BAFI Quiz 2
PV = 560, Rate = 9%, FV = 1,389 NPer = PV = 810, Rate = 10%, FV = 1821 NPer = PV = 18,400, Rate = 17%, FV = 289,715 NPer = PV = 21,500, Rate = 15%, FV = 430,258 NPer =
10.5 8.5 17.6 21.4
You plan on working for another 40 years. If you want to have $250,000 per year in retirement, and you expect to live another 30 years after retiring, how much do you need to save each year you work if you expect to earn 10% on your money? How does your answer change if you expect to earn 5%? 15?
5% $3,843 120.80 $31.81 10% $2,3574 42.59 $5.32 15% $1,641 1,779.09 $0.92
Rate of $240 PV, $297 FV and 4years Rate of $360 PV, $1,080 FV and 18 years Rate of $39,000 PV, $185,382 FV and 19 yrs Rate of $38,261 PV, $531,618 FV and 25 yrs
5.5% 6.3% 8.6% 11.1%
PV of $15,451 for 13 years at 7% PV of $51,557 for 4 years at 13% PV of $886,073 for 29 years at 14% PV of $550,164 for 40 years at 9%
6,412 31,621 19,826 17,516
FV of $2,250 in 11 years at 13% FV of $8.752 in 7 years at 9% FV of $76,355 in 14 years at 12% FV of $183,796 in 8 years at 6%
8,631 15,999 373,155 292,943
What is "time value of money" and why is it important?
A dollar is worth more today than in the future. It's important because we need to compare dollars at present to dollars in the future.
First National Bank charges an APR of 13.2% compounded monthly on its business loans. First United Bank charges an APR f 13.5% compounded semiannually. As a potential borrower, which has a lower effective rate (EAR)?
APR = 13.2% / 13.5% Periodicity = 12 / 2 EAR = 14.03% / 13.96%
A credit card account that charges interest at the rate of 1.25% per month would have an equivalent annually compounded rate of _______ and an APR of _______.
APR would be simply 15.00% EAR would be 16.08%
Draw a timeline, drop in what you know, see what you don't know, see what type of problem it is and then solve it.
An annuity is a special type of cash flow - it's the same each year for a set number of years. A perpetuity is the same forever.
Investment X offers to pay you $5,200 per year for eight years, whereas Investment Y offers to pay you $7,300 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5%? If the discount rate is 15%?
Annuity = 5200 / 7300 Years = 8 / 5 PV at 5% = 33609 / 31605 PV at 15% = 2234 / 24471
"Give me $5,000 today and I'll return $20,000 to you in five years," offers the investment broker. To the nearest percent, what annual rate of return is being offered? Work this out both as a present value problem and a future value problem.
Can be either $5,000 = PV for 5 yrs at r% x $20,000 or $5,000 x FV for 5 yrs at r% = $20,000
A project is expected to have cash flows of $2,480 in year 1, $0 in year 2, $3,920 in year 3 and $2,170 in year 4, what is the present value of this project if the discount rate is 7.38% per year?
CashFlow = 2,480 / 0 / 3,920 / 2,170 Rate of Return = 7.38% PV = 7,108
What is the good "formula for success" in solving PV and FV problems (I covered it in class)?
Draw a timeline, drop in what you know, see what you don't know, see what type of problem it is and then solve it.
You want to be a millionaire when you retire in 40 years. How much do you need to save each month if you can earn an 11% annual return? How much do have to save if you want 10 years to start? 20 years?
FV = 1,000,000 APR = 11.0% Mo. Rate = 0.9% Years = 40 / 30 / 20 Months = 480 / 360 / 240 Mo. PMT = 116 / 357 / 1,155
What is "loan amortization?"
Loan amortization is the repayment of principal on a loan.
You are planning to save for retirement over the next 30 years. To do this, you will invest $800 a month in a stock account and $400 in a bond account. The stock account should grow at 10% per year, and the bond account should grow at 6%. When you retire, you will combine your funds into an account that will return 7% per year. How much can you withdrawn each month assuming you want to fully deplete this account after another 25 years?
Mo. Invest = = 800 / 400 Annual Rate = 10.00% / 6.00% Mo. Rate = 0.83% / 0.50% Months Invest = 360 / 360 FV at Retire = =1,808,390 / 401,806 Value Retire = 2,210,196 Retire Rate = 7.00% Mo. Rate = 0.58% Months Retire = 300 PMT per Mo. = 15,621
Live Forever Life Insurance Co. is selling a perpetuity contract that pays $1,500 monthly. The contract currently sells for $115,000. What is the monthly return on this investment vehicle? What is the monthly return? The APR? The EAR?
Monthly return = PMT/PV = 1.3% APR = 15.7% EAR = 16.8%
In 2010, a gold Morgan dollar minted in 1895 sold for $125,000. What annual compound rate of return did this coin return if the heirs to the original purchaser in 1895 sold the coin for this price?
