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## Introduction to Managerial Finance, week 4 notes

by: Eugene Barretto

32

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4

# Introduction to Managerial Finance, week 4 notes Fin 301

Marketplace > University of Illinois at Chicago > Finance > Fin 301 > Introduction to Managerial Finance week 4 notes
Eugene Barretto
UIC

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These notes covers The Time Value of Money: Valuing Cash Flow Streams in the Ch. 4's reading of Berk, DeMarzo, Harford's Fundamentals of Corporate Finance, 3rd edition.
COURSE
Managerial Finance
PROF.
Stanley Waite
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
finance, Intro to Personal Finance
KARMA
25 ?

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This 4 page Class Notes was uploaded by Eugene Barretto on Wednesday September 7, 2016. The Class Notes belongs to Fin 301 at University of Illinois at Chicago taught by Stanley Waite in Fall 2016. Since its upload, it has received 32 views. For similar materials see Managerial Finance in Finance at University of Illinois at Chicago.

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Date Created: 09/07/16
Introduction to Managerial Finance Ch. 4: Time Value of Money (Valuing Cash Flow) 4.1 Valuing a Stream of Cash Flows: Stream of cash flows – series of cash flows that lasts for several periods and is represented on a timeline. Applying the rules of valuing cash flows to a cash flow stream:  Rule 1 – values in the same point in time can be compared or combined.  Rule 2 – We must compound a cash flow to calculate its future value. Formula: C X (1+r)^n.  Rule 3 – we must discount a cash flow’s future value to find the present value. Formula: C/(1+r)^n. - General formula for the present value of a cash flow stream:  PV= C+C1/(1+r)+C2/(1+r)^2+…+CN/(1+r)^N. o The present value is the amount needed to invest today to obtain the cash flows stream C0, C1, …,CN. 4.2 Perpetuities: Perpetuities – stream of cash flows that are equal in which occurring at regular intervals that last forever. Consol (perpetual bond) – a British government bond that promise the owner equal cash flows every year, forever. - Present value of a perpetuity with payment C and interest rate f is given by: PV= C/(1+r)+C/(1+r)^2+C/(1+r)^3+… - Present Value of a Perpetuity= PV (C in Perpetuity)= C/r 4.3 Annuities: Annuity – stream consisting of a fixed number of equal cash flows paid at regular intervals that ends after a specified time period. Present Value of an Annuity: PV (Annuity of C for N Periods with Interest Rate r) = C X 1/r(1-1/(1+r)^N) Future Value of an Annuity: - In order to know the value N years in the future, we move the present value N periods forward on the timeline. FV (Annuity) = PV X (1+r)^N = C/r(1-1/(1+r)^N) X (1+r)^N = C X 1/r((1+r)^N-1)  This formula is useful for the purpose of knowing how much a savings account will grow over time if the investor deposits the same amount every period. 4.4 Growing Cash Flows: Introduction to Managerial Finance Growing Perpetuity – a stream of cash flows that happens at regular intervals and grows at a constant rate forever.  For example: a growing perpetuity with a first payment of \$200 that grows at a rate of 5% has the following timeline: \$200 for the first year. \$200 X 1.05 = \$210 for the second year. \$210 X 1.05 = \$220.5 for the third year. \$220.5 X 1.05 = \$231.53 for the fourth year. Present Value of a Growing Perpetuity: PV(Growing Perpetuity) = C/r-g Growing Annuity – a stream of N growing cash flows that is paid at regular intervals.  For example: C is year 1. C(1+g) is year 2 … C(1+g)^N-1 is year N. Present Value of a Growing Annuity: PV= C x 1/r-g(1-(1+g/1+r)^N) 4.5 Solving for Variables Other Than Present Value or Future Value: - Used to solve for variables that we are given as inputs to calculate situations such as: the required loan payments needed to repay for a loan or to calculate how long it will take for your balance to reach a certain level when a deposit is made. For example:  Initial Investment: \$120,000  Equal Annual payments for the next 12 years  Interest rate: 6% \$120,000 = PV(12-year annuity of C per year, evaluated at the loan rate) - Use the formula for present value of an annuity 120,000 = C X 1/0.06(1-1/1.06^12) = C X 8.38 C = 120,000/8.38 = \$ 14,319 annually Cash Flow in an Annuity (Loan Payment): C = P/(1/r)(1-(1/(1+r)^N)) Future Value of an annuity:  Amount of money you would like to have saved in the future: \$50,000  When is the future? (For how long): 12 years  Interest rate per year on savings: 5% \$50,000 = FV(annuity) = C X (1/0.05)(1.05^12-1) = C X 15.917 C = 50,000/15.917 = \$3,141. Thus, you need to save \$3,141 per year. If you do, then at a 5% interest rate your savings will grow to \$50,000 in 12 years. Rate of Return Introduction to Managerial Finance - The rate of return of an investment opportunity is the rate at which the benefits exactly makes up the cost. For example:  Suppose you have an investment opportunity that requires a \$1,500 investment today.  It will have a payoff of \$3,000 in 8 years. 1,500 = 3,000/(1+r)^8 Rearranging: 1,500 X (1+r)^8 = 3,000 Solve for r: 1+ r = (3,000/1,500)^(1/8) = 1.091 1.091 – 1 = .0905 r = .0905 or 9.05%. This is the ROR. Making this investment is similar to earning 9.05% per year on your money for 8 years. Investing an amount P today, and receive FV in N years: Formula: P X (1+r)^N = FV 1 + r = (FV/P)^(1/N) - The annuity formulas are used to calculate how long it will take to save a fixed amount of money. 4.6 Non-Annual Cash Flows: - Annual cash flow streams do not only occur every year, it also occur monthly as long as: 1) The interest rate is specified as a monthly rate. 2) # of periods is expressed in months. For example:  Interest rate: 5% per month  Present value: \$2,000  Time frame for not making payments: 4 months FV = C X (1+r)^n = \$2,000 X (1.05)^4 = \$2431.01 - R is equal to the monthly interest rate and N is equal to the number of months. - We apply the same future value formula. Introduction to Managerial Finance

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