### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Intermediate Business Finance FINC 332

RU

GPA 3.67

### View Full Document

## 31

## 0

## Popular in Course

## Popular in Finance

This 12 page Class Notes was uploaded by Anthony Jaskolski on Monday October 19, 2015. The Class Notes belongs to FINC 332 at Radford University taught by Staff in Fall. Since its upload, it has received 31 views. For similar materials see /class/224672/finc-332-radford-university in Finance at Radford University.

## Reviews for Intermediate Business Finance

### 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: 10/19/15

FINC 332 Time is Money The Time Value of Money A friend wants to borrow 100 How much should you charge himher for renting your money for a year The bank pays you 5 interest per year Remember from the Introduction that higher risk should be rewarded with higher return There is more risk that your friend won t pay than the bank won t pay 80 you and your friend agree to a 10 interest rate Time line is Loan 100 at 10 compounded annually gt FV1 100 1001O 100110 110 Note that I am saying that 100 today has the same value as 110 next year Now consider that your friend wants to pay you back after 2 years instead of 1 FV2 FV1 FV11O 1101101O 121 General form FVn PV 1 i quot PV FVIFiYn i interest rate or discount rate per period n number of periods Example 1000 deposited into a 5 compounded annual savings acct on my 10th birthday Today is my 18th birthday How much is in the account FVg 1000 105 8 1000 147746 147745 0 8 1000 FV i5 Compounding The previous example assumes that the bank pays the interest into the account at the end of each year We call this compounding annually Some loans are structured to compound more often EX bonds pay semiannually car loans pay monthly To compound more often than annually we must adjust the tand the rof our equation n must be the number of periods i must be the rate per period annual rate periods per year From example above What if bank compounds monthly Then n 12 x 8 96 months i 512 4167 per month Answer is Fv96 PV x 1iquot 1000x100416796 149063 Note that compounding more often creates more money Present Value The earlier equation was FVn PV 1 i quot solving for PV gives FVn V Fvn PVIFiyn 1z39quot Notice that the PV and FV calculations are the inverse of each other Example You inherit 1 million But the money is to be held in trust for 5 year before you can get your hands on it To get money now you visit a bank It will lend you money at 12 interest How much money can you borrow so that you will owe that bank exactly 1 million in 5 years PV 1 OO0000 i12 PV 10000001125 56742686 Note that this is considerably smallerthan 1 million bucks Calculating present value is often called discounting the present value is smaller and the interest rate is called the discount rate Solving for interest rate discount rate and number of periods In some cases we know the present and future cash flows but we don t know either the interest rate or the number of periods We can solve the PVFV equation for these variables i FVPV quot 1 and n m i n1i Now we are starting to see the usefulness of the financial calculator Solving for iquot example 3 yrs ago I bought a stock for 60 and now is worth 7986 What is the annual return I received what is the implicit discount ratequot 0 3 l l l 60 79 86 I 798660 3 1 i 10 10 On the tables Find FVIF 1331 for n 3 gt 10 What is 1331 In the parenthesis you find 1 holding period return In other words we know that the investment provided a total return of 331 Confirm this FV PV 1iquot FV 60 1331 7986 Evaluating Investmentsquot What if you could have invested the money in a similar stock that provided a 12 return Usually the investment that we are considering should be examined by comparison to the alternative investment recall that higher returns on alternative investments will reduce the value of the current investment Find the PV PV Fvn 1iquot PV 7986 1123 PV 7986 140493 PV 5684 In other words the 60 investment I bought was truly only worth 5684 at that time If I had bought it at 5684 and its price now were 7986 then I would have obtained a 12 return Solving for nquot example Deposit 1000 into an 8 compounded semiannual account now How long will it take to grow to 2000 i 824 t n 20001000 17673 semiannual periods n104 or 88365 years 8yrs 10 mos On the tables Find 20001000 2 under the 4 interest rate for a FVIF It is between 17 and 18 with FVF4Y17 19479 and FVF4Y18 20258 Since our goal is an FVIF 2 then we can guess that it is going to take a little over 175 periods since it comes in about 0521 under on the low side and 0258 over on the high side If we add 19479 20258 then divide by 2 we get 19869 Effective Annual lquot Rate EAR Since the frequency of compounding can significantly affect the amount of real interest paid To make useful comparisons use the effective annual percentage rate EAR EAR1 NW 1 m where iNom is the nominal annual percentage rate the quoted rate and m is the number of compounding periods per year Q Given a choice would you prefer to receive 1 975 compounded annually or 2 95 compounded quarterly Need to compare EAR EAR 975 for annual compounding EAR 1 09544 1 98438 for the quarterly compounding Which rate do you want if you are lending the higher EAR 95 compounded quarterly lf borrowing which rate would you choose The lower EAR Notice how the EAR makes comparison useful Consider comparing these two as investment opportunities for 3 years invest 1000 1 975 compounded annually gt FV PV 1iquot 1000 109753 132195 2 95 compounded quarterly gt 1000 10237512 132534 