H-353

What is a preferred Stock?

- a corporation sells preferred stock, the buyer is promised a fixed cash dividend every period forever. -The dividend must be paid before any dividend can be paid to regular stockholders. -hence the term preferred

What is Annual Percentage Rate (APR)

- annual rate that is quoted by law -period rate times the number of periods per year

What is Average Accounting Rate of Return or ARR or AARR?

- average annual increase in net income/(Initial investment/2)

When do we use EAR?

- comparing two interest rates with with different compound periods - when frequency of compounding is greater or more frequent than the frequency of payment

Advantages of Payback?

- easy calculation - emphasize equity want to know when money is coming in

Disadvantage of payback?

- how do I know what a good number is? is three years too long? - fear this thing will be obsolete before we can get money back

What is payback period?

- is the amount of time it takes for cash inflows to recover the cash outflows of the investment

Future Value

- later money on the time line

Things to remember with EAR and APR

- make sure the interest rate and time period match - if you are looking at annual periods you need an annual rate - if you are looking at monthly periods you need a monthly rate

What is NPER?

- number of periods

What is Internal Rate of Return or IRR?

- the discount rate at which the NPV is equal to 0

Interest Rate

-"Exchange rate" between earlier money and later money - discount rate - cost of capital - opportunity cost of capital - required return

Suppose you can earn 1% per month on $1 invested today. -What is the APR -How much are you effectively earning

-APR= 1(12)= 12% - FV= 1(1.01)^12= 1.1268 Rate= (1.1268-1)/1=.1268= 12.68%

Suppose in another account you earn 3% per quarter -What is the APR -How much are you effectively earning

-APR= 3(4)= 12% - 1(1.03)^4=1.1255 Rate= (1.1255-1)/1= .1255 or 12.55%

Multiple Cash Flows: You think you will be able to deposit $4,000 at the end of the next three years in a bank account paying 8% interest. You currently have $7,000 in the account. How much will you have in three years?

-Find the value at year 3 of each cash flow and add them together. Today(Year 0)= FV=7000(1.08)^3=8,817.98 Year 1= FV= $4,000(1.08)^2=4,665.60 Year 2= FV= 4,000(1.08)= 4,320 Year 3= 4,000 (same as FV=4,000(1.08^0)) Total Value in 3 years = 8817.98+4665.60+4320+4000= 21,803.58

You want to have $1 million to use for retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made in one month?

1,000,000= C((1.01)^420-1/.01)=155.50

Suppose you want to borrow $20,000 for a new car. You can borrow 8% per year, compounded monthly. If you take a 4 year loan, what is your monthly payment?

8/12= .66667% monthly payment 20,000= C(1-1/1.066667^48)/.0066667 C= 488.26

Suppose you are looking at the following possible cash flows: Year 1= $100 Year 2= $200 Year 3= $200 Year 4= $300 Year 5= $300 What is the value of cash flows today

= 100/(1.07)^1=93.45794393 = 200/(1.07)^2=174.6877457 = 200/(1.07)^3=163.2595754 = 100/(1.07)^4=228.8685636 = 100(1.07)^5=213.8958538 =892.18

What is a perpetuity?

Infinite series of equal payments

Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5% how much is the sweepstakes actually worth today?

PV= 333,333.33(1-1/(1.05)^30)/.05=5,124,150.29

What is the future value of $100 in five years if the interest rate is 5% compounded monthly?

FV=(1+.05/12)^60= 128.34

What is the future value of $100 in five years if the interest rate is 5% compounded annually?

FV=100(1.05)^5= 127.63

Suppose your company expects to increase unit sells of widgets by 15% per year for the next 5 years. If you currently sell 3 million widgets in one year, how many wedges would you expect to see in 5 years?

FV=3,000,000(1.15)^5=6,034,072

Suppose you have $500 to invest and you believe that you can earn 8% per year over the next 15 years. How much would you have at the end of the 15 years using compound interest? Using Simple interest?

FV=500(1.08)^15= 1586.084557 Simple= 500+15(500)(.08)=1100

Future Value Equation?

FV=PV(1+r)^t FV=Future Value PV=Present Value r or interest rate= period of interest rate t= number of periods

What is an annuity?

