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## alculating Present Values Imprudential, Inc., has an unfunded pension liability of \$750 million that must be paid in 20 years

Chapter 4: Discounted Cash Flow Valuation
4.7 Calculating Present Values Imprudential, Inc., has an unfunded pension liability of \$750 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 6.25 percent, what is the present value of this liability?4.9 Perpetuities An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays \$160 annually if the next payment occurs one year from today? The market interest rate is 4.5 percent.

4.11 Present Value and Multiple Cash Flows Conoly Co. has identified an investment project with the following cash flows. If the discount rate is 5 percent, what is the present value of these cash flows? What is the present value at 13 percent? At 18 percent?

YEAR CASH FLOW
1 \$850
2 740
3 1,090
4 1,310

4.13 Calculating Annuity Present Value An investment offers \$7,000 per year for 15 years, with the first payment occurring one year from now. If the required return is 8 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

Chapter 5 Interest Rates and Bond Valuation
5.3 Bond Yields Watters Umbrella Corp. issued 15-year bonds two years ago at a coupon rate of 7.8 percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par value, what is the YTM?

5.5 Valuing Bonds Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 25 years to maturity, and a coupon rate of 6.4 per- cent paid annually. If the yield to maturity is 7.6 percent, what is the current price of the bond?

5.17 Bond Yields Wyland Co. wants to issue new 25-year bonds for some much-needed expansion projects. The company currently has 8 percent coupon bonds on the market that sell for \$1,063, make semiannual payments, and mature in 20 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?
6.5 Stock Valuation Shelter, Inc., is expected to maintain a constant 5.2 percent growth rate in its dividends, indefinitely. If the company has a dividend yield of 4.4 percent, what is the required return on the company’s stock?

6.11 Nonconstant Growth Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next 12 years, because the firm needs to plow back its earnings to fuel growth. The company will pay an \$11 per share dividend in 13 years and will increase the dividend by 5.5 percent per year thereafter. If the required return on this stock is 13 percent, what is the current share price?

6.25 Price-Earnings Ratio Consider Pacific Energy Company and U.S. Bluechips, Inc., both of which reported earnings of \$1,100,000. Without new projects, both firms will continue to generate earnings of \$1,100,000 in perpetuity. Assume that all earnings are paid as dividends and that both firms require a 12 percent rate of return.
a. What is the current PE ratio for each company?
b. Pacific Energy Company has a new project that will generate additional earnings of \$220,000
each year in perpetuity. Calculate the new PE ratio of the company.
c. U.S. Bluechips has a new project that will increase earnings by \$440,000 in perpetuity. Calculate the new PE ratio of the firm.

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