exercise price Number of options needed to replicate = Increase in height/ Increase on X-axis  The payoff can be replicated by going long in a call option with strike price $20 and going short in a call option with strike price $40. Replicate with Zero-Coupon Bonds -Buy 100/Payoff Zero-Coupon Bonds (with maturity equal to option expiry date)-Sell one put option with strike price $40-Buy one put option with strike price $20
• Assume that you observe the price on a 5-year Zero-Coupon Bond. Based on this price and the above prices in the table, can you find the price of a 4-year Coupon Bond with a coupon of 5%? The 1-year spot rate is 1000/987.167 – 1 =1.30% The value of $1 two years from now – p - can be derived as So the price of a 2-year ZCB is $963.057 and the 2-year spot rate is No, because you cannot derive the 4-year spot rate and this is necessary to price the bond. Assume that you observe the prices on a 5-year Zero-Coupon Bond and a 5-year Coupon Bond with a coupon of 3.5%. Based on these prices and the above prices in the table, can you find the price of a 4-year Coupon Bond with a coupon of 5%? Yes, because you can back out the 4-and 5-year spot rate from the two 5-year bonds.
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• The working capital is 5% of sales. If the company increases the sales from £1.8 million to £2.0 million, what is the required investment in working capital during the year? Investment in working capital: (£2.0 million - £1.8 million)*0.05 = £0.01 million.
• Assume that CAPM holds. You want to calculate the equity beta of CHL corporation. The market return can either be high or low the next period. If the market is high, the equity return on CHL corporation is 15% and the market return is 10%. However, if the market is low, the equity return on CHL corporation is -10% and the return on the market is -5%. These are the only two possibilities next period. The risk-free rate is 0%. What is the beta of CHL corporation? Since there are only two states the market and CHL corporation is either perfectly negatively or positively correlated. In the above case the correlation is 1. We can find the beta as: beta = Correlation * Std Firm / STD Market beta = REpos REbad / RMgood - RMbad Correlation assumed 1
• The current USD/GBP exchange rate is 1.2, the one year USD risk-free rate is 1% and the one year GBP risk-free rate is 0.5%. The one year forward exchange rate is 1.1. Why is there an arbitrage opportunity? How can you take advantage of it? The forward price should be: 1.2*(1+0.01)/(1+0.005) = 1.206. Hence there is an arbitrage. You buy GBP forward (at 1.1) and for each forward contract you should borrow 1/1.005 GBP and invest  1.1*1/1.01 USD. The payoffs from this strategy in USD isUSD t=0 t=1Buy 1 Forward 0 〖(S〗_1-1.1)USDBorrow 1/1.005 GBP 1/1.005×1.2 USD -S_1 USDInvest 1.1/1.01 USD -1.1/1.01 USD 1.1 USDTotal 1.2/1.005-1.1/1.01=0.105 USD 0 The payoffs from this strategy in USD is USDt=0t=1Buy 1 Forward0 Borrow      Invest         Total    
• The zero-coupon yield curve is flat at 3%. A bond has just paid its most recent yearly coupon, has a face value of 100, and its coupon rate is 3%. Then, this bond is traded at 100. True or False? true. When the coupon rate equals the discount rate then face value equals price.
• Based upon the average current EV/Sales ratio of the comparable firms, if Ideko holds $6.5 million of cash in excess of its working capital needs, then Ideko's valuation of its equity is Average EV / Sales=2.067EV = EV / sales × Sales = 2.067 × $75 million = $155 millionEV = Equity + Debt - Cash in excess of NWC needsEquity = EV - Debt + cash in excess of NWC needs = $155 - $4.5 + $6.5 = $157 million
• The expected free cash flow for X in 2009 is FCFfirm = EBIT (1-T )+ Depreciation - ΔNWC - capital expenditures
• The expected return on a stock with a beta of two is: a. Two times the expected return on a stock with a beta of one b. Two times the market risk premium c. The sum of the yield on government bonds and the market risk premium d. a. and b. e. None of the above. e. None of the above.
• According to the CAPM, which has a higher expected rate of return: an individual stock with a beta of one or a diversified portfolio with a beta of one? They have the same expected rate of return.
• Net working capital is the difference between current assets - current liabilities 
• Give the expression to obtain the NPV for Galt Motors of manufacturing the armatures in house. NPV = −740,000 + ..... > 0
• Calculate after-tax cost of capital for firm with 2 divisions Using the CAPM, (1) calculate the cost of assets for each division first X = 3% + 1.5 x 5% = 10.5%; for division Y = 3% + 1 x 5% = 8%. (3) Weight it to get overall cost of capital = ¾ x 10.5% + ¼ x 8% = 9.875%.
