Financial Management Exam 2

excel functions: annuity type

0/1 = ordinary annuity 1 = annuity due

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?

$1.50/0.03 = $50

You are offered the opportunity to put some money away for retirement. You receive five annual payments of $25,000 each beginning in forty years. How much would you be willing to invest today if you desire an interest rate of 12%?

*****1084.71

Your broker calls you and tells you that he has this great investment opportunity. If you invest $100 today, you will receive $40 in one year and $75 in two years. If you require a 15% return on investments of this risk, should you take the investment?

*****No

What is the APR if the monthly rate is .5?

.5% (12) = 6%

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. 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 will the bank loan you? How much can you offer for the house?

1. Present Value -Monthly income: 36,000/12=3,000 -Max pmt: .28(3,000)=840.00 -n: 30(12)=360 -I/Y: .06/12=0.5 -PV: 140,105 2. Total Price - Loan value: 140,105 - Closing cost: .04(140,105)=5,604 - Down Payment: 20,000-5604=14,396 - Total Price: 140,105+14396= 154,501

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?

12((1+.12)^(1/12)) = 11.39%

APR Formula

APR = periodic rate x number of periods per year

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% **EAR:

Suppose if you put it in another account, you earn 3% per quarter? How much are you effectively earning?

APR: 3% (4)=1.2% ****EAR:

Annual Percentage Rate

Annual rate quoted by law

present value of a perpetuity per period

C/r

EAR Formula

EAR = [1+ (APR/m)]^m -1 APR = quoted rate m = number compounds per year

1,000 due on a credit card Payment = $20 month minimum Rate = 1.5% per month THE SIGN CONVERSION MATTERS Find the number of payments

I/Y: 1.5% PMT: -20 PV: 1,000 N: 93.11

If a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market?

N: 1 I: 7 FV: 10,000 PV: 9345.79

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

N: 12(2) = 24 I/Y: 16.9/12 = 1.40833 PV: 3500 PMT: -172.88

You are saving for a new house and you put $10,000 per year in an account paying 8%. The first payment is made today. How much will you have at the end of 3 years?

N: 3 I/Y: 8 PMT: -10,000 BEGIN FV: 35061.12

You need 15,000 in 3 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?

N: 3(365) = 1095 I/Y: 5.5/365 = 0.015068 FV: 15,000 PV: -12,718.56

Suppose you deposit $50 per 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?

N: 35(12) = 420 I/Y: 9/12 = .75 PMT: -50 FV: 147,089.22

Consider a 4-year loan with annual payments. The interest rate is 8% and the principal amount is 5000. What is the annual payment?

N: 4 I/Y: 8 PV: 5,000 PT: 1,509.60

Suppose you want to borrow $20,000 for a new car. You can borrow at 8% per year, compounded monthly (8/12 = .66667% per month). If you take a 4-year loan, what is your monthly payment?

N: 48 FV: 20,000 I/Y: .66667 PMT:488.26

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?

N=30 I/Y=5 PMT=333,333.33 PV: 5,124,150.29

You can afford $632 per month. The going rate is 1%/month for 48 months. How much can you borrow?

N=48 I/Y=1 PMT=632 PV: 23,999.54

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?

PV: 2000 I/Y: 5 PMT: -734.42 N: 3 years

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

PMT: 5000 N: 60 I/Y: .75 PV: -240866.87

You wan to receive $5,000 per month for the next 5 years. What monthly rate would you need to earn if you only have $200,000 to deposit?

PMT: 5000 N:60 PV: -200000 I/Y: 1.4395

perpetuity equation

PV = pmt/r

Suppose you borrow $10000 from your parents to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate

PV: 10000 PMT: -207.58 N: 60 I/Y: .75%

You want to receive $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?

Present Value Formula N: 12(25)=300 I/Y: .75 PMT: 500 PV: -595,808.11

Suppose you are looking at the following possible cash flows: Year 1 = 100 Year 2 and 3 = 200 Year 4 and 5 = 300. The required discount rate is 7%. What is the value of the CFs at year 5? What is the value of the CFs today?

Present Value: 1: 100/(1.07)^1 2: 200/(1.07)2 3: 200/(1.07)^3 4: 300/(1.07)^4 5: 300/(1.07)^5 Total PV: 874.17 Future Value 1: 100(1.07)^4 2: 200(1.07)^3 3: 200(1.07)^2 4: 300(1.07)^1 5: 300(1.07)^0 Total FV: 1226.07

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?

Year 1 PV: 1000/(1.1)^1 Year 2 PV: 2000/(1.1)^2 Year 3 PV: 3000/(1.1)^3 Total PV: 4,815.92

You are offered an investment that will pay $200 in year 1, $400 the next year, $600 the next year, and $800 at the end of the 4th year. You can earn 12% on similar investments. What is the most you should pay for this one?

Year 1 PV: 200/(1.12)^1 Year 2 PV: 400/(1.12)^2 Year 3 PV: 600/(1.12)^3 Year 4 PV: 800/(1.12)^4 Total PV: 1,432.93

Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%?

Year 1: 100(1.08)^5 Year 2: 300(1.08)^2 *****Total FV in 5 years: 496.85

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 3 years? How much in 4 years?

Year 0: FV=7,000(1.08)^3 = 8,817.98 Year 1: FV =4,000(1.08)^2 = 4,665.60 Year 2: FV =4,000(1.08)^1 = 4,320.00 Year 3 Value: 4,000.00 Total Value in 3 years: 21,803.58 Value at year 4: 21,803.58(1.08)=23,547.87

If you deposit $100 in one year, $200 in two years and $300 in three years, how much will you have in three years at 7% interest? How much in five years if you don't add additional amounts?

Year 1: FV=100(1.07)^2 = 114.49 Year 2: FV=200(1.07)^1 = 214.00 Year 3: FV=300(1.07)^0 = 300.00 total FV at year 3: 628.49 Total FV at year 5: 719.56

Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in 2 years? How much will you have in 5 years if you make no other deposits?

Year 1: FV=500(1.09)^2 Year 2: FV=600(1.09)^1 Total FV in 2 years: 1,248.05 Total FV in 5 years: 1,616.26

periods when they are less than annual

multiplied

rate when the period is less than annual

divided

Amortized Loan with Fixed Payment

each payment covers the interest expense plus reduces principal

annuity

finite series of equal payments that occur at regular intervals

perpetuity

infinite series of equal payments

Effective Annual Rate

interest rate expressed as if it were compounded once per year. Used to compare two alternative investments with different compounding periods

Pure Discount Loans

loans in which principal amount is repaid at some future date and there are no periodic interest payments

annuity due

paid at the beginning of the period (slightly more than ordinary annuity)

ordinary annuity

paid at the end of the period

What is the monthly rate if the APR is 12% with monthly compounding?

r(12) = 1% 12(1%) = 12%