UGBA 180 Lecture Notes - Lecture 1: Cash Flow
25 Jun 2018
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1/16/18
Lecture 1: Time Value of Money
Time Value of Money
●Basics
○PV: present value, the initial deposit, present value of an investment of money
○i: interest rate
○n: number of time periods
○FV: future, value at some specified future period
○m: number of compounding intervals within one year
○PMT: value of periodic payments
●Key relationship: compound interest
●Annual Formula: FV = PV(1 + i)n
●Monthly Formula: FV = PV(1 + i/m)n*m
●PMT Formula: FV = Σt=1n-1 PMT(1 + i)t +PMT
Exercises
●Unknown FV
○Deposit $10k today
○Earn annual interest of 6%
○What is the value of deposit after 1 year?
○ => FV = 10,000 + (10,000 * 0.06) = 10,600
●Multiple periods
○Suppose you leave the $10k for 2 years
○=> FV = 10,000(10,000 * 0.06)*(10,000 * 0.06) = 11,236
●Compounding monthly
○Suppose 6% rate is compounded monthly not annually
○=> FV = PV(1 + i/m)n*m
○=> FV = 10,000 (1 + 0.06/12)1*12= 10,616.78
●Unknown: PV
○Consider an investment that pays $10.6k after 1 year
○If investor requires a 6% return what price should be paid for the investment
today?
○ FV = PV(1 + i)n
○PV = FV / (1 + i)n
○=> PV = 10,600 / (1 + 0.06)1 = 10,000
Annuities
●So far we only have been doing a single deposit or payment made once
find more resources at oneclass.com
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Document Summary
Pv: present value, the initial deposit, present value of an investment of money. Fv: future, value at some specified future period. M: number of compounding intervals within one year. Annual formula: fv = pv(1 + i)n. Monthly formula: fv = pv(1 + i/m)n*m. Pmt formula: fv = t=1 n-1 pmt(1 + i)t +pmt. Suppose you leave the k for 2 years. => fv = 10,000(10,000 * 0. 06)*(10,000 * 0. 06) = 11,236. Suppose 6% rate is compounded monthly not annually. => fv = 10,000 (1 + 0. 06/12)1*12= 10,616. 78. Consider an investment that pays . 6k after 1 year. Pv = fv / (1 + i)n. So far we only have been doing a single deposit or payment made once. But: many investments involve a series of equal deposits (or payments) made at equal intervals over time. Deposit k at the end of each year for 5 years. Interest compounded at annual rate of 5%
