{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ORIE 350 Lecture 9

ORIE 350 Lecture 9 - 1 = Payment at first annuity period =...

This preview shows pages 1–3. Sign up to view the full content.

ORIE 350 Lecture 9 Today: Time value of money Bonds Wednesday: Leases Thursday: prelim 1 HO 110 and B-14 Time value money Interest expense on a construction loan is added to the cost of the asset itself 10,000,000 Building 9,000,000 Loan at 6% (9,000,000) x 0.06= 540,000 Building(A) 10,540,000 Time value of money FV= PV(1+i) n Be careful that i and n match, e.g. i is the monthly rate and n is the number of months (used for monthly compounding) To get i: i = i nom / C i nom = nominal annual rate i = periodic rate C = no. Of compounding periods per year Annuity

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Multiple periodic payment of a fixed and constant amount. Business applications 1. Some loans 2. All bonds (except zero coupon bonds) 3. All leases Personal applications 1. Car loans 2. Home mortages On a time line Give me 8,000 now and I will give u 2,000 dollars every year for 5 years Ordinary annuity-> payment occurs at the end of each period Annuity Due-> payment at the beginning of each period e.g lease for apartments PV
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 = Payment at first annuity period = A/(1+i) PV 2 = A 2 /(1+i) 2 Total present value = PV 1 + PV 2 + PV 3 + . ..+ PV n To make it into a geometric series, add A in front and subtract A from the present value after that PV= A(1-(1+i)-n )/ i) FV= A((1+i) n-1)/i) In class examples 1 a. FV= 120,000 i=9% n= 8 years(matches interest rates) PV=? Single payment today PV= FV/(1+i) 8 = 120,000/(1.09) 8 =60,223.95 b. PV= 120,000(1.05) 8 / (1.09) 8 = 83,973.21 2. PV = 10,000 I nom = 3% C =12 n=42 months FV=? 1. Convert i = i nom /C I= 0.03/12= 0.0025 2. FV= PV(1+) n = 10,000 (1.0025) 42 = 11,105.65 3. Ordinary annuity PV= ? A= \$2,250 per year I= 10% per year N= 15 years Note compounding frequency = payment frequency for annuities PV= 2250 x (1-(1.1)-15 )/0.10)= 17,113.68 4. Deposits are monthly, means compounded monthly FV= A[(1+i) n-1/i] x (1+i) = 200[(1+0.07/12) 180-1/(0.07/12)] x (1+0.07)= 63,762.25...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern