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

your retirement?

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?