CORPORATE FINANCE PROBLEM SET - Chapter 4 TVM (13 ed.)
PV and discount rate
1. You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?
a. The discount rate decreases.
b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same.
c. The discount rate increases.
d. Answers b and c above.
e. Answers a and b above.
Time value concepts
2. Which of the following statements is most correct?
a. A 5-year $100 annuity due will have a higher present value than a 5- year $100 ordinary annuity.
b. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate.
c. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent.
d. Statements a and c are correct.
e. All of the statements above are correct.
Effective annual return
3. Which of the following investments has the highest effective return (EAR)? (Assume that all CDs are of equal risk.)
a. A bank CD which pays 10 percent interest quarterly.
b. A bank CD which pays 10 percent monthly.
c. A bank CD which pays 10.2 percent annually.
d. A bank CD which pays 10 percent semiannually.
e. A bank CD which pays 9.6 percent daily (on a 365-day basis).
PV of an uneven CF stream
4. Hillary is trying to determine the cost of health care to college students, and parents' ability to cover those costs. She assumes that the cost of one year of health care for a college student is $1,000 today, that the average student is 18 when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that parents can save $100 per year to help cover their children's costs. All payments occur at the end of the relevant period, and the $100/year savings will stop the day the child enters college (hence 18 payments will be made). Savings can be invested at a nominal rate of 6 percent, annual compounding. Hillary wants a health care plan which covers the fully inflated cost of health care for a student for 4 years, during Years 19 through 22 (with payments made at the end of years 19 through 22). How much would the government have to set aside now (when a child is born), to supplement the average parent's share of a child's college health care cost? The lump sum the government sets aside will also be invested at 6 percent, annual compounding.
Ch. 4 TVM 13th ed
5.) Assume your father is now 40 years old, that he plans to retire in 20 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $75,000 he has today (he realizes that the real value of his retirement income will decline year-by-year after he retires). His retirement income will begin the day he retires, 20 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 4% per year from today forward; he currently has $200,000 saved up; and he expects to earn a return on his savings of 7% per year, annual compounding. To ht nearest dollar, how much must he save each year for the next 20 years, with the deposits being made at the end of each year, to meet his retirement goal?
6.) Today is Rachel’s 30th birthday. Five years ago, Rachel opened a brokerage account when her grandmother gave her $25,000 for her 25th birthday. Rachel added $2,000 to this account on her 26th birthday, $3,000 on her 27th, $4,000 on her 28th, and $5,000 on her 29th. Rachel’s goal is to have $400,000 in her account by her 40th birthday.
Starting today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 11 contributions, the first one will occur today, and the final contribution will occur on her 40th birthday. Complicating things is the fact that Rachel plans to withdraw $20,000 from the account on her 35th birthday to finance the down payment on a home. How large does each of these 11 contributions have to be for Rachel to reach her goal? Assume that the account has earned, and will continue to earn) an effective return of 12% a year.
7.) You are interested in saving money for your first house. Your plan is to make regular deposits into a brokerage account which will earn 14%. Your first deposit of $5,000 will be made today. You also plan to make four additional deposits at the beginning of each of the next four years. Your plan is to increase your deposits by 10% a year. (That is, you plan to deposits $5,500 one year from now, $6,050 two years from now, etc.) How much money will be in your account in five years?
8.) With a somber face, Adam Rust looked at the equally somber face of his mechanic and sighed. The mechanic had just pronounced a death sentence on his road- weary car. The car had served him well – at a cost of $500 it had lasted through four years of college with minimal repairs. Now, he desperately needed wheels. He had just graduated, and had a good job at a decent starting salary. He had been salivating at the prospect of being able to afford a new car – his first new car ever. The car dealer seemed to be very optimistic about his ability to afford the car payments – car payments would be a first for him too.
Adam was looking at a price of $35,000 for his dream car. The dealer had given him three payment options:
1. Zero percent financing. He would make a $4,000 down payment, and finance the remainder with a 0% APR four-year loan with monthly payments. He had the down payment, thanks to generous graduation gifts from friends and family.
2. No money down. He would get a $4,000 rebate, which he would use for the down payment, and finance the rest with a standard 48 month loan, with an 8% APR. This was attractive. Paying the $4,000 if he chose the 0% financing option would wipe out his savings, and he could think of many other uses for the $4,000 if he didn’t have to use it as a down payment for a car.
3. Pay cash. Get the $4,000 rebate and pay the rest with cash. While Adam didn’t have $35,000, he wanted to look at this option and compare it to the rest. His parents always paid cash when they bought their family car; Adam wondered if this really was a good idea.
Adam’s fellow graduate, Jenna Hawthorne, was lucky. Her parents gave her a car for graduation. Okay, it was a little Hyundai, and definitely not the dream car he was looking at, but it was serviceable, and Jenna didn’t have to worry about buying a new car. In fact, Jenna had been trying to decide how much of her new salary she could save. Adam knew that with a hefty car payment, saving for retirement would be very low on his priority list. Jenna believed she could easily set aside $3,000 of her $45,000 salary. She was looking at putting her savings in a growth stock fund. She was 22 and had a long way to go until retirement at age 65, and thought it was reasonable to take a little risk with her investments. The fund she was looking at had earned an average of 9% over the past 15 years and could be expected to continue earnings this amount, on average.
Adam and Jenna needed to look into what were the best options for each of them.
a. What are the cash flows associated with each of Adam’s three car financing options?
b. Adam had his $4,000 in a savings account earning 5%, with monthly compounding. What was the best option? What if Adam had the full purchase price for the car? Then what would the best option be?
c. Adam also needed to consider his substantial student loans. The loans have a 10% APR, and obviously, any money spent on the car could not be used to pay down the loans. What is the best option for Adam now? (Hint: note that having an extra $1 today saves roughly $1.10 next year since you can pay down the student loans. So, 10% is the time value of money in this case.)
d. Jenna wanted to know who much money she would have if she saved $3,000 a year at 9% from now until she turns 65. Once she retires, Jenna wants those savings to last for 25 years until she is 90. How much could she withdraw each year in retirement? (Assume you begin withdrawing the money from the account in equal amounts at the end of each year once retirement begins.)
e. Jenna expects her salary to grow regularly. While there are no guarantees, she believes an increase of 4% a year is reasonable. Suppose she increases the $3,000 by 4% as her salary grows. Now how much will she have in 43 years, and what yearly payment will she receive from these savings?
f. While her salary will grow regularly, so will inflation. Suppose Jenna assumes there will be 3% inflation each year when she is withdrawing funds. If she wants to keep her purchasing power constant to maintain the same standard of living, how much can she withdraw at the end of the first year of her retirement?
9. You are offered a note which pays $1,000 in 15 months (or 456 days) for $850. You have $850 in a bank which pays a 6.76649% nominal rate, with 365 daily compounding. You plan to leave the money in the bank if you don’t buy the note. The note is riskless. Should you buy it?