• Firm B has a debt-to-equity ratio of 3. Its cost of debt is equal to the risk-free rate plus 6%. Its cost of equity is 20%. When very high D/E ratio > 2 Cost of capital = 0.75 x (3%+6%) x(1-20%) + 0.25 x20% = 10.4% BUT: This firm may not be profitable and benefit from the tax shield in which case the cost of capital would be 0.75 x (3%+6%) + 0.25 x20% = 11.75%
• Firm C is all equity financed. It currently pays no dividends. Its expected annual dividends starting in year five (5 years from now) The cost of capital is given by the following: P = D/(R-2%)* 1/(1+R)^4 Always 1 year less than year when with perpetuity-related CF started
• Draw the zero-coupon yield curve for the first two years. What might explain its upward sloping shape? Downward sloping Yield Curve - "normal"  market usually expects more compensation for greater risk. Longer-term bonds are exposed to more risk, i.e. changes in interest rates & increased exposure to potential defaults.  Lock in money for a long period investing money for a long period of time Investor is compensated for this through the time value of money component of the yield. the slope will move upward to represent the higher yields often associated with longer-term investments. These higher yields are compensating for the increased risk normally involved in a long-term ventures and the lower risks associated with short-term investments. The shape of this curve is referred to as normal, over the additionally applicable term of positive, in that it represents the expected shift in yields as maturity dates extend out in time.   associated with positive economic growth. Yield curves can also remain flat or become inverted. In the first instance, the flat curve demonstrates the returns on shorter and longer term investments are essentially the same. Often, this curve is seen as an economy approaches a recession due to the fact that fearful investors will move their funds into lower risk options, driving up the price and lowering the overall yield. Inverted yield curves present a point where short-term rates are more favorable than long-term rates. Its shape is inverted when compared to a normal yield curve, representing significant changes in market and investor behaviors. At this point, a recession is generally seen as imminent if it is not already occurring.
• Free Cash Flow to the firm Free cash flow is the amount of funds available to all investors in a firm after the firm has paid taxes and required investment needs does not distinguish between equity and debt holders  best, assume firm with 100% Equity (different taxation) 
• Cash Taxes Paid CF Tax = T * (Revenue - COGS - Opex - Dep) 
• Cash Flow from Sales & Purchases Cash flow from sales = CF = Sales - Increase in AR Cash flow from purchasess = CF = COGS +Increase in Inventory - Increase in AP
• FCF with EBIT and EBITDA FCF = (1-T) x EBIT + Depreciation + CaPex - NWC only depreciation tax shield: FCF = (1-T) x EBITDA + T Depreciation + CaPex - NWC
• Assume we have identified the true market portfolio. Its Sharpe Ratio is 1.4. The riskless rate is 5%. One of the individual stocks has the following characteristics: its expected return is 13% and its return volatility is 5%. Conclusion: the CAPM does not hold. TRUE or NOT? The Sharpe Ratio of the individual stock is (13%-5%)/5%=1.6 which is higherthan that of the true market portfolio. Under the CAPM, each stock/portfolio should have itsSharpe Ratio at or below the Sharpe ratio of the true market portfolio.
• Firm D’s equity has a market value of $50 million. Its bonds are traded at 90% of their face value, have a maturity of 10 years and a market value of $30 million. Its annual interest payments are $3 million. It pays total annual dividends of $10 million and these are expected to remain at that level forever 1) Claculate the Equity and Debt weights 2) RA = 3?8 RD + 5/8 RE 3) RD ist determined from the debt contract: - cannot get it Get the Face Value = Market Value / 0.9  Coupon Annuity until maturity, 10 years  PV (Bond)  4) RE is determined from Dividends = 10/RE 5) RA can be obtained
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• Obtain the standalone values the acquirer and the target, assuming that the next dividend will be paid exactly one year from now. 1) calculate the interest payment RF * Bond FV 2) calcultae Dividend = EBIT - interest payment 3) Use CAPM to get the RE 4) Value of Equity = Dividend / RE 5) Value of Debt = Bond outstanding 6) Value of Enterprise = V(Equity) + V(Debt)
• Suppose that the joint company will be able to increase its revenues by 25%, that is, in expected terms they are now ($0.25+$0.25)*1.25 = $0.625 million per year, forever. Compute the value of synergies from this merger. Assume that the operational risk of the joint company is the same as for standalone firms. 1) Calculate the WACC for the joing company (same as old companies) 2) V(Joint) = D / WACC3) V(Synergies) = V(joint) - V(Firm 1) - V(Firm2) 
• Suppose Casper is given an opportunity to invest up to $200,000 at 10 percent risk-free. The interest rate stays at 8 percent. What should he do, and how much can he consume in each period? If opportunity gives r that ishi gher thant RF, Invest 200,000 at 10% for 1 year Borrow x at 8% today  In one year, repay x*1.08 and get 220,000 x = 105,769 NPV (Opportunity) = PV(8%) - PV(10%) = x+x/1.08 - 200,000
• Mike Polanski is 30 years of age and his salary next year will be $40,000. Mike forecasts that his salary will increase at the steady rate of 5 percent per annum until his retirement at age 60. If Mike saves 5 percent of his salary each year and invests these savings at an interest rate of 8 percent, how much will he have saved by age 60? Use growting Annuity Formula to get PV  If he saves 5%, simply take 5% of this PV If Mike plans to spend these savings in even amounts over the subsequent 20 years, how much can he spend each year? Calculate FV of 5% savings Calculate the Annuity for 20 years
• Net working capital Net working capital = Cash + Inventory + AR - AP
• Working capital New projects require an investment (cash outflow) in: inventories (cash expenses not recorded in income statement)accounts receivable (credit given to costumers) They also generate spontaneous financing (cash inflow): accruals / accounts payable (borrowing from suppliers)
• Why don't we take into account Financing cost for FCF? Take into account financing costs when we compute the required rate of return (the discount rate) So taking into account financing costs in cash flows also would be double countingIgnore them
• Inflation & Working Capital investment - Nominal Terms Inflation affects ALMOST each position EBIT Working Capital Capital Gains Taxes Does not affect Depreciation Change in WC(Calculate from Working Capital) Discount with Real Rate - increase our nominal Net Revenues, and therefore our taxes.  - We will also receive more when we sell our capital asset, and our nominal working capital will increase by inflation (assuming WC as a constant % of sales).  The higher NPV is primarily due to the higher after tax profits. 
