1. Which of the following statements are true?
i. 7% compounded half-yearly is equivalent to 6.9398% compounded quarterly.
ii. 9% compounded quarterly is equivalent to 9.1012% compounded half-yearly.
iii. 10% effective annual rate is equivalent to 9.5690% compounded monthly.
A. i and ii
B. i and iii
C. ii and iii
D. All of the above
E. None of the above
2. Which of the following statements are true?
i. 8% compounded continuously is equivalent to 8.0805% compounded quarterly.
ii. 9% compounded monthly is equivalent to 8.8619% compounded continuously.
A. i only
B. ii only
C. Both of the above
D. None of the above
3. The 1-year to 5-year spot rates are 3%, 3.5%, 4%, 4.5%, and 5%, respectively. Consider a 5-year, 6% annual coupon paying bond? The face value of the bond is $1,000. Which of the following statements are true?
i. The price of the bond is $1,048.45
ii. The yield to maturity is 4.88%
a. i only
b. ii only
c. Both i and ii
d. None of the above
4. "If the spot rate curve is increasing, the lower the coupon rate of a bond, the higher is its yield to maturity for a given time to maturity." Is this statement true?
a. True
b. False
5. "Bond A and Bond B have the same maturity and belong to the same risk class, but Bond A has a higher YTM than Bond B. Then Bond A is a better investment than Bond B and will be preferred by all investors." Is this statement true?
a. True
b. False
6. The 1-year to 7-year spot rates are 4.2%, 4.4%, 4.7%, 5.1%, 5.6% , 6.3%, and 6.6%, respectively. Compute the forward rate yield curve at the end of three years. What are the forward rates for 1-year to 4-year maturities? The given rates are effective annual rates.
a. 6.102%, 6.558%, 7.670%, and 7.881%
b. 6.109%, 6.665%, 7.780%, and 7.948%
c. 6.208%, 6.774%, 7.796%, and 7,980%
d. 6.253%, 6.838%, 7,859%, and 8.005%
e. 6.309%, 6.965%, 7.924%, and 8.048%\
7. An investor in an n-year coupon paying bond reinvests coupons until end of year n at forward rates prevailing today. What is the realized rate of return?
a. n-year yield to maturity
b. n-year par yield
c. n-year forward rate
d. n-year zero coupon rate
e. None of the above
8. Consider two bonds having the same credit rating: a 7-year 5% semi-annual coupon paying bond and another 7-year but 8% semi-annual coupon paying bond. Coupon from both bonds are reinvested at the forward rates until the maturity of the bonds. Then, which of the two bonds has a higher realized return?
a. The 5% coupon bond
b. The 8% coupon bond
c. Both have the same realized return
d. The given information is insufficient to answer the question
9. Assume that the spot rates from year 1 to year 5 are as follows: 4.8%, 5.1%, 5.4%, 5.6%, and 5.8%, respectively. An investor buys a 5-year, 6% annual coupon paying bond. Assume that the investor reinvests the coupons at the prevailing spot rates (and not the forward rates as in the above questions) at the time of coupon payments. Also assume that the spot rate curve does not shift during the next five years. What is the realized rate of return? (You can assume any face value of the bond as it does not matter)
a. 5.40%
b. 5.6325%
c. 5.6744%
d. 5.708%
e. 5.760%
10. The 1-year spot rate is 5%, the 1-year forward rate starting after one year is 5.4%, and the 1-year forward rate starting after two years is 6.2%. What is the 3-year spot rate? The given rates are effective annual rates.
a. 5.511%
b. 5.532%
c. 5.587%
d. 5.618%
e. 5.632%
11. The 1-yr spot rate is 4% (call it the short rate). Investors expect the short rate after one year and two years also to 4%. Short-term investors require a liquidity premium of 2%. Assuming the market is dominated by short-term investors, what are the 2-year and 3-year spot rates?
a. 6%, 6%
b. 4%, 6%
c. 5%, 5.33%
d. 6%, 5.48%
e. 7%, 5.48%
12. If the yield curve is upward sloping, the liquidity premium hypothesis implies that the investors expect interest rates to rise in the future.
a. True
b. False
13. If the yield curve is downward sloping, the liquidity premium hypothesis implies that the investors expect interest rates to fall in the future.
a. True
b. False
14. The idea of forward discount factors is useful in determining the forward prices of financial assets. Z(t, T) gives the value of $1 at time t to be paid at time T. Z(t, T) can be expressed in terms of simple discount factors as Z(t, T) = Z(0, T)/Z(0, t).
Suppose the 1-year to 5-year discount factors are 0.96079, 0.90484, 0.83527, 0.75578, and 0.67032. What is the 2-year forward price of a 6% annual coupon bond maturing after 5 years? The face value of the bond is $1,000.
A. $890.77
B. $894.38
C. $897.59
D. $901.22
E. None of the above
15. For the above bond, what is the 3-year forward price?
A. $896.73
B. $899.12
C. $900.48
D. $904.96
E. None of the above
A car manufacturer wants to introduce a new model. The life of the project is five years. The project would require an initial investment of either $4.25 billion with a probability of 0.50 or $4.75 billion with a probability of 0.50. The selling price of the car is $10,000. The variable cost per car is expected to be either $4,600 with a probability of 0.50 or $5,400 with a probability of 0.50. In the first year, the sales are expected to be either 230,000 cars, 250,000 cars, or 270,000 cars with probabilities 0.25, 0.50, and 0.25, respectively. In subsequent years, the sales are given by the following equation:
Year t sales = Year (t-1) sales + Random change
Random change is normally distributed with a mean of 0 and standard deviation of 20,000.
