1) Calculating yield and years till maturity
Fill in the table below for the following zero coupon bonds. The face value of each bond is $1,000.
Price Maturity Maturity
$300 30 ?
$300 ? 8%
? 10 10%
2) Analyze the risk of a portfolio
Use the data below and consider portfolio weights of .60 in stocks and .40 in bonds.
Rate of Return
Scenario Probability Stocks Bonds
Recession 0.2 -5% 14%
Normal 0.6 15% 8%
Boom 0.2 25% 4%
a. What is the rate of return on the portfolio in each scenario?
b. What is the expected return and standard deviation of the portfolio?
c. Would you prefer to invest in the portfolio of stocks only or in bonds only?
3) Calculate IRR
Here are the cash flows for two mutually exclusive projects:
Project C0 C1 C2 C3
A ($20,000) $8,000 $8,000 $8,000
B ($20,000) 0 0 $25,000
a. At what interest rates would you prefer project A to B?
b. What is the IRR of each project?
4) Calculate NPV and IRR
Growth Enterprises believes its latest project, which will cost $80,000 to install, will generate a perpetual growing stream of cash flows. Cash flow at the end of this year will be $5,000 and cash flows in future years are expected to grow indefinitely at an annual rate of 5 percent.
a. If the discount rate for this project is 10 percent, what is the project NPV?
b. What is the project IRR?
5) Calculate project cash flows, NPV, and IRR
Revenues generated by a new fad product in each of the next 5 years are forecasted as follows:
Expenses are expected to be 40 percent of revenues, and working capital required in each year is expected to be 20 percent of revenues in the following year. The product requires an immediate investment of $50,000 in plant and equipment.
a. What is the initial investment in the product? Remember working capital.
b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm's tax rate is 40 percent, what are the project cash flows in each year?
c. If the opportunity cost of capital is 10 percent, what is the project NPV?
d. What is the project IRR?
6) Calculate the Weighted Average Cost of Capital
Find the WACC of William Tell Computers. The total book value of the firm's equity is $10 million; book value per share is $20. The stock sells for a price of $30 per share, and the cost of equity is 15 percent. The firm's bonds have a par value of $5 million and sell at a price of 110 percent of par. The yield to maturity on the bonds is 9 percent, and the firm's tax rate is 40 percent.
7) Determine the capital structure of a firm
Examine the following book-value balance sheet for University Products, Inc. What is the capital structure of the firm based on market value? The preferred stock currently sells for $15 per share and the common stock for $20 per share. There are one million common shares outstanding.
BOOK VALUE BALANCE SHEET
(all values in millions)
Assets Liabilities and Net Worth
Cash and short-term securities $1 Bonds, coupon = 8% paid annually
maturity = 10 years, yield to maturity = 9% $10.0
Accounts receivable 3 Preferred stock (par value $20 per share) 2.0
Common stock (par value $.10) 0.1
Inventories 7 Additional paid in stockholders 9.9
Plants and equipment 21 Retained earnings 10.0
Total $32 $32.0
8) Analyze an IPO
Having heard about IPO underpricing, I put in an order to my broker for 1,000 shares of every IPO he can get me. After 3 months, my investment record is as follows:
IPO Shares Price per
return Allocated to Me Share Initial
A 500 $10 7%
B 200 20 12%
C 1,000 8 -2%
D 0 23%
a. What is the average underpricing of this sample of IPOs?
b. What is the average initial return on my "portfolio" of shares purchased from the four IPOs I bid on? Calculate the average initial return weighting by the amount of money invested in each issue.
c. Why have I performed so poorly relative to the average initial return on the full sample of IPOs? What lessons do you draw from my experience?
9) Calculate break-even points
Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $100. The materials cost for a standard diamond is $30. The fixed costs incurred each year for factory upkeep and administrative expenses are $200,000. The machinery costs $1 million a year and is depreciated straight-line over 10 years to a salvage value of zero.
b. What is the NPV break-even sales assuming a tax rate of 35 percent, a 10-year project life and a discount rate of 12 percent?
10) Calculate and analyze the degree of operating leverage
A project has fixed costs of $1,000 per year, depreciation charges of $500 a year, revenue of $6,000 a year, and variable costs equal to two-thirds of revenues.
a. If sales increase by 5 percent, what will be the increase in pretax profits?
b. What is the degree of operating leverage of this project?
c. Confirm that the percentage change in profits equals DOL times the percentage change in sales.
The attached problems are in the excel worksheet attachment and this is where the problems should be solved.
Answers questions on yield, risk of a portfolio, NPV, IRR, project cash flows, Weighted Average Cost of Capital, capital structure, IPO, break-even points, degree of operating leverage