# MIT 15 414 - Recitation I: Financial Management (7 pages)

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## Recitation I: Financial Management

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- School:
- Massachusetts Institute of Technology
- Course:
- 15 414 - Financial Management

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Recitation I Financial Management Jiro E Kondo July 23 2003 I Net Present Value Methodology De nition N P V CF0 CF1 1 r1 CF2 1 r2 2 In determining cash ows must take into account all revenues costs and risks involved Example Calculate PV of one unit of stock in XYZ Corp What does the investor need to know or forecast What are the relevant cash ows assuming the investor buys the stock and holds it forever Should di erent investors use di erent discount rates Intuition for NPV Method The name says it all we re converting a stream of potentially risky cash ows spread over time into a certain one shot cash ow today producing equal enjoy ment That is individuals are indi erent between re ceiving N P V today and nothing afterwards and receiv ing the cash ow stream CF0 CF1 CF2 The advantage of expressing cash ow streams by the NPVs is that sure payments today are easy to compare People prefer more to less and as a result presumably prefer a higher NPV to a lower one and won t undertake negative NPV projects 1 II NPV Example Qualitative For this example let s focus on cash ows Compensation Policy Changes Fixed income group compensation at Salomon Broth ers in early 1990s Before Bonus based solely on individual perfor mance represents large fraction of a bond trader s com pensation Problems 1 Compensation policy doesn t reward cooperation among di erent traders and xed income desks 2 Lots of competition and ghting within rm for resources and pro t recognition 3 Desks or traders don t care how their decisions e g misbehavior might adversely e ect other parts of the FIG e g by hurting the reputation of the rm After Fixed percentage of bonus pool to be al located in a trust the purchases Salomon stock under employee s name Employee forced to hold this for 5 years How does this change address the aforementioned problems How e ective do you think this change will be Can we use the NPV method to evaluate the merits of this compensation change What are some of the bene ts of this change Some of the costs 2 III PV Examples Quantitative For this example we focus on the discount rate Basic Bond Pricing Let s price the 30 year T bond example from class assuming it s August 2003 Issued in May 2000 maturity in May 2030 face value of 1000 and semi annual coupon rate of 6 25 i e a coupon of 31 25 Assume a xed annual discount rate of 4 We don t consider payments made in the past when calculating PV only future ones Since the rst future payment will be made in Novem ber 2003 we need to know the quarterly discount rate Since the period between payments is 6 months we also need the semi annual discount rate What s the PV of the bond How might you expect this to relate to the price of the bond Why Constant Discount Rates Explicitly assumed in the PV formula given in class Is this reasonable No This is especially the case if the risk involved in cash ows changes over time more on this later However these rates even change when risks are held constant How do we know this One way to infer this by looking at the implied discount rates of U S Trea sury strips i e riskless zero coupon bonds 3 IV Some Present Value Mathematics For each of these formulas we will assume that the discount rate is constant Perpetuity A security that makes a xed payment every period e g year forever starting next period PV derived using formula for a geometric series 0 x 1 a ax ax2 a 1 x This implies that P V perpetuity P 1 r P 1 r 2 P 1 r 1 1 r 1 P r Annuity A security that makes a xed payment ev ery period starting next period for a nite number of periods PV derived from subtracting one perpetuity from an other P 1 P P P V annuity 1 r 1 r 1 T r 1 r T Also have formulas for growth perpetuities growth annuities and many others But for most practical purposes you will use a pro gram like Excel to create spreadsheets that calculate present values 4 V PV Examples Quantitative Let s complete the bond pricing example from page 3 We can think of the bond as consisting of two famil iar cash ow components 1 One face value payment of 1000 in 26 75 years and 2 An annuity that makes 54 payments of 31 25 once every 6 months starting in 3 months We value each stream seperately Face Value Payment P V FV 1000 1 04 26 75 350 23 Annuity P V A 31 25 1 0 0198 1 0099 1 1 0099 107 1009 92 Present Value of the Bond It s simply the sum of the two components P V Bond 350 23 1009 92 1360 15 Let s also price a basic perpetuity Assume a constant annual discount rate of 5 and an annual payment of 100 How much is this asset worth Now assume you promise to give your child one such perpetuity every year starting this Christmas and will continue to do this forever However your child also known as Finance Phenom Jr proposes a change in the gift giving routine He o ers to exchange his perpetuity of perpetuities starting next Christmas for a lump sum payment of 35000 to be paid immediately Should you except the exchange on a pure PV basis Why might you not accept this exchange be creative funny etc 5 V Continued Assume you don t want to make the exchange be cause you use the promise of this gift to encourage good behavior on the part of Jr during the rest of the year i e he understands that Santa only brings gifts to the good kids After hearing your decision Jr is noticeably saddened He explains that all he wanted to do with the lump sum payment is buy one of the new Sony electronic dogs cost 2000 and put the rest of the under his pillow or in an index fund he doesn t seem to care about the residual which makes you question his nickname Of course this breaks your heart and you begin to think if of a way to get Jr his beloved dog while not exceeding your current PV of promised gifts and main taining your child s good behavior You think about it and conclude that promising him perpetuities that pay slightly less than 100 each year might continue to achieve this last goal How might you want to restruc ture your gifts and under what condition would it be acceptable to you 6

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