Finite series of equal payments that occur at regular intervals

Compounding

the process of finding the future value of a lump sum, an annuity, or a series of unequal cash flows.

Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned is 7% per year, how much did your parents invest?

$19,671.51/(1.07)^10=10,000

What is the nominal rate in Excel?

- APR

Multiple Cash Flows of Future Value

- Exponets start big and go small -so if the time period is three years you will start today or year 0 will an exponent of 3

Present Value Relationships?

- For a given interest rate- the longer the time period, the lower the present value - For a given time period- the higher the interest rate, the smaller the present value

What are some situations where you might want to compute the implied interest rate?

-college -buy a new car -Mortgage

What is Net Present Value or NPV?

-evaluating capital investment decisions compares the discounted net cash flows of the investment over its economic life with the initial cash outflows required to purchase the investment

Effects of compounding?

-small for a small number of periods, but increases as the number of periods increase.

What is Effective Annual Rate (EAR)

-this is the actual rate paid or received after accounting for the compounding that occurs during the year -a rate quoted or expressed as though it were compounded once per year

You ran a little short on your spring break vacation and put $1000 on your credit card. You can only afford to make the minimum payment of $20 per month. The interest rate on the card is 1.5 percent per month. How long will you need to pay off the $1,000?

1000=20(1-1/1.015^t)/.015 .75=1-1/1.015^t 1/1.015^t=.25 1/.25=1.015^t t= ln(1/.25)/ln(1.015)= 93.111 months= 7.75 years

What is the payback period for the investment project that has the following cash flows? (Round your answers to 2 decimal places. (e.g., 32.16)) Year Cash Flows 0 -69917 1 26286 2 24564 3 29318 4 20384

2.65

Suppose you only have $200,000 to deposit and can earn .75% per month. How much could you receive every month for 5 years?

200,000= C(1-1/(1.0075)^60/,0075 =4151.67

Suppose you only have $200,000 to deposit and can earn .75% per month. How many months could you receive the $5,000 payment?

200,000=5,000(1-1/1.0075^t/.0075) =47.73 months

Suppose you borrow $2000 at 5% and you are going to make annual payments of $734.42. How long before you pay off the loan?

2000=734.42(1-1/1.05^t)/.05 =3 years

You're trying to determine whether to expand your business by building a new manufacturing plant. The plant has an installation cost of $11412, which will be depreciated straight-line to zero over its four-year life. If the plant has projected net income of $2134, $3473, $2833, and $3393 over these four years, what is the project's average accounting return (AAR)?

2134+3473+2833+3393/11412= 51.84

You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much will you be willing to invest today if you desire an interest rate of 12%? You will be willing to invest $1,084.71 today. Verify that this is true.

25,000/(1.12)^5=14185.67 (today) 25,000/(1.12)^4=15887.95 25,000/(1.12)^3=17794.51 25,000/(1.12)^4=44642.86 25,000/(1.12)^5=22321.43

What is the payback period for the following set of cash flows? (Enter 0 if the project never pays back. Round your answer to 2 decimal places. (e.g., 32.16)) Year Cash Flow 0 -5097 1 1574 2 1647 3 1559 4 1884

3.17

An investment project provides cash inflows of $404 per year for eight years. What is the project payback period if the initial cost is $2388?

5.91

What is a Time Line?

A graphical representation of time and cash flows. -Make it easier to visualize when the cash flows in a particular analysis occur

Suppose you want to earn an effective rate of 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay?

APR= 12[(1+.12)^1/12-1]= .11386 or 11.39%

What is the payback period for the following set of cash flows? (Enter 0 if the project never pays back. Round your answer to 2 decimal places. (e.g., 32.16)) Year Cash Flow 0 -5097 1 1574 2 1647 3 1559 4 1884

Answer= 3.17

An investment project provides cash inflows of $404 per year for eight years. What is the project payback period if the initial cost is $2388?

Answer= 5.91

You're trying to determine whether to expand your business by building a new manufacturing plant. The plant has an installation cost of $11412, which will be depreciated straight-line to zero over its four-year life. If the plant has projected net income of $2134, $3473, $2833, and $3393 over these four years, what is the project's average accounting return (AAR)?

Answer= 51.84

You are ready to buy a house and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan. How much money will the bank loan you? How much can you offer for the house?

