[解题]两道Corporatoin Finance的题，感兴趣的一起来作作

Quiz A

Consider an investment which costs $1,000 and appreciates in market value at the rate of 10% per year over its life of 5 years. After 5 years the investment is sold. During this time it pays a dividend yield of 5%. Dividend yield is measured in the usual way as a percentage of current market value. Dividends are paid at the end of each year.

To finance the investment, the owner borrows $800 and uses $200 of his own money. Interest on the loan is at the rate of 8% per annum paid annually in arrears. Loan repayments include only interest. The capital amount of the loan is repaid at the end of the investment.

Allow for income tax at the rate of 40%. Annual taxable income equals dividends less interest payments. A negative taxable income will result in a tax refund in the same year. Assume no CGT (capital gains tax).

Required

1. Considering this 5 year investment as just a future stream of cash flows (including loan payments), find its NPV over a range of discount rates from say 0-50%. Plot this NPV profile and identify the IRR. If possible, find the exact value of the IRR. Why is IRR so high?

2. Taking time points at the end of each year through to time 4 (end of year 4), find the IRR of the investment (i.e. of what remains of the investment) at each of these instants. Explain why IRR changes through time, and suggest how a clever investor can manage this change.

3. Imagine that instead of borrowing $800, the investor borrows $950 (and uses only $50 of her own). What effect will this have on the answer to Question 1 above (a further IRR calculation will help here)? Explain what this effect means for an investor starting with some finite amount of cash and trying to get rich.

Please include all excel spreadsheets used, including formulas. Maximum length is 10 pages, including write-up, graphs, excel spreadsheets and formulas.

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Quiz B

1. Suppose portfolios A and B have the same cash-flow stream and have the same value at some future time T. Show that if the market is free of arbitrage opportunities, then the two portfolios must have the same value now.

2. It is July 30, 2006. The cheapest to deliver bond in a September 2006 US Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30, 2006. Coupon payments are made on February 4 and August 4 each year. The term structure is flat, and the rate of interest with semi-annual compounding is 12% per annum. The conversion factor for the bond is 1.5. The current quoted bond price is $110. Calculate the quoted futures price for the contract.

3. Suppose the 60-to-150 day FRA rate is 4.30%, the 60-day bill rate is 4.25% and the 150-day bill rate is 4.40%. Show that there exists an arbitrage opportunity and construct an appropriate portfolio to take advantage of this opportunity. Carefully account for all the cash-flows.

4. A company must decide which of two machines to buy. The first has fixed capacity of 100 units. The other has a standard capacity of 100 units but can be upgraded to 300 units capacity by installing bigger motors at a cost of $210,000. Machine capacity will be worth either $1,000 (bad economy) or $1,600 (good economy) per unit in one year, depending on market conditions. The probability of a good economy is 0.8, and of a bad economy 0.2.

Shares in a company (“twin security”) involved in the same manufacturing activity, and employing only non-upgradeable machines, will be worth either $280 (good economy) or $200 (bad economy) in one year, and are trading today at $220. The risk-free rate is 10%.

How much extra should the company be prepared to pay today for the upgradeable machine?

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