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# T-bill Interest Rates to Determine Future Contract Rates

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Suppose the current yields to maturity on 3 month and 6 month T-Bills are 4.0 percent and 5.0 percent, respectively (yields will need to be converted to 90-day returns).
(a) In perfectly efficient markets and risk-neutral pricing, what yield should you expect to find on a 3 month T-bill forward contract deliverable in 3 months?
(b) Show that for the forward yield calculated in (a) the 6 month returns on (i) a 6 month spot bill and (ii) 3 month spot and 3 month futures bills are the same.
(c) Explain what factors would lead to a rejection of (b).

NOTE: From the term structure of interest rates recall: (look at attachment for proper symbol representation)
(1 + oy2)2 = (1 + oy1)(1 + 1F1)
where oy2 = the cash 6 month bill (two period) yield,
oy1 = the cash 3 month bill (one period) yield,
1F1 = the 3 month (one period) forward yield one period from now.

ALSO, in the futures market:
(1 + oy2)2 = (1 + oy1)(1 + 1y1f),
where 1y1f = the 3 month futures yield on futures contracts due in three months.

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#### Solution Summary

This solution uses T-bill interest rates to determine Forward and Future contract rates in a step-by-step calculation, with all workings showed on an excel file.

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1. In the corporate form, the separated structure creates the potential for __________ between owners and managers.
a. A conflict of interest
b. Increased transactions costs
c. Stability in relations
d. None of the above
2. Incentive problems take a variety of forms. They include
a. Moral hazard
c. Principal agent problems
d. All of the above
e. None of the above
3. Suppose the risk-free nominal interest rate on a one-year Canadian Treasury bill is 6% per year, and the expected rate of the inflation is 4% per year. What is the expected real rate of the return on the T-bill?
a. 2.91%
b. -1.92%
c. 1.92%
d. 1.89%
e. None of the above
4. The value of goodwill is the difference between ______________of the acquisition and its prior __________.
a. Market price; book value
b. Book value; market price
c. Historical value; market price
d. Market price; after tax value
e. None of the above
5. ___________ is the process of going from present value to future value; whereas _________ is finding the present value of some future amount.
a. Discounting; compounding
b. Compounding; annualizing
c. Compounding; discounting
d. Discounting; leasing
e. None of the above
6. What is the effective rate on a certificate of deposit that has a nominal rate of 11.5% with interest compounded quarterly?
a. 11.50%
b. 10.90%
c. 12.01%
d. 13.13%
e. None of the above
7. Consider the problem of calculating a loan amortization schedule. The portion of the payment that goes toward the payment of interest is __________________than the previous period's interest payment and the portion going toward repayment of principal is _____________ than that of the previous period.
a. Greater; lower
b. Lower; lower
c. Greater; greater
d. Lower; greater
e. None of the above
8. A major problem with using the internal rate of return is that
a. There may be multiple cash outflows and multiple cash inflows.
b. The internal rate of return may not exist.
c. The internal rate of return may not be unique.
d. All of the above
e. None of the above
9. If the exchange rate between the U.S. dollar and the French Franc is \$0.17 per French Franc, the dollar interest rate is 5.5% per year, and the French Franc interest rate is 4.5% per year, what is the break-even value of the future dollar/ French Franc exchange rate one year from now?
a. \$5.827 per FF
b. \$5.888 per FF
c. \$0.172 per FF
d. \$0.189 per FF
e. None of the above
10. You have determined the present value of an expected cash flow stream. Which of the following would cause the stream to have a higher present value
a. The discount rate increases
b. The cash flows are paid over a shorter period of time
c. The discount rate decreases
d. Statements b and c are both correct.
e. Statement a and b are both correct.
11. Lucinda is currently 30 years old and she plans to retire at age 60. She is expected to live to age 85. Her labour income is \$45,000 per year and she intends to maintain a constant level of consumption, with real interest rate of 4% per year, no taxes, and no growth in real labour income. What is the value of Lucinda`s human capital
a. \$35,196
b. \$40,005
c. \$994,888
d. \$778,141
e. None of the above
12. The relationship between NPV and IRR is such that
a. Both approaches always provide the same ranking of alternative investment projects.
b. The IRR of a project is equal to the firm`s cost of capital if the NPV of a project is \$0.
c. If the NPV of a project is negative, the IRR must be greater than the cost of capital.
d. None of the above.
13. Which of the following statements is most correct?
a. Sunk costs must be included in the project's cash flow.
b. R&D expenditures cannot be a part of the initial cost of a project.
c. Opportunity costs are sunk costs and therefore should not be included in the cost of the project.
d. Depreciation is not a cash expense.
e. All of the above statements are false.
14. The __________ states that in a competitive market, if two assets are equivalent, they will tend to have the same market price.
a. Law of Real Interest Rates
b. Law of One Price
c. Law of Price Equivalency
d. Law of Futures
e. None of the above
15. The ______________ is the proposition that an asset's current price fully reflects all publicly available information about future economic fundamentals affecting the asset's value.
a. Public Markets Hypothesis
b. Efficient Markets Exchange Rates
c. Fundamental Value Proposition
d. Efficient Markets Hypothesis
e. None of the above
16. Compute the current price of Walsingham bonds based on the following information: Walsingham bonds have a \$1,000 per value, have 20 years remaining until maturity, have a 12% coupon rate, are paid semi-annually, and have a yield to maturity of 10.5%.
a. \$858.42
b. \$982.47
c. \$1,119.52
d. \$1,124.41
e. None of the above
17. In the DDM model, if D and k are held constant, what will happen to the price of a stock as the constant growth rate gets higher?
a. The price of the stock will be higher.
b. The price of the stock will not change.
c. The price of the stock will be lower.
d. The model will reduce to zero.
e. None of the above.
18. _________ is a measure of willingness to pay to reduce one's exposure to risk. In evaluating trade-offs between the costs and benefits of reducing risk, ___________ people prefer the lower risk alternatives for the same cost.
a. Risk aversion; risk averse
b. Risk aversion; risk loving
c. Risk love; risk loving
d. Risk neutrality; risk neutral
e. None of the above.
19. When you _________ you pay a premium to eliminate the risk of loss and retain the potential for gain.
a. Insure
b. Diversify
c. Hedge
d. All of the above
e. None of the above
20. The ________ a stock's volatility, the ________ the range of possible outcomes and the ___________ the probabilities of those returns at the extremes of the range.
a. Larger; narrower; larger
b. Larger; narrower; smaller
c. Larger; wider; larger
d. Smaller; wider; larger
e. None of the above
21. Consider the probability distribution of rate of return on RayFran Inc. stock:
Rate of Return Probability
40% 0.25
15% 0.55
-8% 0.20
a. 15.50 %
b. 16.65%
c. 28.65%
d. 19.85%
e. none of the above

