Chapter4b+5+notes

# Chapter4b+5+notes - Chapter 4(Contd Time Value of Money...

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Chapter 4 (Cont’d) Time Value of Money

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2 Spring 2009 Outline Time Value of Money Rules of Time Travel Series of Regular Cash Flows Other Variables Perpetuities Annuities Amount of Cash Flows Number of Periods Rate of Return Series of Growing Cash Flows FV & PV
3 Spring 2009 Growing Perpetuities Example 4.9

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4 Spring 2009 Growing Perpetuities First CF does not grow. Solution: Plan: ± How large does the lump sum have to be in order to support a perpetual growth in the withdrawal?
5 Spring 2009 Growing Perpetuities Execute: ± If the perpetual payment, \$30,000, increases by 4% each year, then the principal in the fund will have to grow at the same rate, 4%, to generate this growing perpetuity. ± Therefore, the perpetual payment can only be: P (8% – 4%). Æ \$30,000 = P (8% – 4%) P = \$30,000 / (8% – 4%) = \$750,000 today Evaluate: ± You need to double the size of your gift!

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6 Spring 2009 Formula of Growing Perpetuities ± Present Value of a Growing Perpetuity ² C = P (r – g) (growing perpetuity) = C PV r g
7 Spring 2009 Outline Time Value of Money Rules of Time Travel Series of Regular Cash Flows Other Variables Perpetuities Annuities Amount of Cash Flows Number of Periods Rate of Return Series of Growing Cash Flows FV & PV

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8 Spring 2009 Focusing Question You are a financial planner wishing to persuade a young client to reconsider her \$50,000 invested in 3%-CDs. Your client believes that stock mutual funds will return about 12% for the foreseeable future, but she is averse to the volatility in returns. Her money will remain fully invested for the next 48 years. How to convince her to take the risk of investing in stock mutual funds?
10 Spring 2009 Learning Objectives 1. Given three out of the following four inputs for a single sum, compute the fourth: (a) present value, (b) future value, (c) number of periods, (d) periodic interest rate. 2. Given four out of the following five inputs for an annuity, compute the fifth: (a) present value, (b) future value, (c) number of periods, (d) periodic interest rate, (e) periodic payment. 3. Given cash flows and present or future value, compute the internal rate of return. 4. Set up TVM questions in Excel.

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11 Spring 2009 Finding the Cash Flows Example 4.10 Solution: Plan: ± We start with the timeline (from the bank’s perspective): ± \$80,000 is the PV of an annuity
12 Spring 2009 Finding the Cash Flows Execute: Evaluate: ± Your firm will need to pay \$7,106.19 each year to repay the loan. The bank is willing to accept these payments because the PV of 30 annual payments of \$7,106.19 at 8% interest rate per year is exactly equal to the \$80,000 it is giving you today. ] 30 0.08) (1 1 [1 0.08 C \$80,000 + = Given: 30 8 -80,000 0 Solve for: 7106.19 Excel Formula: =PMT(RATE,NPER, PV, FV) = PMT(0.08,30,-80000,0)

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13 Spring 2009 Quick Quiz 1. Suppose you have just graduated from college and would like to start saving for a down payment on an apartment. You would like to have \$600,000 saved 10 years from now. If you can earn 7% per year on your savings, how much do you need to save each year to meet your goal?
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Chapter4b+5+notes - Chapter 4(Contd Time Value of Money...

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