PV = 1, FV = 125,000, Years = 115, Rate = 10.7%
One of your customers is delinquent on his accounts payable balance. You've mutually agreed to a repayment of $500 per month. You will charge a 1.7% per month interest on the overdue balance. If the current balance is $16,000, how long will it take for the customer to pay you back?
PV = 16,000 PMT = 500 Rate = 1.7% Months = 46.6
What is "present value" and "future value?" How are they different and how are they related?
PV is the value of future cash flow today. FV is the value of today's cash in the future. They are "reciprocals" of one another.
You've just joined the investment banking firm of Dewey, Cheatum and Howe. They've offered you two different salary arrangements. You can have $75,000 per year for two years, or you can have $64,000 per year for the next two years, along with a $20,000 signing bonus today. The bonus is paid immediately, the salary is paid in equal amounts at the end of each month. If the interest rate is 10% compounded monthly, which do you prefer?
SigningBonus = 0 / 20,000 Annual Salary = 75,000 / 64,000 Month Salary = 6,250 / 5,333 APR = 10.0% / 10.0% / Mo. Rate = 0.8% / 0.8% Months = 24 / 24 PV = 135,443 / 135,578
For loans, what is a "stated annual rate" vs. an "effective annual rate?" How are they different? How are they related?
State annual rate is the same as an APR; it takes the periodic rate and multiples by the number of periods. The EAR takes into account the number of periods by compounding. The formula between the two was given in class.
You've decided to become a speculator in refurbishing rundown homes and reselling them. Your first "prospect" is a home that can be purchased for $100,000 today. During the first year, you'll have to put $25,000 into improvements. Real estate taxes and other costs related to carrying the house are $5,000 per year. You decide to sell the house at the end of the second year. What is the minimum amount you can sell the house for at the end of the second year, and still get a 10% return? You may assume that all of the cash flows fall at the end of each year (other than the original purchase), and that the purchase is financed entirely with equity. Show the annual cash flows as well as your assumptions and calculations. (b) Now let's relax the assumption that the entire purchase is made with equity. If a bank will lend you 80% of the original purchase price, requires 5% interest per year, to be paid at the end of each year, and doesn't require you to pay them back until you sell the house, what is the net present value of your investment if you sell the house at the end of the second year at the minimum required price calculated above? Again, show the annual cash flows as well as your assumptions and calculations. Explain in plain English why this result is different from the answer above.
The IRR of this investment is 20.5% higher than 10% because the loan was only 5% and the return on the investment was 10 (higher) Conclusion: debt is working in our favor!
How much can be accumulated for retirement if $2,000 is deposited annually, beginning a year from today, and the account earns 9% interest compounded annually for 40 years?
This is the FV of an annuity for 40 years at 9% FV = $675,765
A dealer offers to buy your car with four, equal annual payments of $2.500, beginning today. Assuming the interest rate is 10% and that you wan1t to receive the equivalent of $9,000 in today's dollars for the car, should you accept? What is the interest rate at which you would be indifferent?
This is the PV of four payments of $2,500 today at 10% IRR = 7.51%
You want to buy a new sports coupe for $83,500. The finance office of the dealership has quoted you a 6.5% APR loan for 60 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?
Value = 83,500 APR = 6.50% Monthly Rate = 0.54% Months = 60 Monthly PMT = 1,633.77 EAR = 6.70%
A salesperson offers, "Buy this new car for $25,000 cash or, pay $499 per month for 48 months at a 6% APR with the appropriate down payment." Assuming that the salesperson does not offer a free lunch, calculate the "appropriate" down payment.
We first need to calculate the PV of the 48 month payments of 499 at 0.5% per month: 21,247.58 So the down payment is just $25,000 less this amount, or 3,752.42
An investment officer offers $6,100 per year for 15 years, with the first payment occurring one year from now. If the required return is 6%, what is the value of the investment today? What would the value be if the payments were for 40 years? For 75 years? Forever?
Years = 15 / 40 / 75 / forever Annuity = 6100 - - - - Value = 59245 / 91782 / 100381 / 101667
Prepare an amortization schedule for a five year loan of $63,000, assuming the interest rate is 8% per year with equal annual payments. How much interest is paid in the third year? How much total interest is paid over the life of the loan?
year / begin / pmt / interest / principal / ending 1 / 63,000 / 15,779 / 5,040 / 10,739 / 52,261 2 / 52,261 / 15,77 / 94,181 / 11,598 / 40,663 3 / 40,663 / 15,779 / 3,253 / 12,526 / 28,138 4 / 28,138 / 15,779 / 2,251 / 13,528 / 14,610 5 / 14,610 / 15,779 / 1,169 / 14,610 / 0