Financial Planning Problems
4-36. You realize that the plan in Problem 35 has a flaw. Because your income will increase over your
lifetime, it would be more realistic to save less now and more later. Instead of putting the same
amount aside each year, you decide to let the amount that you set aside grow by 3% per year.
Under this plan, how much will you put into the account today? (Recall that you are planning to
make the first contribution to the account today.)
4-37. You are 35 years old, and decide to save $5000 each year (with the first deposit one year from
now), in an account paying 8% interest per year. You will make your last deposit 30 years from
now when you retire at age 65. During retirement, you plan to withdraw funds from the account
at the end of each year (so your first withdrawal is at age 66). What constant amount will you be
able to withdraw each year if you want the funds to last until you are 90?
4-38. You have an investment opportunity that requires an initial investment of $5000 today and will
pay $6000 in one year. What is the IRR of this opportunity?
4-39. Suppose you invest $2000 today and receive $10,000 in five years.
a. What is the IRR of this opportunity?
b. Suppose another investment opportunity also requires $2000 upfront, but pays an equal
amount at the end of each year for the next five years. If this investment has the same IRR as
the first one, what is the amount you will receive each year?
4-40. You are shopping for a car and read the following advertisement in the newspaper: “Own a new
Spitfire! No money down. Four annual payments of just $10,000.” You have shopped around and
know that you can buy a Spitfire for cash for $32,500. What is the interest rate the dealer is
advertising (what is the IRR of the loan in the advertisement)? Assume that you must make the
annual payments at the end of each year.
4-41. A local bank is running the following advertisement in the newspaper: “For just $1000 we will
pay you $100 forever!” The fine print in the ad says that for a $1000 deposit, the bank will pay
$100 every year in perpetuity, starting one year after the deposit is made. What interest rate is
the bank advertising (what is the IRR of this investment)?
4-42. The Tillamook County Creamery Association manufactures Tillamook Cheddar Cheese. It
markets this cheese in four varieties: aged 2 months, 9 months, 15 months, and 2 years. At the
shop in the dairy, it sells 2 pounds of each variety for the following prices: $7.95, $9.49, $10.95,
and $11.95, respectively. Consider the cheese maker’s decision whether to continue to age a
particular 2-pound block of cheese. At 2 months, he can either sell the cheese immediately or let
it age further. If he sells it now, he will receive $7.95 immediately. If he ages the cheese, he must
give up the $7.95 today to receive a higher amount in the future. What is the IRR (expressed in
percent per month) of the investment of giving up $79.50 today by choosing to store 20 pounds of
cheese that is currently 2 months old and instead selling 10 pounds of this cheese when it has
aged 9 months, 6 pounds when it has aged 15 months, and the remaining 4 pounds when it has
aged 2 years?
4-43. Your grandmother bought an annuity from Rock Solid Life Insurance Company for $200,000
when she retired. In exchange for the $200,000, Rock Solid will pay her $25,000 per year until
she dies. The interest rate is 5%. How long must she live after the day she retired to come out
ahead (that is, to get more invaluethan what she paid in)?
4-44. You are thinking of making an investment in a new plant. The plant will generate revenues of $1
million per year for as long as you maintain it. You expect that the maintenance cost will start at
$50,000 per year and will increase 5% per year thereafter. Assume that all revenue and
maintenance costs occur at the end of the year. You intend to run the plant as long as it continues
to make a positive cash flow (as long as the cash generated by the plant exceeds the maintenance
costs). The plant can be built and become operational immediately. If the plant costs $10 million
to build, and the interest rate is 6% per year, should you invest in the plant?
4-45. You have just turned 30 years old, have just received your MBA, and have accepted your first
job. Now you must decide how much money to put into your retirement plan. The plan works as
follows: Every dollar in the plan earns 7% per year. You cannot make withdrawals until you
retire on your sixty-fifth birthday. After that point, you can make withdrawals as you see fit.
You decide that you will plan to live to 100 and work until you turn 65. You estimate that to live
comfortably in retirement, you will need $100,000 per year starting at the end of the first year of
retirement and ending on your 100th birthday. You will contribute the same amount to the plan
at the end of every year that you work. How much do you need to contribute each year to fund
4-46. Problem 45 is not very realistic because most retirement plans do not allow you to specify a fixed
amount to contribute every year. Instead, you are required to specify a fixed percentage of your
salary that you want to contribute. Assume that your starting salary is $75,000 per year and it
will grow 2% per year until you retire. Assuming everything else stays the same as in Problem
45, what percentage of your income do you need to contribute to the plan every year to fund the
same retirement income?