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FIN Assignment 2 Chapter 4: Time Value of Money Problems

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Question;Show work completely (including time-line where applicable) to receive credit1. Dr. Vision has been working on an advanced technology in laser eye surgery. Thetechnology is expected to be available to the medical industry five years from today andwill generate annual income of $900,000 and it will grow at 4 percent perpetually startingthat year. What is the present value of the technology if interest rate is 8 percent?N= 5i= 8%FV= 900,000PV=?PV= FVN(1+i)^N=4,500,000(1.08)^5=$3,062,682.912.What is the present value of end-of-year cash flows of $7,000 per year, with thefirst cash flow received six years from today and the last one 40 years from today?Assume interest rate of 8%.3.What is the value of a 20-year annuity that pays $1500 a year? The annuitys firstpayment will be received on year 6. Also, assume that the annual interest rate is 5 percentfor years 1 through 5 and 6 percent hereafter.N= 20PMT= 1500i= 5% for years 1-5 & 6% from year 6 onFVAN= PMT(1=i)^N-1 +..FVAN= 1500(1.05)^19 + 1500(1.05)^18 + 1500(1.05)^17 + 1500(1.05)^16 +1500(1.05)^15 + 1500(1.06)^14 + 1500(1.06)^13 + 1500(1.06)^12 + 1500(1.06)^11 +1500(1.06)^10 + 1500(1.06)^9 + 1500(1.06)^8 + 1500(1.06)^7 + 1500(1.06)^6 +1500(1.06)^5 + 1500(1.06)^4 + 1500(1.06)^3 + 1500(1.06)^2 + 1500(1.06)^1=4.You are saving for the college education of your three children. They are one yearapart in age, one will begin college in 8 years, another at year 9 and another at year 10.You estimate your childrens college expenses to be $25,000 per year per child, paid atthe beginning of each college year (first payment for first child is at year 8 and so on).The annual interest rate is 4 percent. How much money must you deposit in anaccount each year to fund your childrens education? You will begin payments one yearfrom today. You will make your last deposit the year before your oldest child enterscollege. Also assume that each child will take 4 years to graduate from college.5.You are saving for your retirement. You have decided that one year from today youwill deposit 5 percent of your annual salary in an account which will earn 10 percent peryear. Your salary currently (today) is $50,000, and it will increase at 2 percent per yearthroughout your career. How much money will you have for your retirement, which willbegin in 40 years? Assume your first payment into the account is one year from todayafter your first increase.6.Amy has received a job offer from a large investment bank as an assistant to thevice president. Her base salary will be $70,000 today. Assuming for simplicity that shewill receive her first annual salary payment with the appropriate increment one year fromthe day she begins to work. In addition, she will get an immediate $15,000 bonus forjoining the company today. Her salary will grow at 3 percent each year. Each year shewill receive a bonus equal to 10 percent of her salary. Mary is expected to work for thenext 40 years. What is the present value of the offer if the discount rate is 8 percent? Alsowhat is her future value of her salary in 40 years (in a world of no tax!)7.Your younger brother has come to you for advice. He is about to enter college andhas two options open to him. His first option is to study petroleum engineering. If he doesthis, his undergraduate degree would cost him $30,000 a year for four years. Havingobtained this, he would need to gain two years of practical experience: in the first year hewould earn$30,000, in the second year he would earn $40,000. He would then need toobtain his masters degree, which will cost $35,000 a year for two years. After that hewill be fully qualified and can earn $90,000 per year for 30 years. His other alternative isto study finance. If he does this, he would pay $25,000 a year for four years and then hewould obtain his masters degree, which will cost $30,000 a year for one year. After thathe would join a firm and anticipate to earn $85,000 per year for 31 years.The effort involved in the two careers is the same, so he is only interested in the earningsthe jobs provide. All earnings and costs are paid at the end of the year. What advicewould you give him if the market interest rate is 4 percent? A day later he comes backand says he took your advice, but in fact, the market interest rate was 6 percent. Will youadvise him differently and if so, why?8.You anticipate that you will need $2,000,000 when you retire 35 years from now.You just join a new firm and your first annual salary is $80,000 to be received one yearfrom today. You also received one time signing bonus of $20,000 today. You decided thatyouwill put all you signing bonus into your account plus you will contribute $X every yearstarting next year for the next 34 years. In other words, after your initial deposit of$20,000, your first payment will be made on year 1 and last payment will be on year 34.How much is $X if you want to have $2,000,000 in Year 35. Assume that interest rate is9%, annually compounded during this duration.9.You are saving for your child's education since you did not participate in the TexasTomorrow Fund. Your child is two year old today. Starting next quarter, you will deposit$200 every quarter until you child turns 17. Your last payment will be on his 17th year.You can to withdraw $X very year starting his 18th birthday for 4 years, first payment onhis 18th birthday. Assuming you have investing your money in an account is provides12% return and the interest is compounded daily (365 days).10.Today is Oct. 1, 2012. Starting today you plan to invest $2000 every year, firstdeposit today and last deposit on Oct. 1, 2030. After that, you plan to leave the money inthe same account until Oct. 1, 2050. However, the interest rate is 10% compoundedquarterly until your last deposit and only 6% compounded annually after that. How muchmoney will you have in your account on Oct. 1, 2050?

 

Paper#48045 | Written in 18-Jul-2015

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