Bank Loan - Monthly income= 36,000/12= 3,000 - Maximum payment= .28(3,000)= 840 - Maximum loan amount= PV=840(1-1/1.005^360)/.005= 140,105 Total Price - Closing costs= .04(140,105)= 5,604 - Down Payment= 20,000-5604= 14,396 - Total Price= 140,105+ 14,396= 154,501

You need $15,000 in three years for a new car. If you can deposit money into an account that pays an APR of 5.5% based on daily compounding, how much would you need to deposit?

Daily rate= .055/365= .00015068493 Number of days= 3(365)= 1095 FV= 15,000/(1.00015068493)^1095= 12,718.56

Suppose you had a relative who deposited $10 at 5.5% interest 200 years ago. How much would the investment be worth today?

FV=10(1.055)^200=447,189.84 -this means what it is worth today

What is the difference between simple interest and compound interest?

Compound- earning interest on interest simple- only earning interest on original investment

You are looking at two saving accounts. One pays 5.25%, with daily compounding. The other pays 5.3% with semiannual compounding. Which account should you use?

EAR= (1+.0525/365)^365-1= 5.39% EAR= (1+.053/2)^2-1= 5.37% Choose 5.39%

What is the future value of an annuity of $100 in five years if the interest rate is 5% compounded monthly?

EAR= 1+(.05/12)^12-1 FV-A=100((1.0512)^5-1/.0512= 553.89

What is the effective annual rate of 7% that is compounded continuously?

EAR=e^.07=.0725 or 7.25 % e=2.71828

What is the future value of an annuity of $100 in five years if the interest rate is 5% compounded annually?

FV-A= 100((1.05)^5-1/.05= 552.56

Suppose you leave the money in for another year. How much will you have now?

FV= 1,000(1.05)^2= 1,102.50

Suppose you invest $1,000 at 5% per year for 5 years. How much will you have?

FV= 1,000(1.05)^5= 1,276.28

Suppose you are looking at the following possible cash flows: Year 1= $100 Year 2= $200 Year 3= $200 Year 4= $300 Year 5= $300 What is the value of cash flows at year 5?

FV= 100(1.07)^4=131.079601 FV= 200(1.07)^3=245.0086 FV= 200(1.07)^2=288.98 FV= 300(1.07)^1= 321 FV= 300(1.07)^0= 300 131.079601+245.0086+321+300= 1,286.068201

Suppose you begin saving for your retirement by depositing $2000 per year in an IRA. If the interest rate is 7.5% how much will you have in 40 years?

FV= 2000(1.075^40-1)/.075= 454,513.04

Suppose you invest $1,000 for one year at 5% per year. What is the value in one year?

Future Value equation= 1,000(1.05)^1= 1,050

What is the future value of a monthly annuity payments of $100 in five years if the interest rate is 5% compounded annually?

Interest rate= .05/12=.0042 FV-A= 100((1.0042)-1)/.0042

Why is Time Value Analysis important to healthcare?

It is an important part of healthcare financial management because most financial investment analyses involve the valuation of future cash flows.

Suppose you want to buy a new computer system and the store is willing to sell it to allow you to make monthly payments. The entire computer system costs $3,500. The loan period is 2 years and the interest rate is 16.9% with monthly compounding. What is your monthly payment.

Monthly rate= .169(12)= .0140833 Number of months is 24 3500=C[1-1/(1.0140833)^24]/.0140833 C=172.88

Suppose you deposit $50 a month into an account that has an APR of 9%, based on monthly compounding. How much will you have in the account in 35 years?

Monthly rate= .09/12=.0075 Number of months= 35(12)=420 FV= 50(1.0075^420-1)/.0075= 147,089.22

You know the payment amount for a loan and you want to know how much was borrowed. Do you compute present value or future value?

PV

You want to receive $5,000 per month for the next five years. How much would you need to deposit today if you can earn. 75% per month.

PV-A= 5000(1-1\(1.0075)^60\.0075 =240867

You want to revive 5000 per month in retirement. If you can earn .75% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement?

PV= 5,000(1-1/1.0075^300)/.0075= $595,808.1108 - this is PV because you want to have this at the beginning of retirement - 300 because everything has to be in the same value of time

After carefully going over your budget, you have determined you can afford to pay $632 per month towards a new sports car. You call up your local bank and find out that the going rate is one percent per month for 48 months. How much can you borrow?

