BMGT340 Class Notes Ch 04

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University of Maryland *

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340

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Finance

Date

Jan 9, 2024

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7

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Business Finance – Chapter 4 Part 1 General Cash Flow Streams, Perpetuities, & Annuities I. General Cash Flow Streams a. Example: You are considering an investment that will pay you $1390 in one year, $2300 in two years and $3661 in three years. If you want to earn 12% on your money, how much will you be willing to pay? Round and answer to the nearest cent. i. Timeline: 0 1 2 3 1390 2300 3661 ii. Present Value Formula: 1390/1.12+2300/1.12^2+3661/1.12^3=5680.44 iii. Cash Flow Register: iv. LC#2 You have the following cash flows: Year 1 CF = 100, Years 2 and 3 = 200, Years 4 and 5 = 300. The discount rate is 7%. What is the value of the cash flows today? 874.14 v. You have the following cash flows: Year 1 CF = $100, Years 2 and 3 = $200, Years 4 and 5 = $300. The discount rate is 7% What is the value of the cash flows at year 5? PV=874.14 PV*(1+r)^t=FV 874.14 * 1.07^5= 1226.07
vi. LC#3 What is the value of the cash flows at year 3? vii. LC#22 Basketball phenom, Duncan McNet, is negotiating a four year contract to play in the NBA. He wants the present value of the contract to be $20 million. The first three years are already set below. What is the minimum he should demand in year four at a 9% interest rate? Year 1 $7,000,000 Year 2 $6,000,000 Year 3 $5,000,000 Year 4 ??? (7/1.09) + (6/1.09^2) + (5/1.09^3) + (x/1.07^4) =20 6587
Perpetuities viii. Timeline: ix. Present Value Formula: x. LC #6 Acme Corp.'s preferred shares pays dividends of $5 annually. The market's discount rate on these dividends is 12%. What is the market price of Acme Corp.'s preferred shares? 5/.12= 41.67 xi. LC #7 You are considering preferred stock that pays a quarterly dividend of $1.50. If your desired return is 3% a quarter, how much would you be willing to pay? C/r= 1.5/.03= 50
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xii. LC#16 You want to endow an annual graduation party at your alma mater. You want the event to be a memorable one, so you budget $30,000 per year forever for the party. If the university earns 8% per year on its investments, and if the first party is in one year’s time, how much will you need to donate to endow the party? C/r= 30,000/.08= 375,000 xiii. LC #8 Entrepreneur Zark Muckerberg is starting a company out of his dorm room and is asking for you to invest in it in exchange for a special preferred share that initially will not pay any dividends. In 11 years, the first annual dividends of 10,000 USD will be paid. (You will be paid this dividend every year after that.) You require at least a 20% expected annual return on this investment. What is the most you are willing to invest in Mr. Muckerberg's company? C/r=10000/.2=50000= year 10 value PV today= 50000/1.2^10= 8075 b. (Ordinary) Annuities i. Timeline
Present Value Formula ii. Future Value Formula iii. Financial Calculator iv. LC#13 You want to receive $5,000/month for the next 5 years. How much would you need to deposit today if you can earn 0.75% per month? v. LC#14 You decide to begin saving towards the purchase of a new car in 5 years. If you put $2,000 at the end of each of the next 5 years in a savings account paying 5% compounded annually, how much will you accumulate after 5 years? vi. Exam Question: You are planning to retire 50 years from today. Starting one year after the day you retire, you will withdraw money every year from your retirement savings for 30 years. You will save $5,000 per year starting one year from today. At an annual rate of return of 9%, what is the most amount you can withdraw per year in retirement? A) $5,334.85
B) $135,847.26 C) $8,333.33 D) $153,334.38 E) $396,686.30 Annuities Due: Cash flows occur at the _beginning_ of every period. Every annuity due problem can be rephrased as an ordinary annuity problem because the beginning of one period is the same as the end of the _previous_ period. vii. Example: The lottery advertises the jackpot with what is calls an "annuitized value" which is just the sum of 30 nominal dollar payouts over a 29 year period. (The first payout is immediate, and the remaining 29 payments are every year afterwards.) If you, the winner, think your investments can earn 5% per year, then what lump sum would you accept today instead of the 30 $10 million payouts? A. $154,275,000 B. $161,411,000 C. $325,869,000 D. $286,210,000 E. $243,572,000 viii. Timeline
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ix. Formula x. Financial Calculator - Suggestion: Reframe annuity due problems as ordinary annuities and leave your calculator set to “END”.