The cost of capital is 10%.
All this information has been entered for you in columns A and B of the worksheet "NPV" in the file Assignment 1-NPV.xls.
1,000 random numbers for all relevant variable have been generated for Year 0, Year 1, and Year 2. Complete this for the remaining three years and calculate the NPV. Using this information, answer the next four questions.
16. What is the expected NPV of the project? Choose the closest answer.
A. $120 million
B. $160 million
C. $200 million
D. $240 million
E. $280 million
17. Create a frequency distribution table starting with bin value 0 and with increments of $250 million and ending with bin value $4 billion. What is the probability of the project ending up with a loss (NPV less than 0)? This would be the frequency corresponding to bin 0 divided by 1,000 (total observations). Choose the closest answer.
A. 0.15
B. 0.20
C. 0.25
D. 0.30
E. 0.35
18. Using the frequency distribution table produced above, find the probability of the NPV being between $0.75 billion and $1 billion (use the frequency corresponding to the bin value of $1 billion)?
A. 0.04
B. 0.09
C. 0.14
D. 0.19
E. 0.24
19. What is the probability of the NPV exceeding $1 billion?
A. 0%
B. 10%
C. 20%
D. 30%
E. 35%
A TSB (Tax Saver Benefit plan) of a certain country allows its citizens to deposit money in this plan at the beginning of the calendar year, and this money can be used for medical expenses. Money deposited in this plan is not subject to income tax, which is 40%. All medical expenses up to the money deposited can be met out of the plan. However, any money left in the plan at the end of the year will be lost. The medical expenses during the year are expected to be either $3000, $4000, $5000, $6000, or $7000 with equal probability. The net benefit is the tax savings on the money deposited in the plan minus the amount left in the plan at the end of the year (which is lost). Generate 1,000 random numbers for the medical expenses and answer the following three questions.
20. What is the expected net benefit if $5,000 is deposited in the plan?
A. $1,000
B. $1,200
C. $1,400
D. $1,600
E. $1,800
21. What is the expected amount left unclaimed in the plan if a deposit of $6,000 is made?
A. $1,170
B. $1,490
C. $1,880
D. $2,120
E. $2,330
22. Which of the following deposits is expected to yield the greatest net benefit?
A. $3,000
B. $4,000
C. $5,000
D. $6,000
E. $7,000
23. Alpha Inc. plans to sell a new electronic devise. If the devise is sold without test marketing, the present value of a successful launch is $30 million with a probability of 0.50 and that of an unsuccessful launch is $10 million with a probability of 0.50. However, the company can first test market the product this year, improve the product based on the results, and then launch the product next year. With this the probability of a successful launch improves to 0.75. If the test marketing costs are $4 million, is it beneficial to first test market the product before it is launched. The discount rate is 8%. Make sure you take into account time value of money properly.
A. Yes
B. No
24. What should the test marketing costs be so that the company will be indifferent between launching the product without test marketing and launching the product after test marketing?
A. $3.148 million
B. $3.371 million
C. $4.083 million
D. $4.772 million
E. $5.00 million
25. Beta Inc. has been invited to make a bid on a government contract for a certain number of scientific instruments. The company estimates that it will cost $5,000 to prepare a bid and $95,000 to deliver the scientific instruments if it wins the contract. The company believes that there is a 30% chance that there will be no competing bids. However, when there are competing bids, it believes that the low bids (the lowest bidder wins the contract) will be as follows:
Low Bid Probability
Less than $115,000 0.20
Between $115,000 and $120,000 0.40
Between $120,000 and $125,000 0.30
Greater than $125,000 0.10
The company is contemplating whether to bid or not. If it is going to bid, it will bid either $115000, $120000, or $125000. What is the best course of action for Beta Inc.?
A. Don't bid
B. Bid $115,000
C. Bid $120,000
D. Bid $125,000
26. What is the expected monetary value (EMV) of the best decision?
A. $11,800
B. $11,900
C. $12,000
D. $12,100
E. $12,200
27. First do problems 9.12 to 9.14 in your textbook before you answer the next three questions. The initial investment of a new project is $2.5 million and is expected to sell 10,000 units at $60 net cash in the first year. After the first year, the expected sales will be revised to 12,000 units per year for the remaining life of the project is a success in the first year; if it is a failure in the first year, the expected sales are 5,000 units per year for the remaining life of the project. Success and failure in the first year are equally likely. There is an option to abandon the project after the first year for an abandonment value of $1.75 million. The discount rate for this project is 18%. What is the NPV of the project with the abandonment option?
A. $62,786
B. $87,932
C. $100,349
D. $106,012
E. $110,533
28. In the above problem, what is the value of the abandonment option?
A. $153,229
B. $164,812
C. $171,439
D. $184,712
E. $194,531
29. In the above problem, if the scale of the project can be doubled after 1 year if success is observed, what is the value of the option to expand?
A. $999,498
B. $1,000,412
C. $1,138,763
D. $1,200,559
E. $1,312,786
30. "Many research articles support that financial markets are semistrong efficient." Is this statement true or false?
A. True
B. False