PV= 632(1-1\(1.01)^48/.01)= 23,999.54

you are considering preferred stock that pays a quarterly dividend of $1.50. If your desired return is 3% per quarter, how much would you be willing to pay?

PV=1.5/.03=50

Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?

PV=10,000/(1.07)^1= 9,345.79

You are considering an investment that will pay you $1000 in one year, $2000 in two years and $3000 in three years. If you want to earn 10% on your money, how much would you be willing to pay?

PV=1000/(1.1)^1= 909.09 PV=2000/(1.1)^2=1652.89 PV=3000/(1.1)^3=2253.94 PV=909.09+1652.89+2253.94= 4815.93

Suppose you need $15,000 in 3 years. If you can earn 6% annually, how much do you need to invest today?

PV=15,000/(1.06)^3=$12594.3893

You want to begin saving for your daughter's college education and you estimate that she will need $150,000 in 17 years. If you feel confident the you can earn 8% per year, how much do you need to invest today?

PV=150,000/(1.08)^17= 50,540.34

Present Value Equation

PV=FV(1/(1+r)^t)

Suppose the Fellini Co. wants to sell preferred stock at $100 per share. A very similar issue of preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every quarter. What dividend will fellini have to offer if the preferred stock is going to sell.

Perpetuity formula: PV=C/r Current required return: 40=1/r r=.025 Dividend for new preferred 100=C/.025 C=2.50 per quarter

Suppose you want to buy a new house. You currently have $15,000 and you figure you need to have a 10% down payment blues and additional 5% in closing costs. If the house you want to buy costs $150,000 and you can earn 7.5% per year, how long will it be before you have enough money for the down payment and closing costs.

Step 1: Down Payment= .1(150,000)=15,000 Closing costs=. 05(150,000-15,000)=6,750 Total needed= 15,000+6,750=21,750 Step 2: t= ln(21,750/15,000)/ln(1.075)=5.14 years

Multiple Cash Flows- PV: You are offered an investment that will pay you $200 in year one, $400 the next year, $600 the next year, and $800 at the end of the fourth year. You can earn 12% on very similar investments. What is the most you should pay for this one. (What is the value)

Year 1: 200/(1.12)^1=178.57 Year 2: 400/(1.12)^2=318.88 Year 3: 600/(1.12)^3=427.07 Year 4: 800/(1.12)^4=508.41 Total PV= 178.57+318.88+427.07+508.41= 1432.93

Present Value

The beginning amount or current worth of an investment of a lump sum, an annuity, or a series of unequal cash flows. -Earlier money on a timeline

Time Value Analysis

The use of time value of money techniques to value future cash flows.

What is an annuity due?

first payment occurs at the beginning of the period

What is an Ordinary Annuity?

first payment occurs at the end of the period

What is the relationship between present value and future value?

inverse relationship

You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today. What is the implied rate of interest?

r=(1200/1000)^1/5-1= .03714= 3.714%

Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. what is the implied rate of interest?

r=(20,000/10,000)^1/6-1=.122462= 12.25%

Suppose you are offered the following investment choices: -you can invest $500 today and receive $600 in 5 years. -you can invest the $500 in a bank account paying 4% -What is the implied interest rate for the first choice and which investment should you choose?

r=(600/500)^1/5-1=.03715= 3.714% Second account at 4% is the better option.

Suppose you have a one year old son and you wanton provide $75,000 in 17 years for his college education. You currently have $5,000 to invest. What interest rate must you earn to have the $75,000 when you need it?

r=(75,000/5,000)^1/17-1=.172688= 17.27%

Discount Rate Equation=

r=(FV/PV)^1/t-1

What is a lump sum?

single starting amount.

You want to purchase a new car and you are willing to pay $20,000. If you invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?

t=ln(20,000/15,000)/ln(1.1)= 3.02 years

Suppose you want to buy some new furniture for your family room. You currently have $500 and the furniture you want costs $600. If you can earn 6%, how long will you have to wait if you don't add any additional money?

t=ln(600/500)/ln(1.06)= 3.129 years

Finding the number of periods equation

t=ln(FV/PV)/ln(1+r)