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The present value (at n=o) of the following cash flow stream is $6,000 when discounted at 12% annually. That stream consists of payments made at the end of each four periods. One of the payments, the second one, is missing. The others are $1,000 at n=1, $2,000 at n=3, $2,000 at n=4. What is the value of the missing cash flow?

*make a timeline* 0. 1 2. 3 4 1,000. x. 2,000. 2,000 rate: 12% pv for year 1: (1,000/ (1+12%)^1) for year 3: (2,000/(1+12%)^3) for year 4: (2,000/(1+12%)^4) sum of year 1,3,4: $3,587 - known pv: $6,000 = pv of 2 value of cash flow: =fv( 12%, 2,, -pv of 2)

A friend calls you with a great investment opportunity, that will produce a return to you of $12,000 per year for 6 years starting at the end of 2 years from now and $5,000 the year after that. Assuming you could invest in an investment of similar risk elsewhere at an annual interest rate of 8% What is the most you should be wiling to pay for in this investment?

*make a timeline* 0. 1. 2. 3. 4. 5. 6. 7. 8 0. 2,000-----------------------------5,000 rate 8% pv- =pv(8%,2,,-2,000) total pv= sum of all

The engineering staff at the sun shipping company has informed decision-makers that substantial money can be saved on fuel bills if the ship's engines are adapted. Based on the cost of fuel, they estimate the firm will save $50,000 each year for the first 4 years and save $75,000 in the next 6. If the estimates are accurate, what would the company be willing to pay to adapt the engines? earning 10% annually on its investments.

*make timeline* 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 5,000 ------------- 7,500----------------------- rate 10% pv for 5,000: =pv(10%,1,,5,000), =pv(10%,2,,5,000) etc pv for 7,500: =pv(10%,5,,7,500) Total pv ----sum of all pv just calculated

Higher money bond price characteristics

- higher rating -protective covenant -higher senority

Agency relationship

-Principal hires an agent to represent his/her interests -Stockholders (principals) hire managers (agents) to run the company

lower money bond price characteristics

-call provision -higher ytm -non inv. grade vs inv grade -illiquid issue

French corporation's stock currently sells for $50 per share. The company just paid a dividend of $2 and the growth rate is 6%: 1) What is the expected rate of return for this stock? 2) If the required rate of return on this stock were 12%, what would the stock price be?

1) rate of return = (D0* (1+g)/P0) = g (2* (1+6%)/50) + 6% 2) price = DO * (1+g)/r-g. = D1/r-g 2* (1+6%) / (12%-6%)

Warren Buffet began buying shares in Berkshire Hathaway in 1962. At the time a share of the company was traded ay $18. A recent price in 2019 was $308,139. Considering only the capital gain (and not the dividends paid) what is the average annual return for this company?

2019-1962=57 =rate( 57,, -18, 308,129,, 10)

You have just purchased a share of preferred stock for $60. The preferred stock pays an annual dividend of $5.60 per share forever. What is the annual rate of return on your investment?

5.6/60 9.33%

Bond value

= PV of coupons + PV of par = PV of annuity + PV of lump sum as interest rate increase, pv and bond prices decrease

A broker offers you an investment opportunity that will pay you $5,000 a year for the next 5 years, with the first payments on year from today. To take advantage of this opportunity, you need to invest $14,000 today. Assuming you require a 12% annual return on this type of investment, should you do it? What is the most you should be willing to pay?

= pv( 12%, 5, -5,000) =18,023.88 good investment, only have to pay 14000 get back 18000

A bond with 20 years to maturity, a 10% coupon rate that pays coupons semi-annually, and is selling for $875 will have a yield to maturity of?

