Finance Chapter 6 Practice Problems

Island News purchased a piece of property for $1.36 million. The firm paid a down payment of 12 percent in cash and financed the balance. The loan terms require monthly payments for 10 years at an annual percentage rate of 4.75 percent, compounded monthly. What is the amount of each mortgage payment?

A. $12,548.18 Work: 1st Part - 12% x 1.36 million = 163,200 - 1.36 million - 163,200 = 1,196,800 2nd Part - PV = 1,196,800 - I/Y = 4.75 / 12 months = .3958 per month - N = 10 x 12 months = 120 months - CMPT PMT

Your employer contributes $60 a week to your retirement plan. Assume you work for your employer for another 20 years and the applicable discount rate is 9 percent. Given these assumptions, what is this employee benefit worth to you today?

A. $28, 927 Work: - I/Y = 9/52 weeks = .17308 per week - N = 20 years x 52 weeks = 1,040 weeks - PMT = 60 per week - CMPT PV

Your parents have made you two offers. The first offer includes annual gifts of $10,000, $11,000, and $12,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 8 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer?

A. $28,216 Work: ASK

Racing Engines wants to save $750,000 to buy some new equipment four years from now. The plan is to set aside an equal amount of money on the first day of each quarter (4) starting today. The firm can earn 4.75 percent on its savings. How much does the firm have to save each quarter to achieve its goal?

A. $42,337 Work: NOTE: Annuity due!!!! - I/Y = 4.75/4 = 1.1875 per quarter - N = 4 years x 4 = 16 quarters - FV = 750,000 - CMPT PMT

Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $187,000, $220,000, and $245,000 over the next three years, respectively. After that time, they feel the business will be worthless. Southern Tours has determined that a 13.5 percent rate of return is applicable to this potential acquisition. What is Southern Tours willing to pay today to acquire Holiday Vacations?

A. $503,098 Work: ASK Formula??

You have been investing $250 a month for the last 13 years. Today, your investment account is worth $73,262. What is your average return on investment?

A. 8.94 percent Work: - N = 13x12 months = 156 months - PMT = -250 per month - FV = 73,262 - CMPT I/Y

You estimate that you will owe $39,950 in student loans by the time you graduate. The interest rate is 3.75 percent. If you want to have this debt paid in full within 10 years, how much must you pay each month?

B. $399.74 Work: - PV = $39,950 - I/Y = 3.75/12 months = .3125 per month - N = 10 x 12 months = 120 months - CMPT PMT

You are considering a project that will provide annual cash inflows of $16,500, $25,700, and $18,000 at the end of each year for the next three years. What is the present value of these cash flows, given a discount rate of 12.5 percent?

B. $47,615 Work: NOTE: CF method on calc. !!!!!!

Your car dealer is willing to lease you a new car for $190 a month for 36 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.5 percent, what is the current value of the lease?

B. $6,232.80 Work: NOTE: Annuity due!!!!! (2nd BGN, 2nd SET) - I/Y = 6.5/12 months = .542 per month - N = 36 months - PMT = 190 per month - CMPT PV

Your grandmother is gifting you $150 a month for 4 years while you attend college to earn your bachelor's degree. At a 4.8% percent discount rate, what are these payments worth to you on the day you enter college?

B. $6,539.14 Work: - I/Y = 4.8/12 months = .4% per month - PMT = 150 per month - N = 4 x 12 months = 48 months - CMPT PV

Travis International has a one-time expense of $2.86 million that must be paid three years from now. Since the firm cannot raise that amount in one day, it wants to save an equal amount each month over the next three years to fund this expense. If the firm can earn 2.1 percent on its savings, how much must it save each month?

B. $77,037.69 Work: - I/Y = 2.1 / 12 months = .175 per month - N = 3 x 12 months = 36 months - FV = 2.86 million - CMPT PMT

Today, you turn 23. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $75 a day, every day, until you turn 40. You open an investment account and deposit your first $75 today. What rate of return must you earn to achieve your goal?

