TVOM LECTURE

.pdf

School

Arizona State University *

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Course

300

Subject

Finance

Date

Apr 25, 2024

Type

pdf

Pages

6

Uploaded by vivi_foreverr on coursehero.com

FIN 300 TVOM: Time Value of Money The value of any asset (investment) is determined by: 1) Return the benefit from investing current income vs. capital gains income 2) Time how long you will have to wait to receive the return 3) Risk the chance that you will not receive the expected return Valuation areas: 1) Future Value of a Lump Sum (a single deposit) FVIF: Future Value Interest Factor Present Value ------------------> Future Value “compounding over time” You invest $3000 into an account earning 5%. After 5 years, what has the account grown to? FV = PV (FVIF) = $3000 (FVIF 5%, 5 = 1.276) =$3828 If you leave the $3000 in the account for 10 years, what would the account grow to? FV = PV (FVIF) = $3000 (FVIF 5%, 10 = 1.629) = $4,887 The “Rule of 72” shows how long it would take to double your money 72 = Number of years needed to Int. Rate double your money 72 = Annual interest rate earned # of years
You invest $5000 at 8%, how long will it take to double your money? 72 = 9 years 8 If your investment doubled in 6 years, what annual interest rate were you earning? 72 = 12% 6 2) Future Value of an Annuity an annuity is a series of equal payments (or benefits) made at equal time intervals Annuity due-payment is made at the beginning of the period Ordinary (or regular) annuity- payment is made at the end of the period FVIFA: Future Value Interest Factor of an Annuity You invest $5000 annually into your Roth IRA which is earning 8% annually. After 35 years, what is the balance of your IRA? FV = annuity (FVIFA) = 5000(FVIFA 8%, 35 = 172.31) = $861,550 What if you could earn 9% over the 40 years instead of 8%, what would your IRA balance be? FV = annuity (FVIFA) = $5000(FVIFA 9%, 40 = 337.87) = $1,689,350 Any assumptions being made here? 3) Sinking Fund (FVIFA) Deposits that are needed to accumulate a future amount
You are planning on retiring in 40 years and would like to save an additional $2,500,000 in addition to your retirement savings. How much will you need to save annually- earning 8% interest-in order to reach your goal? FV = sinking fund annuity FVIFA 2,500,000 = $9651 (FVIFA 8%,40=259.05) If you could earn 10% interest (instead of 8%), how much would you need to save annually? 2,500,000 = $5649 (FVIFA 10%,40=442.58) In 30 years, you would like to establish a charitable foundation worth $1,000,000. If you plan to invest in the stock market-hopefully earning an average of 10% annually-how much would you have to deposit yearly in order to accumulate the $1,000,000? 1,000,000 = $6079 (FVIFA10%,30=164.49) 4) Present Value of a Lump Sum What is a future benefit worth to you today? PVIF: Present Value Interest Factor Present Value <--------------------Future Value Discounting over time You have just won a $2,000,000 court settlement which will be paid to you in 10 years. In other words, you won’t receive anything until the end of the tenth year. Assuming 7% interest, what is your settlement worth to you today? PV = FV (PVIF) = $2,000,000(PVIF 7%,10=.508) = $1,016,000 Assuming 9% interest instead of 7%, what is your settlement worth today? PV = FV (PVIF) = 2,000,000(PVIF 9%,10=.422) = $844,000
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