= rate(

How much money will you have at the end of an investment? interest rate: 12% # of years: 3 initial investment: 400

=FV(12%,3,0,-4000)

You are going to save for retirement and the first deposit will be made today. How much will you have when you are ready to retire? Beg. of period annuity deposit: 2,000 # of years: 35 interest rate: 10%

=Fv(10%, 35, -2,000,,1) Use type 1 when its at the beg,

Find the interest rate you'll need to earn on your investment in order to send your kid to college PV: 35,000 FV: 80,000 # of periods: 8

=Rate ( 8, 0, -35,00, 80,000)

You are going to save an equal amount annually for retirement, but you also have a little bit currently save. How much will you have when you retire? pv: 25,000 annual savings: 2,500 # of years: 45 interest rate: 11%

=fv( 11%, 45, -2,500, 25,000)

You are saving for retirement. Based on the following assumptions, how much will you have when you retire? annual savings: 3,000 # of years: 30 interest rate: 11%

=fv(11%, 30, -3,000)

You are saving up to buy the Godo + Company and have the following information. How long must you wait to buy the new company? PV: 2,300,000 FV: 10,000,000 Rate: 5%

=nper( 5%,0,-2,300,00, 10,000,000)

You ran a little short on spring break, so you charge your credit card, With the following assumptions, how long will it take you to pay it off? amount paid: 1,000 monthly payment: 20 monthly rate: 1.5%

=nper(1.5%, -20, 1,000) ---months to get years divide by 12`

You are buying a house. What is the monthly mortgage payment? purchase price: 175,000 # of months: 240 monthly interest rate: 5%

=pmt(5%, 240, -175,000)

Suppose you want to buy a new car. How much do you have to invest today in order to buy the car in the future? FV: 68,500 # of periods: 2 Rate: 9%

=pv( 9%, 2, 0, -68,00)

You just won the lottery. Based on the following assumptions, what is the present value of you winnings? annual payment: 100,000 # of years: 25 Interest rate: 11%

=pv(11%, 25, -100,000)

You put $250 into an account at the end of each year for 5 years. At the end of the 5th year the account was worth $1,750. What annual rate of return did you earn?

=rate (5, -250,, 1,750)

You are saving for retirement and know how much you will save every year, as well as a target retirement balance. What interest rate is necessary for you to reach your goal? retirement goal: 1,500,000 Annual savings: 3,000 # of years: 35

=rate(25, -3000,0, -1,500,000)

agency problem

Conflict of interest between principal and agent

Corporation Disadvantages

Double taxation (income taxed at the corporate rate and then dividends taxed at the personal rate)

Sole Proprietorship advantages

Easiest to start Least regulated Single owner keeps all the profits Taxed once as personal income

a general partner ?

Is personally responsible for all the partnership debts.

Corporation Advantages

Limited liability Unlimited life Separation of ownership and management Transfer of ownership is easy Easier to raise capital

Sole Proprietorship disadvantages

Limited to life of owner Equity capital limited to owner's personal wealth Unlimited liability Difficult to sell ownership interest

Present value of annuity

Pv + PMT

You deposit your scholarship of $1,000 in an account paying, 6% annually, compounded quarterly. Eighteen months later, you close out your account after graduating. How much money can you withdrawal?

Pv: -1,000 Rate: 6%/12= 1.5% NPER: 18/3= 6 =fv( -1,000, 1.5%, 6)

15 years from now, your 2-year-old son will be attending Harvard. You have determined he will need $70,000 per year for tuition and living expenses (each year he needs $70,00 at the beginning of the year, the first payment is 15 years from today). In 15 years, you will give him a lump sum payment for the entire amount he will need, assuming that he will be able to invest the money not yet needed at 5% interest. You have found an investment opportunity that will yield an annual return on 75 on your monthly payments (monthly payments will be deposited at the end of the month) How much will you have to invest each month to give your sun the money he needs for his education?

Step 1: find pv 0 1 2 3 70,000. 70,000 70,000. 70,000 rate 5% total pv: =pv(5%,4,-70,000,,1)------- 260,637.36 step 2: find pmt fv: -260,637.36 rate: 7%/12= 5.8% nper: 15*12 = 180 =pmt( 5.8%, 180,,-260,637.36 )

You want to buy an Audi A8 on your 27th birthday. You have priced these cars and found out that they are currently selling for $83,800. You believe that the price will increase by 10% per year until you are ready to buy one. You can presently invest to earn 10% annually. If you have just turned 20, how much must you invest per year to be able to purchase the audi in 7 years?

