a) What is the present value of a security that will pay $5,000 in 20 years if securities of equal
risk pay 7% annually?
b) If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 10 years?
c) What is the present value of a $200 perpetuity if the interest rate is 7%? If interest rates doubled to 14%, what would its present value be?
d) You are negotiating a contract with your employer. You have been offered three possible 4 year contracts. Your opportunity cost is 10%. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows:
Year 1 Year 2 Year 3 Year 4
Contract A $55,000 $55,000 $55,000 $55,000
Contract B $55,000 $56,000 $58,000 $60,000
Contract C $80,000 $40,000 $50,000 $50,000
Which contract would you accept? Show workings.Page 3 of 6
Question 2: Interest Rates (chapter 5)
a) The nominal interest is 12% with interest paid quarterly. What will be the effective annual rate?
b) Minnie has taken a 30-year mortgage for $500,000. The mortgage requires monthly payment of $5,143.06 with an interest rate of 12% per annum.
i. How much interest is in the first payment?
ii. How much repayment of principle is in the first payment?
c) Mickey is planning to save $50,000 per quarter for 10 years. Savings will earn interest at an (nominal) interest rate of 12% per annum. Calculate the present value for this annuity if interest is compounded semi-annually. Page 4 of 6
Question 4: Investment Decision Rules
A firm with a 14% WACC is evaluating 2 projects for this year's budget. After-tax cash flows are as
follows:
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Project A -$8,000 $2,200 $2,200 $2,200 $2,200 $2,200
Project B -$20,000 $5,700 $5,800 $6,000 $6,200 $6,500
i. Calculate NPV for each project.
ii. Calculate IRR for each project.
iii. Calculate MIRR for each project.
iv. Calculate payback for each project.
v. Calculate discounted payback for each project.Page 5 of 6
Question 4: Risk and Return (chapters 11 and 12)
a)
Consider the following information for two stocks, Stocks Y and Z and the returns on the two stocks are positively correlated.
Stocks Expected return Standard deviation
Y 9% 15%
Z 15% 17%
i. Assume you held a portfolio consisting of 60% of Stock Y and 40% of Stock Z. Calculate the average return of the portfolio during this period.
ii. Calculate the standard deviation of the portfolio if the correlation between Stock Y and Stock Z is 10%.
b) An Italian restaurant chain will generate the following rates of return in the following
scenarios:
State of economy Probability Rates of return if state of economy occurs
Boom 30% 125%
Normal Economy 50% 15%
Recession 20% -100%
i. Calculate the expected rate of return.
ii. Calculate the standard deviation of return for its shareholders.a)
XYZ Limited current share price is $20 and it has just paid a $1 dividend. As XYZ is a mature firm, this $1 dividend is expected to grow at a rate of 4% per year. What is an estimate of the return shareholders of XYZ Ltd expected to earn?
b) XYZ also has preference shares outstanding that pays $2 per share fixed dividend. If this stock is currently priced at $24, what is the return that preference shareholders expect to earn?
c) XYZ has issued a 5 year bond with a coupon rate of 11% and par value of $1,000. The price received by XYZ was $1,200. What is XYZ's pre-tax cost of debt?
d) XYZ has 5m ordinary shares outstanding and 1 m preference shares outstanding. Its equity has a total book value of $50m and its liabilities have a book value of $20m. If XYZ's ordinary and preference shares are priced as in parts a) and b), what is the market value of the XYZ's assets?
e) XYZ faces a 30% tax rate. Given the information in parts a) - d), and your answer to those problems, what is XYZ's WACC?