• Assume that you are a manufacturer that relies on imported raw materials from only one country. Assume that your domestic currency weakens against the currency of the one country from which you import all of your raw materials. What will be the effect on your working capital flow? Assuming nothing else changes, the devaluation of my currency will force me to invest more money in order to maintain the same stock level, and assuming that I am selling only to my domestic market, my income (and my current assets) will not be positively influenced by the weakening of my domestic currency.  The result is a negative WC flow, which together with increased costs and stable income, would lead to a decrease in the NPV.  
• EAR convert  interest rate (as stated by the bank) into the effective annual yield APR = r (stated interest) compounded n times Effective Annual Yield EAR = (1+ 1/n)n
• IRR the rate of return on a project that makes the NPV equal to zero Accept the project if the IRR is greater than the opportunity cost of capital. Advantages:– Does not demand input cost of capital– Many people find it more intuitive measure than NPV– Usually gives the same signal as NPV Criticism 1: “The IRR rule sometimes is misleading: Borrowing or Lending?” Project A: -1000+1500 Project B: -1000-1500  Same IRR: “We invest in both Project A and Project B if the opportunity cost of capital is smaller than 50%.” Criticism 2: No Solution or multiple solutions IRR Rule could sound like:“Since both IRR’s are larger than the opportunity cost of capital, then we should undertake the project”. - WRONG, At r = 10% NPV=-1.934 Criticism 3: IRR is misleading for mutually exclusive projects. IRR is not affected by the scale of the project - Incremental IRR Rule The initial costs of both projects differ so the IRR rule cannot be used! Investing in project A might deliver more value in dollars compared to B even though its % return is lower.
• Suppose that the interest rate is 8% APR with monthly compounding. What is the present value of an annuity that pays $100 every six months for 5 years? 1. Semi-annual r 1/m = (1+APR/12)6 2. Calculate Annuity with APR and 2*t periods
• Borstel Company - machines: Suppose you actually do buy one of the machines and rent it to the production manager. How much would you actually have to charge in each future year if there is a steady 8% per year inflation? 1. Nominal View Calculate nominal rate 1.08*inflation cost increase PV stays the same 2) calculate new EAC with r as nominal rate 3) Adjust rental payments by inflation
• ICAPM Financial Market Integration - World CAPM With both financial and product markets integrated = Wold CAPM, no Exchange Rate Risk Premium With segmented product markets there is exchange rate risk when 𝐶𝑜𝑣(𝑟_𝑗,𝑠)≠0. NO Financial Market Integration - Home CAPM With segmented financial markets, the domestic stock market is the relevant market portfolio With segmented product markets, again include the real exchange risk premium
• Is the bond worth more or less than a USD bond with face value of 100 USD and ?^???? Exchange Rate Risk Transder to the Seller This is an option to the seller of the bond, so the price must be lower to compensate the buyer for the currency risk. optimal repayment strategy of the borrower
• Without doing any calculations, determine whether this bond is trading at premium or at discount. Explain. C > Spot Rate This bond must be trading at a premium because the coupon rate is higher than the 5 different spot rates.
• Arbitrage Opportunity REVERSE OUT CALL PARITY PUT = -STOCK + CALL + K/1.04 heisst hier: Buy Stock, Sell Call, Sell K/1.04 (Borrow)
• Growth Model DCF Option 1: Expexted Return = Dividend Yield & Growth r = DIV/P + g Option 2: Long-term Growth estimated by Plowback Ratio = 1- DIV / EPS Return on Equity / Return on New Investments RONI = EPS / BV g = Plowback Ration * RONI 
• Usually the rental payments you derived in part (a) are just hypothetical – a way of calculating and interpreting equivalent annual cost. Suppose you actually do buy one of the machines and rent it to the production manager. How much would you actually have to charge in each future year if there is a steady 8% per year inflation? To have the payments match the fact that costs are growing with inflation, a more fair payment scheme is the growing annuity Caluclate EAC with growing Annuity and a Nominal Rate r = nominal Rate g = inflation (2) Let annual EAC payment increase by the Inflation g

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