More And the EAR can be used to confirmgt FV PV 1EARquotyears 1000 1 0984383 132534 How do we take an EAR and convert it into a quoted rate We already know this EAR 12ij 1 m 1 EAR 1 iNommquot 1 EAR 1 iNomm 1 EAR m 1 iNomm m1 EAR 1 im By law the APR Annual Percentage Rate is the quoted rate That s messy look at what s going on 1 EAR 1 1098438 4 1 02375 gt 02375 x 4 95 Multiple Cash Flows Assume that you are interested in starting a business selling ice cream on campus You have estimated your revenues and expenses and placed those estimates in a proforma income statement to then create a cash flow estimate The estimates are as follows PV 4761 6312 7863 6312 3986 To find the present value we must find the present value of each of the five cash flows and then add them together Based on the risk of the project a 12 discount rate is used CF CF CF V 711 722 7 11 1z39 1z39 For this problem we use five cash flows 4761 6312 7863 6312 3986 7 7 7 1121 1122 1123 1124 1125 425089 503189 559673 401139 226176 2115266 So the present value of accepting the ice cream project is 21153 and we can compare this to the cost of entering the project You will have to spend 20000 to get the project rolling Should you accept the project Why We can also compute the future value of a series of cash flows Fvn CF01iquot CF11iquot391 CF21iquot392 CFn Perpetuities The name Perpetuity refers to a constant cash flow stream that has no end The cash flows must all be the same but they go on forever Examples Preferred stock consols Luckily the infinite series of the equation presented earlier reduces to PVPerpetuity PMT i Example How much will you pay to receive 100 per year forever considering your required rate of return is 12 PV 100 12 83333 Annuities An annuity is a fixed payment C for a specific period of time Examples are auto loans and home mortgages The present value of these fixed payments can be calculated as PVA PVAquot PMTL1ZJ PMTPVFA 1 An example Congratulations you won the lottery You won 4 million to be paid as 200000 per year for 20 years with payments beginning next year What is the present value of the prize given a 9 discount rate all are 200000 answer PVA 200000 9128546 182570913 What ifl get the first payment today This is called an annuity due Also see PVA 200OOO111O92 O9 109 182570913 109 199002296 General form PVA FVAquot Due PMTM11 PMTPVFAin1i z The equation for the future value of an annuity of fixed payments is FVA FVA PMT1l H PMTFVFA 1 An example You put 100 per month into your savings account which earns 7 per year and compounds monthly for 5 years beginning next month How much money is available to you then All are 100 FV i 712 FVA 1OO1OO58336 1005833 715922 FVA 100715922 715922 What if the first payment is now General form FVADue FVA PMT 1i 11i PMTFVFAin1i I It is difficult to solve for n or i in the two annuity equations Solving for PMT n i Payments Example You need to obtain a mortgage to buy a house To buy the house you want you need to borrow 200000 Assume the mortgage interest rates for 30 year loans are 750 What are your monthly payments 1 2 3 359 360 I I I I I I I 200000 all are i 75012 PVA PMT 11l1in PMTPVIFAin 1 1 10062536 PVA PMT 00625 J PMT143017627 200000 PMT 143017627 PMT 139843 Oh no the bank says that we can only afford 850 in monthly payments How much of a home can we afford PVA 850 143017627 12156498 Amortized Loans We have examined how we can calculate the payment that must be made on an annuity with a given number of periods interest rate and initial amount initial principle Show amortization schedule The interest paid each payment is merely the periodic interest rate times the amount of the loan outstanding The difference in the total amount paid the PMT and the interest paid for the period equals the amount of principle paid with the payment Consider our 12156498 30 year loan with payments of 850 per month How much principle remains to be paid off after 10 years 120 payments made Just set n 240 the number of periods remaining and calculate the present value 1 1 100625 PVA 850 00625 J 850 124132131 PV 10551231 You still have a lot left to pay off the mortgage Number of payments Example You are buying a car and need a loan of 10621 69 A car loan will cost 12 and we can afford to pay 500 per month starting next month How long of a loan should you get 1062169 soorwl 01 2124338 PVIFA1t From the tables we see that n 24 Or longhand solution n n1iPVAPMI ln1i The tradeoff of operating leverage and financial leverage Operating leverage the responsiveness of the firm s earnings to fluctuations in sales A firm s earnings will be more impacted by changes in sales levels if they have a higher ratio of fixed costs to variable costs This relationship is clearly exhibited if we recall the impact of variable and fixed costs in computing the breakeven point Breakeven point Number of units that must be sold in orderto make EBIT 0 Sales price per unit x Units sold Variable cost per unit x Units sold Fixed costs EBIT 0 Manipulate PxQ VCx Q FC 0 P VC x Q FC QBE FC P VC so as FC like bond payments increase the number of BE Units increases Let s look at DOLbase Q PVC QPVC FC change in EBIT change in sales DFLEBIT EBIT EBIT change in EPS change in EBIT then DTL DOL x DFL change in EPS change in sales Notice that this only refers to leverage not total risk Let us assume that a firm has Q 100000 P 10 VC 5 FC 400000 interest for period 50000 t30 10000 shares of common stock

### 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

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "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.