Step1: find fv --- how much you need to buy the car in 7 years pv: 83,800. Rate: 10% nper: 7 =Fv( 10%, 7, -83,800) --- 163,302.49 Step 2: find pmt fv: -163,302.49 rate: 10% nper: 7 =pmt( 10%, 7,, -163,302.49)---17,212.98

Partnership Advantages

Two or more owners More capital available Relatively easy to start Income taxed once as personal income

Partnership Disadvantages

Unlimited liability General partnership Limited partnership Partnership dissolves when one partner dies or wishes to sell Difficult to transfer ownership

capital budgeting

What long-term investments or projects should the business take on?

what best illistruates that the management of a firm is adhering to the goal of financial management?

an increase in the market value per share

You plan on buying yourself a retirement cabin in the mountains 40 years from now. At an interest rate of 6% per year, how much must you invest each year to have $156,000 in you cabin fun in 50 years?

fv: 156,000 rate: 6% nper: 40 =pmt( 6%, 50,,156,00)

You have won a game show prize of a trip across europe in one year valued at $25,000. If instead you are able to take the present value of the trip in cash, how much would you want if the rate you can earn is 8% annually, compounded quarterly?

fv: 25,000 rate: 8%/4 = 2% nper: 4 =pv(2%, 4,, -25,000)

You are working for humdrum corp. You are so bored, you want to start your own business. A new business takes money, so you start a 5 year plan. At an interest rate of 9% per year, how much should you invest each year to have $80,000 in your new business fund in 5 years?

fv: 80,000 rate: 9% nper: 5 =pmt( 9%, 5,0, 80,000)

a limited partnership?

has at least one partner who has unlimited liability for all of the partnerhsip debts

example of capital strucutre

how much debt should be assumed to fund a project? or decide to share additional shares of stock

capital structure

how should we pay our assets? use debt or equity?

The growth of both sole prop. and partnerships is frequently limited by the firms :

inability to rasie cash

which one is correct?

income from both sole prop. and partnerships that is taxable is treated as individual income

actions by a financial manager that is most apt to create an agency problem?

increasing current profits when doing so lowers the value of the companies equity

which of the following is LEAST apt to help convince managers to work in the best interest of stockholders?

increasing managers base salaries

if the price of a bond that currently sells at par increases, what happens to its yield to maturity?

it decreases

If the price of a bond that currently sells at par increases, what happens to its coupon rate?

it stay the same

Goal of Financial Management

maximize the current value per share of the existing stock or shareholder value

Treasurer

oversees cash management, credit management, capital expenditures, and financial planning

controller

oversees taxes, cost accounting, financial accounting and data processing

limited partnership

partnership in which only one partner is required to be a general partner

General Partnership

partnership in which partners share equally in both responsibility and liability

Air atlantic has leased out a 3 year old jet under a 10 year arrangement. The lease requires the lessee to pay Air Atlantiv annual payments of $450,000 beginning next year. If Air Atlantic can invest at 10% annually, what is the lease arrangement worth?

pmt: 450,000 nper: 10 Rate: 10% =pv()

Ms. Davis is saving money for her son Stephens's college education. He will begin college in 9 years. If ms. Davis invests $6,000 at the end of each year, how much will she save when Stephen starts? the annual interest rate is 5% compounded annually.

pmt: 6,000 rate: 5% nper: 9 =fv(5%, 9, -6,000)

Best Practice Consulting has just paid a dividend of $1.8. They expect to grow at a rate of 5% indefinitely. What is the price of this stock if the expected rate of return is 10%?

price= DO * (1+g)/R-g 1.8*(1+5%)/(10%-5%)

Company x's preferred stock is expected to pay a $10 annual dividend forever. If the required rate of return on equivalent investments is 10%, then a share of it is worth?

price= dividend/rate

example of capital budgeting

purchase new machine?