B. 8.09 percent Work: - N = 40-23 = 17 years x 365 days = 6,205 days - PMT = -75 per day - FV = 1,000,000 - CMPT I/Y

Phil can afford $240 a month for five years for a car loan. If the interest rate is 8.5 percent, how much can he afford to borrow to purchase a car?

C. $11,697.88 Work: - I/Y = 8.5/12 months = .71 per month - PMT = 240 per month - N = 5 x 12 months = 60 months - CMPT PV

You borrow $230,000 to buy a house. The mortgage rate is 4.5 percent and the loan period is 25 years. Payments are made monthly. If you pay the mortgage according to the loan agreement, how much total interest will you pay?

C. $153,524 Work: 1st Part - I/Y = 4.5/12 months = .375 per month - N = 25 x 12 months = 300 months - PV = 230,000 - CMPT PMT = 1,278.45 2nd Part - Total Payment = 1,278.45 x 300 = $383,524.5 - Total Interest = 383,524.5 - 230,000 = $153,524

Your great aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,400 on the first of each year, starting immediately and continuing for 20 years. What is the value of this inheritance today if the applicable discount rate is 6.75%?

C. $27,677.34 Work: NOTE: Annuity due!!!!! - I/Y = 6.75 per year - N = 20 years - PMT - 2,400 per year - CMPT PV

You want to start your own consulting business and believe it could produce cash flows of $5,600, $48,200, and $125,000 at the end of the next 3 years. At the end of the three years you think you can sell the business for $450,000. At a 14 percent discount rate, what is this business worth today?

C. $430, 109 Work: ASK - PV = $5,600 / 1.14 + $48,200 / 1.142 + ($125,000 + 450,000) / 1.143 = $430,109 Formula??

An insurance annuity offers to pay you $1,000 per quarter (4) for 20 years. If you want to earn a rate of return of 6.5 percent, what is the most you are willing to pay as a lump sum today to buy this annuity?

C. $44,591.11 Work: - PMT = 1,000 per quarter - I/Y = 6.5/4 = 1.625 per quarter - N = 20 x 4 = 80 quarters - CMPT PV

Your insurance agent is trying to sell you an annuity that costs $50,000 today. By buying this annuity, your agent promises that you will receive payments of $250 per month for the next 20 years. What is the rate of return on this investment?

C. 1.88 percent Work: - PV = -150,000 - PMT = 250 per month - N = 20x12 months = 240 months - CMPT I/Y

Today, you borrowed $6,200 on your credit card to purchase some furniture. The interest rate is 14.9 percent, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $120?

C. 6.93 years Work: - I/Y = 14.9/12 months = 1.24 per month - PV = -6,200 - PMT = 120 - CMPT N

Rosina plans on saving $2,000 a year and expects to earn an annual rate of 8.8 percent. How much will she have in her account at the end of 43 years?

D. $831,532 Work: - I/Y = 8.8 per year - N = 42 years - PMT = 2,000 - CMPT FV

Today, you are retiring. You have a total of $289,416 in your retirement savings. You want to withdraw $2,500 at the beginning of every month, starting today and expect to earn 4.6 percent, compounded monthly. How long will it be until you run out of money?

D. 12.71 years Work: NOTE: Annuity due!!!!! - PV = 289,416 - PMT = -2,500 per month - I/Y = 4.6/12 months = .383 per month - CMPT N

You are considering an annuity that costs $160,000 today. The annuity pays $17,500 a year at an annual interest rate of 7.5 percent. What is the length of the annuity time period?

D. 16 years Work: - I/Y = 7.5 per year - PMT = 17,500 per year - PV = -160,000 per year - CMPT N

You are borrowing $21,800 to buy a car. The terms of the loan call for monthly payments for five years at 8.25 percent interest. What is the amount of each payment?

E. $444.64 Work: - I/Y = 8.25/12 months = .6875 - N = 5 x 12 months = 60 months - PV = 21,800 - CMPT PMT