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University Of Chicago *

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MISC

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Finance

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Jan 9, 2024

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3

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Homework O -- You are expected to know this material from the Prerequisites We will use this material immediately and repeatedly. Please try this before the first lecture. If you can't do these problems go to the first TA help session. The homework is not graded. The solutions will be posted separatel y in C an v as 1 . Assessing the Payback method of capital budgeting Payback is defined as the number of years before cumulative cash inflows exceed the initial investment. Consider the following projects, where each cash flow comes in a different year. Project A Project B Project C Year 0 Year 1 Year 2 Year 3 -1000 2000 -1000 500 -1000 3000 500 -1500 2000 -500 (a) Calculate payback and PV for each project if the discount rate were 10%. Which project would you pick if you were using the payback criterion? (b) Explain the difference between payback and PV. (Explain the problems of payback criterion) 2 . Assessing IRR (You cannot solve this problem by hand; use a calculator.) Businesses often use internal rate of return (IRR) to evaluate projects. This question looks at what can happen when you use IRR. C 'd h fi 11 ons1 er t e o ( h h owmg proJects t at ave cas Year0 Project A -1000 Project B 1000 a) Calculate the IRR for these projects. h fl ows m year 0 d an Year 1 1200 -1200 year 1 . d ' as m 1cated) b) Suppose your hurdle rate for discounting was 15%, explain why IRR gives a different answer than PV. Consider a third project, with cash flows starting in year 0 and continuing through year 4 as indicated. Year0 Year1 Year2 Year 3 Year4 Project C -460 350 350 350 -600 c) Calculate the IRR and explain why IRR does not give a unique solution
3. Jamie Hill, the Finance Director of Gentler Lenz, a maker of expensive cars, has to set the terms for the loans that Lenz will make to customers who want to finance the purchase of the new Sigma cars. Each car has a non-negotiable sticker price of $55,000. The discount rate is 8%. (a) Suppose Jamie decides to ask for a down payment of $5000. What annual repayment should she ask buyers to make so that the firm breaks even on the loan and the loan is entirely paid off at the end of 4 years? (b) After setting the above terms, Jamie finds that car sales are very sluggish. Lenz's closest competitor is offering an identical car for $48000. Jamie does not want to cheapen the Sigma car's image by offering a rebate. Instead, she retains the downpayment of $5000, but asks for a lower annual payment such that the customer's effective interest rate on the oustanding amount is 2.9%. Are these terms more attractive than the competitor's if the loan continues to be repaid in four years? 4. Personal Financing Decision You decide to buy a Bonda Discord Lx automobile. You have $4,000 in cash. If you purchase the car (at a price of $16,000), then you will spend all your cash in making a down payment. You can borrow the remaining at an interest rate of 10.5% on the outstanding balance. (a) Assume (for simplicity) that loan repayments have to be made annually and you pay $2000 every year. How long will it be before you pay off your loan? (b) Suppose Bonda offers you a rate of 2. 9% on your outstanding balance. How long would it take for you to repay the loan if you repaid $2000 every year? What is the net present value of the loan to you? Bonda offers to lease the Discord at $199 a month with no down payment. The car reverts to Bonda at the end of four years. Its resale value at that point is $9500. (c) Are you better off leasing or buying the car and financing at 2.9%? How would your answer change if you estimate the resale value to be $7500? Note: As far as possible, try not to use the "brute force method" (where you type all the cash flows into a spreadsheet) for this question. But, you may have to sacrifice your pride and use a spreadsheet for this question and the next one.
5. Home mortgages and the APR (annual percentage rate). When banks loan money for a mortgage they no longer charge just an interest rate; they also charge points. One point is equal to one percent of the loan amount. You can view points as an up front interest charge (that is the way the IRS views it). Assume you obtain a $200,000 loan at 9 percent with four points. The bank will actually lend you 192,000 ($200,000 - .04*$200,000). Your monthly payments, however, are based on a $200,000 face value. In what follows, assume the loan is a 15 year loan. a) What is the APR on your loan? The loan is for 15 years and is repaid in monthly installments. What bankers call APR, you may know of as the IRR. b) You expect to move in five years. Thus although the loan is for fifteen years, you plan to repay it at the end of the fifth year (in the 60th month). What is the real APR of the loan? Before you start crunching numbers, should your answer be larger or smaller than your answer to a? c) Banks often offer a menu of financing choices. In addition to the above loan your bank aJso offers a 9. 75% loan with no points. Given your expected tenure, which loan should you choose?
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