Consider a person who begins contributing to a retirement plan at age 25 and contributes for 40 years until retirement at age 65. For the first ten years, she contributes $3,000 per year. She increases the contribution rate to $5,000 per year in years 11 through 20. This is followed by increases to $10,000 per year in years 21 through 30 and to $15,000 per year for the last ten years. This money earns a 9 percent return. First compute the value of the retirement plan when she turns age 65. Then compute the annual payment she would receive over the next 40 years if the wealth was converted to an annuity payment at 8 percent.
> Approximately what interest rate is needed to double an investment over five years?
> Approximately how many years does it take to double a $500 investment when interest rates are 10 percent per year?
> Approximately how many years does it take to double a $100 investment when interest rates are 7 percent per year?
> Compute the present value of $5,000 paid in two years using the following discount rates: 8 percent in the first year and 7 percent in the second year.
> Compute the present value of $1,000 paid in three years using the following discount rates: 6 percent in the first year, 7 percent in the second year, and 8 percent in the third year.
> HiLo, Inc., doesn’t face any taxes and has $150 million in assets, currently financed entirely with equity. Equity is worth $7 per share, and book value of equity is equal to market value of equity. Also, let’s assume
> Explain what the efficient frontier is and why it is important to investors.
> Compute the present value of an $850 payment made in 10 years when the discount rate is 12 percent.
> What is the present value of a $1,500 payment made in nine years when the discount rate is 8 percent?
> Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using the average approach? Year: 2012 2013 2014 2015 2016 Sales $1,500,000 $1,750,000 $1,400,000 $2,000,000 $1,600
> What is the present value of a $200 payment in one year when the discount rate is 7 percent?
> What is the present value of a $350 payment in one year when the discount rate is 10 percent?
> A deposit of $750 earns interest rates of 9 percent in the first year and 12 percent in the second year. What would be the second year future value?
> Compute the value in 25 years of a $1,000 deposit earning 10 percent per year.
> How much would be in your savings account in eleven years after depositing $150 today if the bank pays 8 percent per year?
> What is the future value of $400 deposited for one year earning an interest rate of 9 percent per year?
> What is the future value of $500 deposited for one year earning a 8 percent interest rate annually.
> Ultra Petroleum (UPL) has earnings per share of $1.56 and a P/E ratio of 32.48. What’s the stock price?
> Show the time line for a $400 cash outflow today, a $518 cash inflow in year 3, and a 9 percent interest rate.
> Show the time line for a $500 cash inflow today, a $605 cash outflow in year 2, and a 10 percent interest rate.
> A deposit of $350 earns the following interest rates: • 8 percent in the first year, • 6 percent in the second year, and • 5.5 percent in the third year. What would be the third year future value?
> Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using the naïve approach? Year: 2012 2013 2014 2015 2016 Sales $2.500,000 $3.750,000 $2,400,000 $2,000
> You own $10,000 of Denny’s Corp stock that has a beta of 2.9. You also own $15,000 of Qwest Communications (beta = 1.5) and $5,000 of Southwest Airlines (beta = 0.7). Assume that the market return will be 11.5 percent and the risk-free rate is 4.5 percen
> At age 30 you invest $1,000 that earns 8 percent each year. At age 40 you invest $1,000 that earns 12 percent per year. In which case would you have more money at age 60?
> You are scheduled to receive a $500 cash flow in one year, a $1,000 cash flow in two years, and pay an $800 payment in three years. If interest rates are 10 percent per year, what is the combined present value of these cash flows?
> Ten years ago, Hailey invested $3,000 and locked in an 8 percent annual interest rate for 30 years (end 20 years from now). Aidan can make a 20-year investment today and lock in a 10 percent interest rate. How much money should he invest now in order to
> Ten years ago, Hailey invested $2,000 and locked in a 9 percent annual interest rate for 30 years (end 20 years from now). Aidan can make a 20-year investment today and lock in a 10 percent interest rate. How much money should he invest now in order to h
> What annual rate of return is implied on a $2,500 loan taken next year when $3,500 must be repaid in year 4?
> A preferred stock from Hecla Mining Co. (HLPRB) pays $3.50 in annual dividends. If the required return on the preferred stock is 6.8 percent, what is the value of the stock?
> What annual rate of return is earned on a $4,000 investment made in year 2 when it grows to $6,500 by the end of year seven?
> You invested $3,000 in the stock market one year ago. Today, the investment is valued at $3,750. What return did you earn? What return would you suffer next year for your investment to be valued at the original $3,000?
> You invested $2,000 in the stock market one year ago. Today, the investment is valued at $1,500. What return did you earn? What return would you need to get next year to break even overall?
> At age 25 you invest $1,500 that earns 8 percent each year. At age 40 you invest $1,500 that earns 11 percent per year. In which case would you have more money at age 65?
> People have had a fascination with gold for thousands of years. Archaeologists have discovered gold jewelry in Southern Iraq dating to 3000 BC and gold ornaments in Peru dating to 1200 BC. The ancient Egyptians were masters in the use of gold for jewelry
> Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using the naïve approach? Year: 2012 2013 2014 2015 2016 Sales $1.500,000 $1.750,000 $1,400,000 $2,000
> How can you add a cash flow in year 2 and a cash flow in year 4 in year 7?