A firms dividends per share grew from $1 to $2 in six years, making its total growth over that period 100%.What is the annual growth rate?

pv: -1 fv: 2 nper: 6 =Rate( 6,, -1, 2)

A company invest $2 million to clear land and plant pine trees. The trees will mature in 10 years and the company expects to sell them for $6 million. What will be its annual rate of return?

pv: -2 fv: 6 nper: 10 =rate( 10,, -2,6)

An industrial bank will loam you $10,600 for two years to buy equipment for your firm. The loan must be repaid in equal monthly payments. The annual interest rate is 10% of the unpaid balance. How large are the monthly payments?

pv: 10,600 rate: 10%/12= .83% nper: 2*12= 24 =pmt( .83%, 24, 10,600)

The third national bank of haslett has agreed to give you a 4 year loan to buy a designer bag priced at $12,000. The annual interest rate is 9%. If the bank requires you to make a 10% down payment on the car, how much will your monthly payments be if you make the purchase?

pv: 12,000 rate: 9%/12 nper: 4*12 = 48 =pmt

Jake borrows $25,000 to finance the expansion of his business. He promises to repay with equal quarterly payments for 10 years. The annual interest rate is 8%. What is the amount of jake's quarterly payment?

pv: 25,000 rate: 8%/4 = 2% nper: 10*4 = 40 =pmt(2%, 40, 25,000)

You want to buy a parcel of land in an area of town in the direction of future development. The lot cost $50,000. The annual payments on a loan to buy that lot would be $6,202.94. If the bank is charging you 9% interest per year, how many payments must you make before you own the land?

pv: 50,000 fv: 0 rate: 9% pmt: -6,202.94 =nper( 9%, -6,202.94, 50,000 , 0)

After graduating, you decide that you can pay $203.24 per month extra on your statement (standard monthly payment is $302.99), which has a balance of $50,000 and 20 years of monthly payments remaining, The annual interest rate is 4% . How many years early will you be able to pay off the loan?

pv: 50,000 rate: 4%/12 = .33% pmt: 203.24+ 302.99 = 506.23 =nper( .33%, -506.23, 50,000) - 120 total payments- 20*12 = 240 new no. of payments = 120 payments left = 240-120 = 120

You're on your way to Spring Break, credit card waiting to be used for all of the trip's expenses. You've calculated that, when you get back, you will only be able to afford monthly payments of $40. The card has an annual interest rate of 15%, and you have decided that you must have the card paid in full im 3 years. How much will you be able to spend on Spring break?

rate: 15%/12= 1.25% pmt: 40 months: 3*12= 36 =pv(1.25%, 36, -40)

Your credit card has a balance of $2,500. The credit card issuer applies an annual rate of 18%. How long will it take you to pay off your balance if you don't incur any additional expenses and you pay $50 per month?

rate: 18%/12= 1.5% =nper

today you won a small sweepstakes prize. your winnings will be split into 12 monthly payments of $2,000 starting from today. If the annual rate of return you can get at your bank is 3%, what is the present value fo your winnings?

rate: 3%/12= .3% Type 1 =pv(.3%,12,-2,000,,1)

While on spring break, you bought a ticket for the Lotto de Cancun, and you won 3 million Pesos. You are given a choice between receiving a check for 2 million Pesos immediately, or taking you winnings in annual installments over the next 10 years. From a financial perspective, using an annual discount rate of 10% , which is the optimal choice?

step 1: find pv of annual installments =pv(10%,10, -300,000)= 1,843,247 3mill *!0%= 300,000 immediate check

You want to start saving for you daughters college education now. She will enter college at age 18 and will pay fees of $4,000 at the end of each four years (18,19,20,21) You will start your savings by making deposits in one year at the end of every year until she begins college. If annual deposits of $2,458.79 (from today/onward) will allow you to reach your goal, Assume you can earn 6% annual interest how old is your daughter now?

step 1: use pv function fv: 0 pmt: -4,000 rate: 6% nper: 4 =pv(6%,4,-4,000,0)---13,860.42 Step 2: use nper function pv: 0 fv: 13,860.42 rate: 6% pmt: -2,458.79 =nper( 6%, -2458.79, 13,860.42, 0 )

Corporate dividends are?

taxable income of the recipient even though the income was perviously taxed