Answer all questions and shows all work.
Question 1. a) Calculate the present value of $500 with a discount interest rate of 7% for a period of 10 years.
b) Calculate the future value of $ 1,000 with a compounded interest rate of 5% for a period of 20 years.
c) What is the annual interest rate if the present value is $100, future value is $200 and the time period is 5 years?
d) What is the sum of the present values of the following cash flows at an interest rate of 5%?
Year 1: $200 year 2: $500 year 3: $700.
Question 2. a) You believe you will need to have saved $500,000 by the time you retire in 40 years. If the interest rate is 4% per year, how much must you save each year until retirement to meet your retirement goal?
b) A couple thinking about retirement decides to put aside $3,000 each year in a saving plan that earns 8% interest. In 5 years they will receive a gift of $10,000that also can be invested.
How much money will they have accumulated 30 years form now?
c) If the couple in (b) has a goal to retire with $800,000 of saving, how much extra do they need to save every year?
Question 3. A $1,000 General Electric bond pays an annual coupon rate of 8%, has 9 years until maturity, and sells at a yield to maturity of 7%.
a) What interest payments will bondholders receive each year?
b) At what price does the bond sell if semi-annual interest payments are made?
c) What will happen to the bond price if the yield to maturity falls to 6% compared to the price form part (b)?
Question 4. Eastern Electric currently pays a dividend of $1.64 per share and sells for $ 27 a share.
a) If investors believe the growth rate of dividends is 3% per years, what rate of return do they expect to earn on the stock?
b) If investors' required rate of return is 10%, what must be the growth rate they expect of the firm?
c) If the sustainable growth rate is 5% and the plowback ratio is .4, what must be the rate of return earned by the firm on its new investments?
Question 5. Machines A,B,C, and D projects are mutually exclusive and are expected to produce the following real cash flows with the real opportunity cost of capital is 12%.
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Machine
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Year 0
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Year 1
|
Year 2
|
Year 3
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Year 4
|
Year 5
|
|
A
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-$1,000
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$1,100
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$1,210
|
|
|
|
|
B
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-$1,200
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$1,100
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$1,210
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$1,330
|
|
|
|
C
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-$5,000
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$0
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$500
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$1,000
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$2,000
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$3,000
|
|
D
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-$6,000
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$500
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$1,000
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$2,000
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$3,000
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$4,000
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a) Calculate the NPV of each machine.
b) Calculate the equivalent annual cash flows form each machine.
c) Which machine should you buy?
Question 6. Machinery works forecasts the following cash flows on a project under consideration. The company uses the IRR rule to accept or reject projects. Should this project be accepted if the required returnis 12%?
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Year 0
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Year 1
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Year 2
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Year 4
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-$10,000
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0
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+$7,500
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+8,500
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Question 7. Afirm can lease a truck for 4 years at a cost of $30,000 annually. It can instead buy a truck at a cost of $80,000 with annual maintenance expenses of $10,000. The truck will be sold at the end of 4 years for $20,000. What is the better option if the discount rate is 10%?
Question 8. Growth enterprises believes its latest project, which will cost $80,000 to install, will generate streams of cash flows, cash flow at the end of the first year will be $5,000, and cash flows in future years are expected to grow indefinitely at an annual rate of 5%.
a) if the discount rate for this project is 10%, what is the project NPV?
b) What is the IRR?
Question 9. What will be the monthly payment if you borrow with a $100,000 15 years mortgage at an interest rate of 1% per month? How much of the first payment is interest? How much is principal amortization?
Question 10. Assume that the average firm in your company's industry is expected to grow at a constant growth of 6% and its dividend yield is 7%. Your company is as risky as the average firm in the industry. However, it has successfully completed some R&D work with investors expecting its earnings and dividends to grow 50% this year, 25% in the following year, with growth returning to the industry average of 6% in th third year and afterwards, if the last dividend paid (D0) was $1.00 per share , what is the estimated value per share of the firm's stock?