> The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful in reducing taxes than in the later years?
> Would you rather pay $10,000 for a 5-year $2,500 annuity or a 10-year $1,250 annuity? Why?
> Use the idea of compound interest to explain why EAR is larger than APR.
> A preferred stock from Duquesne Light Company (DQUPRA) pays $3.55 in annual dividends. If the required return on the preferred stock is 6.7 percent, what’s the value of the stock?
> Explain why you use the same adjustment factor, (1 + i), when you adjust annuity due payments for both future value and present value.
> When you discount multiple cash flows, how does the future period that a cash flow is paid affect its present value and its contribution to the value of all the cash flows?
> People can become millionaires in their retirement years quite easily if they start saving early in employer 401(k) or 403(b) programs (or even if their employers don’t offer such programs). Demonstrate the growth of a $250 monthly contribution for 40 ye
> Since perpetuity payments continue forever, how can a present value be computed? Why isn’t the present value infinite?
> How can you use the present value of an annuity concept to determine the price of a house you can afford?
> How can you use the concepts illustrated in computing the number of payments in an annuity to figure how to pay off a credit card balance? How does the magnitude of the payment impact the number of months?
> Suppose that Gyp Sum Industries currently has the following balance sheet, and that sales for the year just ended were $10 million. The firm also has a profit margin of 25 percent, a retention ratio of 30 percent, and expects sales of $8 million next yea
> Given a certain amount of savings, how much can I spend annually during retirement? Your annual income is estimated to be $70,000. Information entered 1. Savings Amount saved…………………………………… ………………………$1,000,000 Rate of return……………………………………. …………………………
> When paying off a home mortgage, extra principle payments can have a dramatic impact on the time needed to pay off the mortgage. (a) Create an amortization schedule for a $200,000, 3-year mortgage with a 6% APR. (b) After the 5th year, add an extra $100
> You would like to sell 100 shares of Echo Global Logistics, Inc. (ECHO). The current ask and bid quotes are $15.33 and $15.28, respectively. You place a limit sell-order at $15.31. If the trade executes, how much money do you receive from the buyer?
> Consider Gavin, a new freshman who has just received a Stafford student loan and started college. He plans to obtain the maximum loan from Stafford at the beginning of each year. Although Gavin does not have to make any payments while he is in school, th
> Phoebe realizes that she has charged too much on her credit card and has racked up $6,000 in debt. If she can pay $200 each month and the card charges 18 percent APR (compounded monthly), how long will it take her to pay off the debt?
> Joey realizes that he has charged too much on his credit card and has racked up $5,000 in debt. If he can pay $150 each month and the card charges 17 percent APR (compounded monthly), how long will it take him to pay off the debt?
> To borrow $800, you are offered an add-on interest loan at 7 percent. Three loan payments are to be made, one at four months, another at eight months, and the last one at the end of the year. Compute the three equal payments.
> To borrow $500, you are offered an add-on interest loan at 8 percent. Two loan payments are to be made, one at six months and the other at the end of the year. Compute the two equal payments.
> What annual interest rate would you need to earn if you wanted a $600 per month contribution to grow to $45,000 in six years?
> What annual interest rate would you need to earn if you wanted a $1,000 per month contribution to grow to $75,000 in six years?
> Suppose that Wind Em Corp. currently has the following balance sheet, and that sales for the year just ended were $7 million. The firm also has a profit margin of 27 percent, a retention ratio of 20 percent, and expects sales of $8 million next year. If
> What’s the interest rate of a 7-year, annual $4,000 annuity with present value of $20,000?
> What’s the interest rate of a 6-year, annual $5,000 annuity with present value of $20,000?
> You would like to sell 200 shares of Xenith Bankshares (XBKS). The current ask and bid quotes are $4.66 and $4.62, respectively. You place a limit sell-order at $4.65. If the trade executes, how much money do you receive from the buyer?
> Payday loans are very short-term loans that charge very high interest rates. You can borrow $500 today and repay $590 in two weeks. What is the compounded annual rate implied by this 18 percent rate charged for only two weeks?
> Payday loans are very short-term loans that charge very high interest rates. You can borrow $225 today and repay $300 in two weeks. What is the compounded annual rate implied by this 33.33 percent rate charged for only two weeks?
> A perpetuity pays $50 per year and interest rates are 9 percent. How much would its value change if interest rates decreased to 7.5 percent? Did the value increase or decrease?
> A perpetuity pays $100 per year and interest rates are 7.5 percent. How much would its value change if interest rates increased to 9 percent? Did the value increase or decrease?
> You are looking to buy a car. You can afford $650 in monthly payments for five years. In addition to the loan, you can make a $750 down payment. If interest rates are 8% APR, what price of car can you afford?
> You are looking to buy a car. You can afford $450 in monthly payments for four years. In addition to the loan, you can make a $1,000 down payment. If interest rates are 5% APR, what price of car can you afford?
