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Financial Planning Problems

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Question;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?

 

Paper#50930 | Written in 18-Jul-2015

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