### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Introduction to Managerial Finance, week 4 notes Fin 301

UIC

### View Full Document

## About this Document

## 32

## 0

## Popular in Managerial Finance

## Popular in Finance

This 4 page Class Notes was uploaded by Eugene Barretto on Wednesday September 7, 2016. The Class Notes belongs to Fin 301 at University of Illinois at Chicago taught by Stanley Waite in Fall 2016. Since its upload, it has received 32 views. For similar materials see Managerial Finance in Finance at University of Illinois at Chicago.

## Reviews for Introduction to Managerial Finance, week 4 notes

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/07/16

Introduction to Managerial Finance Ch. 4: Time Value of Money (Valuing Cash Flow) 4.1 Valuing a Stream of Cash Flows: Stream of cash flows – series of cash flows that lasts for several periods and is represented on a timeline. Applying the rules of valuing cash flows to a cash flow stream: Rule 1 – values in the same point in time can be compared or combined. Rule 2 – We must compound a cash flow to calculate its future value. Formula: C X (1+r)^n. Rule 3 – we must discount a cash flow’s future value to find the present value. Formula: C/(1+r)^n. - General formula for the present value of a cash flow stream: PV= C+C1/(1+r)+C2/(1+r)^2+…+CN/(1+r)^N. o The present value is the amount needed to invest today to obtain the cash flows stream C0, C1, …,CN. 4.2 Perpetuities: Perpetuities – stream of cash flows that are equal in which occurring at regular intervals that last forever. Consol (perpetual bond) – a British government bond that promise the owner equal cash flows every year, forever. - Present value of a perpetuity with payment C and interest rate f is given by: PV= C/(1+r)+C/(1+r)^2+C/(1+r)^3+… - Present Value of a Perpetuity= PV (C in Perpetuity)= C/r 4.3 Annuities: Annuity – stream consisting of a fixed number of equal cash flows paid at regular intervals that ends after a specified time period. Present Value of an Annuity: PV (Annuity of C for N Periods with Interest Rate r) = C X 1/r(1-1/(1+r)^N) Future Value of an Annuity: - In order to know the value N years in the future, we move the present value N periods forward on the timeline. FV (Annuity) = PV X (1+r)^N = C/r(1-1/(1+r)^N) X (1+r)^N = C X 1/r((1+r)^N-1) This formula is useful for the purpose of knowing how much a savings account will grow over time if the investor deposits the same amount every period. 4.4 Growing Cash Flows: Introduction to Managerial Finance Growing Perpetuity – a stream of cash flows that happens at regular intervals and grows at a constant rate forever. For example: a growing perpetuity with a first payment of $200 that grows at a rate of 5% has the following timeline: $200 for the first year. $200 X 1.05 = $210 for the second year. $210 X 1.05 = $220.5 for the third year. $220.5 X 1.05 = $231.53 for the fourth year. Present Value of a Growing Perpetuity: PV(Growing Perpetuity) = C/r-g Growing Annuity – a stream of N growing cash flows that is paid at regular intervals. For example: C is year 1. C(1+g) is year 2 … C(1+g)^N-1 is year N. Present Value of a Growing Annuity: PV= C x 1/r-g(1-(1+g/1+r)^N) 4.5 Solving for Variables Other Than Present Value or Future Value: - Used to solve for variables that we are given as inputs to calculate situations such as: the required loan payments needed to repay for a loan or to calculate how long it will take for your balance to reach a certain level when a deposit is made. For example: Initial Investment: $120,000 Equal Annual payments for the next 12 years Interest rate: 6% $120,000 = PV(12-year annuity of C per year, evaluated at the loan rate) - Use the formula for present value of an annuity 120,000 = C X 1/0.06(1-1/1.06^12) = C X 8.38 C = 120,000/8.38 = $ 14,319 annually Cash Flow in an Annuity (Loan Payment): C = P/(1/r)(1-(1/(1+r)^N)) Future Value of an annuity: Amount of money you would like to have saved in the future: $50,000 When is the future? (For how long): 12 years Interest rate per year on savings: 5% $50,000 = FV(annuity) = C X (1/0.05)(1.05^12-1) = C X 15.917 C = 50,000/15.917 = $3,141. Thus, you need to save $3,141 per year. If you do, then at a 5% interest rate your savings will grow to $50,000 in 12 years. Rate of Return Introduction to Managerial Finance - The rate of return of an investment opportunity is the rate at which the benefits exactly makes up the cost. For example: Suppose you have an investment opportunity that requires a $1,500 investment today. It will have a payoff of $3,000 in 8 years. 1,500 = 3,000/(1+r)^8 Rearranging: 1,500 X (1+r)^8 = 3,000 Solve for r: 1+ r = (3,000/1,500)^(1/8) = 1.091 1.091 – 1 = .0905 r = .0905 or 9.05%. This is the ROR. Making this investment is similar to earning 9.05% per year on your money for 8 years. Investing an amount P today, and receive FV in N years: Formula: P X (1+r)^N = FV 1 + r = (FV/P)^(1/N) - The annuity formulas are used to calculate how long it will take to save a fixed amount of money. 4.6 Non-Annual Cash Flows: - Annual cash flow streams do not only occur every year, it also occur monthly as long as: 1) The interest rate is specified as a monthly rate. 2) # of periods is expressed in months. For example: Interest rate: 5% per month Present value: $2,000 Time frame for not making payments: 4 months FV = C X (1+r)^n = $2,000 X (1.05)^4 = $2431.01 - R is equal to the monthly interest rate and N is equal to the number of months. - We apply the same future value formula. Introduction to Managerial Finance

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.