• Calculate the NPV of a project with the following cash flows and a 12% discount rate:

Year 0 1 2 3 4

Cash Inflows $0 $125 $150 $200 $225

Cash Outflows $400 $150 $100 $50 $50

From years 5 ? 9, you will receive net cash inflows of $100 per year (hint: use ordinary annuity valuation formula with 12% as the interest rate, and be careful when deciding how many periods it takes to discount it to the present value).

Yourcompany?sCEOisoldandsenile,damagingboththecompany?sreputationalongwiththeshareholders?value.Lastyear,hissalaryandbonuscombinedtobe$12.5million.For$25million,youcanbuyouthiscontracttodaywhilespending$10milliontorecruitanewCEO(alsoassumedtooccurtoday?thenewCEOwillhavethesamecompensationpackageastheoldone).Youestimatethatthecompany?smarketvaluationwillincreaseshareholdervalueby$15milliononthesamedate,thedateoftheannouncement.Inaddition,profitswillincreaseby$5millionperyearforthenext10years.Allpaymentscanbeviewedasbeingmadebyshareholders;calculatethepaybackperiodforshareholdersonthisinvestmentYouwinthelotteryandselecttheoptiontoreceive20yearlypaymentsofonemilliondollars(anordinaryannuity).IftodayisJanuary1,2016,andthefirstpaymentismadeJanuary1,2017,whatwillbethevalueoftheremainingsixpaymentsonJanuary2,2030iftheinterestrateis5%?(Hint:usetheordinaryannuityformulawiththenumberofpaymentsremainingfromJanuary2,2030untilthe20^thoverallpayment.)IBM ended trading on 7/21/2015 with a stock price of $163.07, and it?s most recent year of dividend payments was $5.20 per share. If dividend payments are expected to grow at a constant annual rate of 8% following last year?s dividend of $5.20, what is the expected annual return of an investment in this stock at today?s price?Calculate the retention rate required for the following company to have a sustainable growth rate of 12%. Assume all ratios (profit margin, debt/equity, ROE, etc) will remain constant.

2014 Company Data

Sales = $500M All Costs (excluding taxes) = $300M

Taxes = $50M Assets = $2B

Equity Multiplier = 2.5

1. Calculate the NPV of a project with the following cash flows and a 12% discount rate: Year 0 Cash Inflows Cash Outflows 1 2 3 4 $0 $125 $150 $200 $225 $400 $150 $100 $50 $50 From years 5 - 9, you will receive net cash inflows of $100 per year (hint: use ordinary annuity valuation formula with 12% as the interest rate, and be careful when deciding how many periods it takes to discount it to the present value). 2. Your company's CEO is old and senile, damaging both the company's reputation along with the shareholders' value. Last year, his salary and bonus combined to be $12.5 million. For $25 million, you can buy out his contract today while spending $10 million to recruit a new CEO (also assumed to occur today - the new CEO will have the same compensation package as the old one). You estimate that the company's market valuation will increase shareholder value by $15 million on the same date, the date of the announcement. In addition, profits will increase by $5 million per year for the next 10 years. All payments can be viewed as being made by shareholders; calculate the payback period for shareholders on this investment. 3. You win the lottery and select the option to receive 20 yearly payments of one million dollars (an ordinary annuity). If today is January 1, 2016, and the first payment is made January 1, 2017, what will be the value of the remaining six payments on January 2, 2030 if the interest rate is 5%? (Hint: use the ordinary annuity formula with the number of payments remaining from January 2, 2030 until the 20th overall payment.) 4. IBM ended trading on 7/21/2015 with a stock price of $163.07, and it's most recent year of dividend payments was $5.20 per share. If dividend payments are expected to grow at a constant annual rate of 8% following last year's dividend of $5.20, what is the expected annual return of an investment in this stock at today's price? 5. Calculate the retention rate required for the following company to have a sustainable growth rate of 12%. Assume all ratios (profit margin, debt/equity, ROE, etc) will remain constant. 2014 Company Data Sales = $500M All Costs (excluding taxes) = $300M Taxes = $50M Assets = $2B Equity Multiplier = 2.5 Q-1 Ans Interest Rate Year Cash Inflows Cash Outflows Effective Cash Flows Net Present Value = 12% 0 1 2 3 4 0 125 150 200 225 -400 -150 -100 -50 -50 -400 -25 50 150 175 $2,126.42 (MS Excel "NPV" Function Is Used) 5 1000 0 1000 6 1000 0 1000 7 1000 0 1000 8 1000 0 1000 9 1000 0 1000 Q-2 Ans Year Buying the contract Cost Recruiting new C Increase in Value of Sh $ Increase In Profits Effective Cash Flows Payback Period Q-3 Ans 0 ($25) ($10) 15 1 2 3 4 5 6 7 8 9 10 5 ($20) $5 4 Years 5 $5 5 $5 5 $5 5 $5 5 $5 5 $5 5 $5 5 $5 5 $5 2018 2 1 2019 3 1 2020 4 1 2021 5 1 2022 6 1 2023 7 1 2024 8 1 2025 9 1 2026 10 1 Interest Rate Year No. Of Years 0 Cash Flows (In Million) PV of CFs for last 6 Yrs Value Of Last Six Payments on 2030 Q-4 Ans Q-5 Ans 5% 2017 1 1 $ 5.08 Ending Trading Stock Price on 7/21/2015 Recent Dividend Payment per share Constant Growth Rate in Dividend Price of the stock considering constant growth Return on stock investment today Rate of Return On Investment = = = = = = 163.07 5.20 8% $ 65.00 $ 98.07 151% Expected sustainable growth rate = 12% Sales Less: Costs Profit Before Tax Less: Taxes Profit After Tax = = = = = 500 Milion 300 Million 200 Million 50 Million 150 Million Total Assets Equity Multiplier Total Stock holders Equity ROE = = = = 2000 Million 2.5 800 0.1875 Sustainable Growht Rate 12% (1-Dividend Payout Ratio) Dividend Payout Ratio So Retaintion Ratio = = = = = $ ROE * (1 -Dividend Payout Ratio) =0.1875 * (1- Dividend Payout Ratio) 0.64 0.36 0.64 2027 11 1 2028 12 1 2029 13 1 2030 14 1 2031 2032 2033 2034 2035 2036 15 16 17 18 19 20 1 1 1 1 1 1 0.952381 0.9070295 0.863838 0.822702 0.783526 0.746215