An oil painting by the late Carl Barks comes up for auction: Under an open-outcry, ascending-price auction, who will buy the painting? How much will they pay?

Working on two questions regarding auctions and Retirememnt planning, they are attached here, just need some direction on the manner in which I need to proceed and some background on auctions and types.

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1. An oil painting by the late Carl Barks comes up for auction. Though not a household name, his work is highly admired among certain collectors. Six collectors compete to buy the painting at auction, each anxious to hang the work in their home. (Each collector knows only his/her own personal valuation, as well as the existence of six potential bidders.) Collector A personally values it at $100,000; Collector B at $125,000; Collector C at $150,000; Collector D at $125,000; Collector E at $100,000; Collector F at $75,000. (You may assume that the collectors all try to bid optimally.)

A. Under an open-outcry, ascending-price auction, who will buy the painting? How much will they pay?

B. Under a sealed-bid, second-price auction, who will buy the painting? How much will they pay?

C. Under a sealed-bid, first-price auction, who will buy the painting? How much will they pay?

D. Collector F unfortunately passes away before the auction, leaving only five collectors to bid. In the small world of Barks fans, this news becomes quickly known. Should the bidding strategies [that is, the dollar amount planned to bid] of the remaining collectors change in scenarios (A), (B), and (C) above?

2. You buy a townhouse in October 2005, taking out a 30-year mortgage of $120,000 at 4.50% interest (compounded monthly). You make the required monthly payments.

A. What is the monthly payment?

B. In October 2010, you receive an inheritance, and consider paying off the mortgage at that time. How much money would be required to do so?

3. Your brother asks you to help him with retirement planning. He is currently age 20, and has saved nothing towards retirement. As he plans to own his home outright by retirement, he believes that his annual spending needs during retirement will be the equivalent of $40,000 in today’s purchasing power. (That is, based on today’s prices, he would spend $40,000 annually.) He would like to retire at age 60. Assume he can earn 7% annually on his investments, and that annual inflation will be 3%. Treat cash flows as occurring annually in this problem.

A. When he is 60, how many dollars will he actually need to spend annually?

B. To stay on the conservative side (protecting himself against outliving his savings), your brother assumes he will live forever. Assuming the above spending rate, how much money should he have accumulated by age 60? (In other words, what lump-sum amount at retirement is equivalent to his projected retirement spending needs?)

C. What is the present (i.e., at age 20) value of your brother’s projected retirement spending needs?

D. Suppose your brother saves an equal number of dollars annually for the forty years from now until retirement. How much does your brother need to save each year?

4. Akbar and Jeff’s BBQ Tofu Hut is thinking of adding to their famed chain of fast-food outlets, by locating in downtown St. Louis. They estimate upfront costs of the restaurant to be $60,000. Of these cost, half (i.e., $30,000) are expensed [for corporate income tax purposes], and half are allowed to be fully depreciated, straight-line over the next five years; treat depreciation and taxes as occurring monthly. Operating expenses are expected to be 87% of revenue (leaving a margin of 13%). Working capital needs are minimal, thanks to Akbar and Jeff’s famous “from our delivery truck … right into your mouth” inventory control operation/advertising campaign. The corporate income tax rate is 30%. Akbar and Jeff analyze restaurant operations using a discount rate of 1% per month.

A. If the restaurant has an expected lifespan of five years (60 months), and estimated monthly revenue of $10,000, should the restaurant be opened? [Due to Akbar and Jeff’s justifiably admired streamlined organization, assume that, if desired, the restaurant can be opened essentially immediately.]

B. If instead the restaurant has an expected lifespan of eight years, again with estimated monthly revenue of $10,000, should the restaurant be opened? [Note that the depreciation schedule for upfront costs is left unchanged.]

5. It is late November 2005. The prices of zero-coupon US government bonds with various maturities are as follows:
Maturity date: (Nov) 2006 2007 2008 2009 2010
Price: 98.00 94.50 88.25 84.25 80.75

A. What is the four-year (annually compounded) yield [i.e., interest rate]?

B. What is the price of a 4% 2009 US government bond (assuming annual coupons)?

6. Suppose a ten-year 6% coupon US government bond has a 5% yield. What is the quoted price? (Assume the coupon is paid and the yield is compounded semiannually.)
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