22. _________ is a contract that obliges the guarantor to make the promised payment on a loan if the borrower fails to do so.
a. An exclusion
b. A loan guarantee
c. A copayment
d. An interest rate cap
e. None of the above
23. The primary goal of corporate management is to _________ shareholder wealth.
a. Minimize
b. Maximize
c. Leverage
d. Mitigate
24. A disadvantage of sole proprietorship is the fact that the sole proprietor has
a. Limited liability for the firm's debts.
b. Unlimited liability for the firm's debts.
c. Expensive costs to establish the firm.
d. Limited authority over the firm's day-to-day business decisions.
25. __________instruments are also called fixed-income instruments.
a. Debt
b. Equity
c. Derivative
d. All of the above
26. The ________ curve depicts the relation between interest rates on fixed-income instruments issued by the U.S. Treasury and the maturity of the instrument.
a. Long-term
b. Short-term
c. Yield
d. Exchange rate
27. If the average inventory for a firm is \$17 million and inventory turnover is 0.9 times, what is its cost of goods sold?
a. \$15.3 million
b. \$18.89 million
c. \$153 million
d. \$188.9 million
28. The CFO of CyberChain Inc. plans to unleash a media campaign that is expected to cost \$15 million four years from today. How much cash should she set aside to pay for this if the current interest rate is 13%?
a. \$9.2 million
b. \$13.3 million
c. \$14.4 million
d. \$16.9 million
29. As one gets older, the ______ declines, so ________falls steadily until it reaches zero at age 65.
a. Future value of remaining labour income; human capital
b. Future value of remaining labour income; initial wealth
c. Present value of remaining labour income; human capital
d. Present value of initial wealth; optimization
30. A project's IRR is _______ its scale, which makes IRR not a good measure for ranking mutually exclusive projects.
a. Contingent on
b. Independent of
c. Inversely proportional to
d. Half of
31. You are travelling in FarOut where you can buy 130 kranes (a krane being the unit of currency of FarOut) with a U.S. dollar at official FarOut banks. Your tour guide has a relative who dabbles in the black market and this particular relative will sell you kranes for just \$0.00833 each on the black market. How much will you lose or gain by exchanging \$200 on the black market instead of going to the bank?
a. You would gain approximately 1,660 kranes
b. You would lose approximately 1,660 kranes
c. You would gain approximately 1,990 kranes
d. You would lose approximately 1,990 kranes
32. What happens to the value of a four-year fixed-income security promising \$100 per year if the market interest rate falls from 6% to 5% per year?
a. A fall of 1% causes a drop of \$4.87 in market value
b. A fall of 1% causes a rise of \$4.87 in market value
c. A fall of 1% causes a drop of \$8.09 in market value
d. A fall of 1% causes a rise of \$8.09 in market value
33. The relation between earnings and dividends in any period, assuming no shares are issued or repurchased, is
a. Dividends = earnings/ net new investment
b. Dividends = earnings x net new investment
c. Dividends = earnings + net new investment
d. Dividends = earnings - net new investment
34. By definition, ________ are investors who take positions to reduce their exposures.
a. Operations insurers
b. Foreign exporters
c. Hedgers
d. Speculators
35. You are interested in taking a vacation to Yemen next year, but you are worried about the price of the trip. Over the past three years, the price of a trip to Yemen has ranged between \$3,500 and \$4,500. The current price is \$4,000. You wish to maintain the possibility of a lower price. How would you eliminate the possibility of rising prices, but still maintain the possibility of a gain from lower prices?
a. Purchase an option today from the sponsor, which would allow you to pay the lower of \$4,000 or the market price at the time you take your Yemen vacation.
b. Purchase an option today from the sponsor, which would allow you to pay the higher of \$4,000 or the market price at the time you take your vacation to Yemen.
c. Leave it to the market
d. Arrange a futures contract through the newspaper.

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