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# Week 4 FIN300 FIN 300

Long Beach State

GPA 3.56

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This 4 page Class Notes was uploaded by a-tark on Saturday February 13, 2016. The Class Notes belongs to FIN 300 at California State University Long Beach taught by Dr. Chanwit Phengpis in Winter 2016. Since its upload, it has received 64 views. For similar materials see Business Finance in Finance at California State University Long Beach.

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Date Created: 02/13/16

These are additional notes that I take during Dr. Phengpis’ lectures. The actual class notes are posted on his own website. The intention is to provide extra help. Chapter 4: Introduction to Valuation: The Time Value of Money Introduction and Initial Discussion: One year from now (<$1) < today’s value (must be $1) Because opportunity lost to consume, spend, or invest right now. Two Types of Money 1. Future Value of Money How much will your money grow to after one or more periods? The process of finding future value is called “compounding” because FV of $X is typically larger than $X. FV of $X must be bigger. 2. Present Value of Money How much money is needed today to generate some future value of money? How much is the today’s value of cash flows expected in the future? The process of finding present value is called “discounting” because PV of $X is typically less than $X. o Typically: when there is interest. You must deposit less than FV because with the interest it would reach FV. Present value calculations are important: o In finding the fair price of an asset because the fair price is equal to PV of future cash flows expected from the asset. EX: stock or a project o In evaluation of investment projects – Ch. 4,5,8,9 o Capital budgeting – Ch. 4,5,8,9 o Pricing of bonds and stocks – Ch. 6 & 7 o Firm valuation – Ch. 10-13 1. Future Value of Money I. Investing for a single period FV = $X (1+r) EX: at the ending of the year = ending amount = future amount = FV! PV = $ 100, so FV must be >$100 because we earn interest. FV = X (1+r) FV = 100 (1+0.10) -> FV=$110 ($100: principal, $10: interest) II. Investing for more than a single period i. If using simple interest rule: The second year interest will be earned on only the original principal of $100. Thus, the interest earned will be another $10 during the second year and the investment will be worth 110 + 10 =$120 at the end of year 2. (#s from pg.3) ii. If using the compounding interest rule: The second year interest will be earned on the new principal of $110. FV = 110(1.10) = 100(1.10)(1.10) = 100(1.10)^2 = $121 [new principal is 110(1.10)] Part Amount The original principal $100 The first year interest $10 The second year interest earned on the original principal $10 The second year interest earned on the first year interest $1 Total $121 FV = $X (1+r)^t EX: (pg.5) FV = $100 (1+0.10)^5 FV = $161.0510 Financial Calculator: 100 PV 5 N 10 i/yr FV If you’re a lender you would choose compound interest method and if you’re a borrower you would choose single interest method. EX: What if the investment earns simple interest, rather than compound interest. FV = ? Total interest = 0.10 x 100 = $10 $10 x 5 = $50 FV @ the end of 5 years = principal + total interest = $100 + $50 = $150 2 The interest rate & Time (pg.6) The higher the r (interest rate), the greater the FV is. The higher the t (number of time periods), the higher the FV. EX: PV = $500 , t = 15 , r = 20% = 0.2 Using the financial calculator -> FV = $7703.5108 2. Present Value of Money I. Investing for one period PV = $X / (1+r) r; discount rate = opportunity cost of capital = required return these are there different wordings for the interest rate r used in PV calculation: i. The discount rate because the process of finding PV is called discounting. ii. The opportunity cost of capital or the highest return available in capital markets on the investment of asset with similar risk. This is based on the “law of one price”: “similar risk, similar return” , “same risk, same return.” iii. The required return because it is the rate of return that should be received by investors given the risk of investment or asset. Otherwise, investors will invest in a similar risk asset that provides at least the required return. EX: PV = 500 / (1+0.035) -> PV = $483.0918 If you deposit $483.09 today, after 1 year it’ll be $500. EX: (T-Bill) PV = 10000 / (1+0.07) -> PV = $9354.7944 As of today, Feb 2016, 1 year T-bill rate = 0.25% II. Investing for more than one period PV = $X / (1+r)^t EX: PV = 30500 / (1+0.09)^2 -> PV = $25671.2398 EX: PV = 10000 / (1+0.065)^10 -> PV = $5327.2604 The interest rate & Time (pg.10) The higher the r (interest rate), the lower the PV is. (inverse relationship) The higher the t (number of time periods), the lower the PV. (inverse relationship) EX: FV = $500 , t = 5 , r = 5% = 0.05 3 PV = 500 / (1.05)^5 -> PV = $391.7631 EX: FV = $500 , t = 5 , r = 10% = 0.1 PV = 500 / (1.1)^5 -> PV = $310.4607 EX: FV = $500 , t = 8 , r = 10% = 0.1 PV = 500 / (1.1)^8 -> PV = $233.2537 ---skipped the page with the examples, and went to pg.11--- Present Values and Future Values Finding the Discount Rate r = [FV/PV]^(1/t) -1 EX: PV = $100, FV = $122, t = 4yrs., r = ? r = [(122/100)^(1/4)] – 1 r = 0.0509 -> r = 5.09% with the FC: 100 +/- PV 122 FV 4 N i/yr , r = 5.0969 +/- before PV: lender/investor; because you have toinvest 100 to receive 122 in the future, this sign shows that you paid 100 today. If you put +/- before FV: borrower; (you will get the same result) EX: PV = $10000, FV = millionaire, t = 50 yrs., r = ? 10000 +/- PV 1000000 FV 50 N i/yr , r = 0.09647 -> r = 9.647% Caution: account for cash flow sign properly when we input more than 1 sets of cash flows into financial calculation. Finding the Number of Periods t = [ln(FV/PV)] / [ln(1+r)] EX: PV = $115, FV = $155, r = 4% = 0.04, t? t = [ln(155/115)] / [ln(1+0.04)] -> t = 7.6107 with the FC: 115 +/- PV 155 FV 4 i/yr N , t = 7.6107 RULE 72; approximately (72/r), r% EX: r = 5% = 0.05, t? 72/5 = 14.4000 FC (exact); if PV = 100, FV = 200, r = 5% 100 +/- PV, 200 FV, 5 i/yr, N -> t = 14.2067 years Caution: account for cash flow sign properly when we input more than 1 sets of cash flows into financial calculation. 4

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