Can) ou are in the process of purchasing a new automobile that will cost you $27,500. The dealership is offering you either a $2,500 rebate (applied toward the purchase price) or financing at a 0.9% APR for 48 months (with payments made at the end of the month) and no rebate. You have been pre-approved for an auto loan through your local credit union at an interest rate of 5.5% APR for 48 months. If you take the $2,500 rebate and finance your new car through your credit union calculate your monthly payments. 25. Calculate the monthly payments if you forgo the $2,500 rebate and finance your new car through the dealership. Investment Decision Rule Problems (2 points each) 26. A $25 investment produces $27.50 at the end of the year with no risk. If the OCC = 10% annually is this a good investment? 27. The Wilson Landscaping Company can purchase a piece of equipment for $3,600 today. The asset has a two-year life, will produce a cash flow of $600 in the first year and $4,200 in the second year. The fair interest rate is 15%. Calculate the project's IRR and NPV. Should the project be taken? 28. You are offered an investment opportunity that costs you $28,000, has an NPV of $2278, lasts for three years, and produces the following cash flows: Date $10,000 $15,000 -$28,000 Cash flow If the OCC = 10% what is the missing cash flow? - v se Projects, WILT STUUU ILCHUUSE! 8. (3 points) Xia Corporation is a company whose sole assets are $100,000 in cash and three projects that it will undertake. The projects are risk free and have the following cash flows: Project Cash Flow Today (8) Cash Flow in One Year (8) -20,000 30,000 - 10,000 25,000 60,000 80,000 Xia plans to invest any unused cash today at the risk-free interest rate of 10%. In one year, all cash will be paid to investors and the company will be shut down. a. What is the NPV of each project? Which projects should Xia undertake and how much cash should it retain? b. What is the total value of Xia's assets (projects and cash) today? c. What cash flows will the investors in Xia receive? Based on these cash flows, what is the value of Xia today? d. Suppose Xia pays any unused cash to investors today, rather than investing it. What are the cash flows to the investors in this case? What is the value of Xia now? e. Explain the relationship in your answers to parts (b), (c), and (d). 9. (3 points) The table here shows the no-arbitrage prices of securities A and B that we calculated. Cash Flow in One Year Security Market Price Today Weak Economy Strong Economy Security A 231 0 600 Security B 346 600 a. What are the payoffs of a portfolio of one share of security A and one share of security B? b. What is the market price of this portfolio? What expected return will you earn from holding this portfolio? c. If these are the only two possible states of the economy? Explain why your answer in b above is the risk free rate. . You believe you will need $125,000 annually to live comfortably while retired. You plan on retiring when you are 65 and will begin withdrawing funds from your retirement account on your 66th birthday. If you expect to need 30 years of retirement income how much money will you need at retirement (when you are 65) to meet this goal assuming the fair interest rate is 7%? 18. If today is your 35th birthday, and you decide, starting next year and on every birthday up to and including your 65th birthday (30 years total), you will invest the same amount how much must you invest annually To meet the retirement savings goal you have set in #17 above? Again the fair interest rate is 7% annually. 19. You realize that in the analysis above you forgot to include the impact of inflation. Recalculate the answer to # 17 assuming inflation is 3% per year (the real rate is 3.89%) and the $125,000 annually is stated in real dollars instead of nominal dollars. 20. Given your new answer above in real dollars, calculate the amount you must invest annually in real dollars to meet your retirement goal. Again assume 7% is the fair nominal rate and inflation is 3% per year (the real rate is 3.89%). 21. The annual payments you calculated in the previous problem are in real dollars. Since your first annual investment will be made next year, what is the nominal (actual) amount you need to invest next year to account for inflation? 22. Based on the real dollar value you calculated in #19 above, how much will you need in your retirement account in nominal dollars when you retire at age 65? 23. Based on the $125,000 real dollar annual required withdrawals from your retirement account, what amount will you withdraw from your retirement account, in nominal dollars, on your 66th birthday, the first year of retirement?, What is the amount in nominal dollars will you withdraw from your retirement account on your 85th birthday