Lecture04

Lecture04 - Corporate Finance Theory ECON Zhiguo He E-mail...

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1 Corporate Finance Theory ECON 360-0-30 Zhiguo He E-mail: [email protected] Office hours: Thursday 5:00-6:00 pm Room 404, Kellogg Finance Dept 4 th Floor, Andersen Hall Course website: Blackboard http://courses.northwestern.edu/webapps/login
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2 “Just-to-Remind-You” Quiz Last Time: What is net present value (NPV) ? What is opportunity cost of capital ? What is the essence of the NPV rule ? Why unlike the NPV rule, neither profit nor rate of return can be used as alternative universal investment decision rules?
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3 Lecture 4 At a Glance Today: Quoting Interest Rates and Compounding Inflation and Nominal vs. Real Interest Rates Different Currencies and Interest Rate Parity
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4 Compound vs. Simple Interest Definitions: Compound interest: reinvestment of each interest payment to earn more interest Simple interest: interest is calculated only once on the initial investment (no interest is earned on the interest paid). t 0 r) (1 C + = t FV t) r 1 ( C 0 × + = t FV
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5 Quoting Interest Rates “the Certificate of Deposit (CD) offers a 6% A.P.R. compounded quarterly” Okay…so what is the effective annual interest rate? A.P.R. – annual percentage rate. Often called Stated. A.P.R. must be divided by the number of periods to obtain the periodic interest rate for compounding in this case the quarterly interest rate is 6% / 4 = 1.5% the effective annual interest rate is known as effective annual yield – EAY, in this case: (1.015) 4 = 6.14% In general you could get 106.14 in the end if you invest 100 initially. But be careful. INGDirect: Interest on your Orange CD is accrued daily and compounded annually . Citibank: Interest can be paid monthly to your CD, checking or savings.
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6 Quoting Interest Rates Let r= A.P.R. and k = # of compounding intervals . EAY is given by 1+ EAY = (1+r/k) k Always check that you obtain EAY close to r but higher Example: A.P.R. = 6% k 1+EAY 1 1.06 2 (1+0.06/2) 2 = 1.0609 4 (1+0.06/4) 4 = 1.0614 12 (1+0.06/12) 12 = 1.0617 365 (1+0.06/365) 365 = 1.06183 8,760 (hourly) (1+0.06/8760) 8760 = 1.061836
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7 Mortgage Example You buy your first house for $250,000, where the down payment is $50,000. Your local bank offers you a 9% APR (compounded monthly) 30 year mortgage. a) What is your monthly payment? b) How long would it take you to pay back the mortgage if you are willing to increase the monthly payment by $200? Key: adapt yourself to the case of non-annual payment. t=0,1,2,… could be quarterly, monthly, weekly, daily. . After all, “year” is just a length of one specific period. Similarly we can have annuity for monthly payments
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8 Monthly payment (9% A.P.R., monthly compounding, 30 years): $200 larger monthly payments: 609 , 1 $ X 0.09/12) (1 1 1 0.09/12 X 000 , 200 $ 12 30 = + - = × 5 . 236 ) 1708 . 0 ln( ) 0075 . 1 ln( = = - n n 1708 . 0
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Lecture04 - Corporate Finance Theory ECON Zhiguo He E-mail...

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