Chapter 5 Time Value of Money - TMC Business



Chapter 5 Time Value of MoneyWhat is the difference between simple interest and compound interest?Compounding InterestSimple interest pays only on principalCompound is the way the world works In the worksheet, is there something special that needs to be done for a present value amount?Negative cash flows represent outflows ; investmentsWe must “tell” the computer which way the cash is flowingIf you were to invest $3,000 today, what would it be worth in 1 year if you can earn 10% on your investments on average? 2 Years? 5 years?862498308346003000 * 1.10 = $3,30087947527940000What is the difference between 1 year and 2 years above? Can you explain the difference?Interest earns interestWhat does the word value or worth mean to you?What would you payWhat should the price be?If you could hold it in your hands, how much would you have?When you were 10 years old your grandfather tells you that upon college graduation he will give you $30,000. Inflation is expected to be 3.5%. What is this amount worth as a 10 year old? Assume graduation at 22.When you retire at age 65, your retirement fund promises to pay you $150,000 the first year of your retirement. If inflation is 4%, what is this worth to you in today’s money? How old are you? N = 79838617062300If the company can earn 12% on its retirement investments, how much must they put away today to get the above payment?959724866300What are some examples of cash flows that are annuity cash flow streams?LoansRetirement plan contributionsSystematic savings plansWhat is the difference between an annuity due and an ordinary annuity?Annuity due starts today / investment problemsOrdinary annuity starts end of the period / corporate cash flows & loansDraw time lineIf you started at age 19 to save 2,000 per year at the end of the year and could average 11% per year in earnings, how much would you have at retirement at age 65?80708514160500Would it make a difference if you started at the beginning of the year instead of the end? How much?97736121084400If you started saving $1,500 per year on a monthly basis for 18 years for your child’s college education, how much would you have if you invested and earned 8%? 12%?9525016383000You have analyzed your retirement plan and have concluded that you need 3,850,000 at age 62. If you can invest at 12% on average, how much must you invest monthly to achieve the financial goal? Age 25center23962300Lets assume that at age 62 you have saved the amount in problem 13. You think you will live to be 88 years old. During retirement, you plan to earn 8% on your investments. How much can you withdraw every month for the remainder of your life?7241873590700You win a prestigious sweepstake award. The company offers you $50,000 per year for the next 30 years or a lump sum. Answer the following questions.If the company can invest at 7%, how much would they need to invest to pay the promised cash flow stream? This is the amount of the lump sum offer?66611513716000If you could invest at 9%, how much could you withdraw for the 30 years, if you invest the lump sum?11968291714500At retirement you want to receive $60,000 per year for 25 years and can earn 13%. How much must you invest to achieve this goal?If you are concerned about the 3.75% inflation rate, how much must you invest?92392513779500If you wanted to receive $10,000 per year forever, how much would you need to invest at 12%?53877321712100What kind of cash flow stream is this?perpetuityA company is planning a project that will provide the following cash flow stream. If they can earn 14% on average, what is the value of this project?180,000270,000370,000450,000550,000660,000775,000right27392900If the company could reinvest the above cash flow stream at 14%, what would they have at the end of the 7th year?How do you change the compounding frequency in a time value problem?M = P/Y periods per yearWhat is the Effective interest rate for a 12%, monthly compounded investment? Quarterly?50409216998500A newly married couple is considering buying a new home. The house of their dreams costs $325,000. They have 10% to put down on the home and can borrow at 3.95%. What are the monthly payments on a 30 year mortgage?How much interest is paid out of the first month’s payment?6677761475200When the couple pays their 180th payment, what is the balance?111359417154800If they paid an extra 50 per month, how much interest would they save?825011757100If they paid biweekly payments, how much would they save? (divide monthly payments by 12)80889217208500What is a loan amortization table?Segments annuity payment s into principal and interest componentsWhy is this importantWhen I was born my Grandfather purchased a stock for $25. When I was 25 the stock was worth $75. What did I earn on the investment?8437201045300What did I earn at age 65 when the stock was worth $250?85539411874500Describe the rule of 72.Setup the following table:3%6%12%02,0002,0002,00064,000124,0008,0001816,000244,0008,00032,0003064,0003616,000128,00042256,000488,00032,000512,000Do one column at a timeDiscuss how doubling Interest rate does not double the amountHow long will it take for your money to double in a savings account?Time Retirement exampleYou currently earn $50,000 and have been able to save $15,000 in a retirement account. You expect to retire in 35 years at age 60. Inflation is expected to be at 3% for the foreseeable future. (age 30)What will you need to receive as income in year one of retirement to maintain your current lifestyle?FVPVI/YNMPMT-500003251457200381000If you live to be 90, how much do you need to accumulate to pay the cashflow in question 1, if you can earn 8% during retirement?FVPVI/YNMPMT8301140693457200317500If you want your retirement income to keep up with inflation, how much do you need to accumulate?FVPVI/YNMPMTG8301140,693352387520129500How much must you invest each month in your retirement plan to get the amount needed for retirement, if you can earn 12% on your invested dollars?FVPVI/YNMPMT2,135,115-15,0001235123905254508500If you are investing a certain amount today, what return do you need to receive to get the desired amount?FVPVI/YNMPMT2,135,115-15,0003512-15045720020002500Offline Homework (25 points) ______BUA321 CH05 Homework 25 points1) If you invested 12,000 today in a mutual fund that is expected to provide an annually compounded average return of 13% over the next 7 years, how much will you have in your account at the end of the 7th year?28,2314953001333500What if the investment compounded interest monthly? $29,6662) Your company wants to buy a piece of equipment that will cost 500,000 in 12 years. If you can invest your company’s money at an average return of 10%, how much do you need to invest in a lump sum today to pay cash for the asset? 159,3155334008509000What would the monthly investment requirement be? 1,80843815053975003) I have just won the LOTTO. The jackpot was 20 million dollars. The state has offered me one million dollars per year for 20 years (ignore taxes) or a lump sum. The lump sum is the present value of the payments. How much must the state invest today (the lump sum amount) to payout the annuity, if they can invest at the T-Bond rate of 6%? (ignore taxes)11,469,92156197510541000If I can invest at an average of 12%, how much can I withdraw from the lump sum per year over the 20 year window? 1,535,579100965022034500Should I take the lump sum or the 1 million dollar annuity? WHY? 4) Our company is considering a project that will provide the following after tax cash flows to the firm:CF1 90,000CF2125,000CF3175,000CF4200,000CF5190,000CF6 – 9165,000CF10145,000If we have a required return of 14% for this project, what is the value of the project to the company? 799152center18669000If we had to pay 700,000 for the project today, should we purchase the project? yes5) When you retire you will initially require an annual income of 125,000 per year. You anticipate living for 25 years during retirement with an 8% investment return. How much do you need in your pension plans to cover this need? 133434755245018478500How much will you have to invest monthly over the next 35 years to acquire that amount of money, if you can earn 13% on your investments? 593.81center99695006) I want to purchase a house in Florida. The current value is $350,000. I would like to put 25% down and make the purchase in 5 years. Houses in the area are appreciating at 6% per year. The forecasted mortgage rate at the time of purchase is 7.5% for 30 years.Future cost of the house? 468378left20193000Down payment? 117,094Mortgage amount? 351,284Monthly payments to get down payment, if I can invest at 15%?17366136207514351000Monthly payment of the mortgage? 245652387517399000Copy and Paste Special the first 6 months of the amortization table from the worksheet. What is the reduction in principal in month 1? (3)1004570000If you made an additional payment per year (1/12 more per month or made biweekly pmts), How much interest would you save? 139614center15748000 ................
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