> Assume that you contribute $200 per month to a retirement plan for 20 years. Then you are able to increase the contribution to $300 per month for another 30 years. Given a 7 percent interest rate, what is the value of your retirement plan after the 50 ye
> You wish to buy a $25,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be?
> Sara’s Ice Cream Shop is closed for six months out of the year, but has had the monthly sales amounts listed as follows for the last four years. Assuming that there is both seasonality and a trend, estimate monthly sales for each month
> If you start making $75 monthly contributions today and continue them for four years, what is their future value if the compounding rate is 12 percent APR? What is the present value of this annuity?
> You would like to buy shares of Coldwater Creek, Inc. (CWTR). The current ask and bid quotes are $20.70 and $20.66, respectively. You place a market buy-order for 200 shares that executes at these quoted prices. How much money did it cost to buy these sh
> If you start making $50 monthly contributions today and continue them for five years, what’s their future value if the compounding rate is 10 percent APR? What is the present value of this annuity?
> A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $1,500 per month for the next three years and then $500 per month for two years after that. If the bank is charging customers 8.5 percent APR, how much
> A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $1,000 per month for the next three years and then $2,000 per month for two years after that. If the bank is charging customers 7.5 percent APR, how m
> Given a 7 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $1,000, $1,300, $1,300, and $1,400.
> Given a 6 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,500.
> Assume that you contribute $150 per month to a retirement plan for 15 years. Then you are able to increase the contribution to $350 per month for the next 25 years. Given an 8 percent interest rate, what is the value of your retirement plan after the 40
> Given a 5 percent interest rate, compute the year 6 future value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,300, $1,300, and $1,400.
> Given a 4 percent interest rate, compute the year 6 future value of deposits made in years 1, 2, 3, and 4 of $1,100, $1,200, $1,200, and $1,500.
> You wish to buy a $10,000 dining room set. The furniture store offers you a 3-year loan with an 11 percent APR. What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be?
> Suppose that the 2016 actual and 2017 projected financial statements for Comfy Corners Catbeds are initially shown as follows. In these tables, sales are projected to rise by 22 percent in the coming year, and the components of the income statement and b
> You would like to buy shares of Sirius Satellite Radio (SIRI). The current ask and bid quotes are $3.96 and $3.93, respectively. You place a market buy-order for 500 shares that executes at these quoted prices. How much money did it cost to buy these sha
> Consider that you are 35 years old and have just changed to a new job. You have $80,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $3,600 each year into
> You have secured a loan from your bank for two years to build your home. The terms of the loan are that you will borrow $100,000 now and an additional $50,000 in one year. Interest of 9 percent APR will be charged on the balance monthly. Since no payment
> You have secured a loan from your bank for two years to build your home. The terms of the loan are that you will borrow $200,000 now and an additional $100,000 in one year. Interest of 10 percent APR will be charged on the balance monthly. Since no payme
> Say that you purchase a house for $150,000 by getting a mortgage for $135,000 and paying a $15,000 down payment. If you get a 15-year mortgage with a 7 percent interest rate, what are the monthly payments? What would the loan balance be in five yea
> Say that you purchase a house for $200,000 by getting a mortgage for $180,000 and paying a $20,000 down payment. If you get a 30-year mortgage with a 7 percent interest rate, what are the monthly payments? What would the loan balance be in ten years? If
> A local furniture store is advertising a deal in which you buy a $5,000 living room set with three years before you need to make any payments (no interest cost is incurred). How much money would you have to deposit now in a savings account earning 4 perc
> A local furniture store is advertising a deal in which you buy a $3,000 dining room set and do not need to pay for two years (no interest cost is incurred). How much money would you have to deposit now in a savings account earning 5 percent APR, compound
> Your client has been given a trust fund valued at $1.5 million. She cannot access the money until she turns 65 years old, which is in 15 years. At that time, she can withdraw $20,000 per month. If the trust fund is invested at a 5 percent rate, how many
> Your client has been given a trust fund valued at $1 million. He cannot access the money until he turns 65 years old, which is in 25 years. At that time, he can withdrawal $25,000 per month. If the trust fund is invested at a 5.5 percent rate, how many m
> Consider that you are 45 years old and have just changed to a new job. You have $150,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $7,200 each year in
> At your full-service brokerage firm, it costs $135 per stock trade. How much money do you receive after selling 250 shares of International Business Machines (IBM), which trades at $96.17?
> John’s Bait and Fish shop has had the monthly sales amounts listed as follows for the last four years. Assuming that there is both seasonality and a trend, estimate monthly sales for each month of the coming year. Year: 2013 2014 20
> A loan is offered with monthly payments and a 13 percent APR. What’s the loan’s effective annual rate (EAR)?
> A loan is offered with monthly payments and a 10 percent APR. What’s the loan’s effective annual rate (EAR)?
> If the future value of an ordinary, 6-year annuity is $8,500 and interest rates are 9.5 percent, what’s the future value of the same annuity due?
> If the future value of an ordinary, 7-year annuity is $6,500 and interest rates are 8.5 percent, what is the future value of the same annuity due?
> If the present value of an ordinary, 6-year annuity is $8,500 and interest rates are 9.5 percent, what’s the present value of the same annuity due?
