End of Main Chapter Problems

Q 3.25 A tall Starbucks coffee costs $1.65 a day. If the bank's quoted interest rate is 6% per annum, compounded daily, and if the Starbucks price never changed, what would an endless, inheritable free subscription to Starbucks coffee be worth today?

Q 3.26 If you could pay for your mortgage forever, how much would you have to pay per month for a $1,000,000 mortgage, at a 6.5% annual interest rate? Work out an answer change if the 6.5% is a bank quote and one if it is a true interest rate?

Q 3.27 What is the PV of a perpetuity paying $30 each month, beginning next month, if the annual interest rate is a constant 12.68% per year?

Q 3.28 What is the prevailing cost of capital if a perpetual bond were to pay $100,000 per year beginning next year and cost $1,000,000 today?

Q 3.29 What is the prevailing cost of capital if a perpetual bond were to pay $100,000 per year beginning next year (time 1), payments growing with the inflation rate at about 2% per year, assuming the bond cost $1,000,000 today?

Q 3.30 A tall Starbucks coffee costs $1.65 a day. If the bank's quoted interest rate is 6% per annum and coffee prices increased at a 3% annual rate of inflation, what would an endless, inheritable free subscription to Starbucks coffee be worth today?

Q 3.31 Economically, why does the growth rate of cash flows have to be less than the discount rate?

Q 3.32 Your firm just finished the year, in which it had cash earnings of $400 (thousand dollars). You forecast your firm to have a quick growth phase for 5 years, in which it grows at a rate of 40% per annum. Your firm's growth then slows down to 20% per annum for the next 5 years (i.e., from year 5 to year 6, the growth rate is 20%). Finally, beginning in year 11, you expect the firm to settle into its long-term growth rate of 2% per annum. You also expect your cost of capital to be 15% over the first 5 years, then 10% over the next 5 years, and 8% thereafter. What do you think your firm is worth today? (Note: this problem is easiest to work in a computer spreadsheet.)

Q 3.33 A stock pays an annual dividend of $2. The dividend is expected to increase by 2% per year (roughly the inflation rate) forever. The price of the stock is $40 per share. At what cost of capital is this stock priced?

Q 3.34 A tall Starbucks coffee costs $1.65 a day. If the bank's quoted interest rate is 6% per annum, compounded daily, and if the Starbucks price never changed, what would a lifetime free subscription to Starbucks coffee be worth today, assuming you will live for 50 more years? What should it be worth to you to be able to bequeath or sell it upon your departure?

Q 3.35 What maximum price would you pay for a standard 8% level coupon bond (with semiannual payments and face value of $1,000) that has 10 years to maturity if the prevailing discount rate (your cost of capital) is 10% per annum?

Q 3.36 If you have to pay off a 6.5% loan within the standard 30-years, then what are the per-month payments for the $1,000,000 mortgage? As in question 3.26, consider both a real 6.5% interest rate per year, and a bank quote of 6.5% per year.

Q 3.37 Structure a mortgage bond for $150,000 so that its monthly payments are $1,000. The prevailing interest rate is quoted at 6% per year.

Q 3.38 (Advanced:) You are valuing a firm with a "pro-forma" (that is, with your forward projection of what the cash flows will be). The firm had cash flows of $1,000,000 today, and is growing by a rate of 20% per annum this year. That is, in year 1, it will have a cash flow of $1.2 million. In each following year, the difference between the growth rate and the inflation rate of 2% (forever) halves. Thus, from year 1 to year 2, the growth rate is 20%, then 2% + (20% - 2%)/2 = 11%, then 2% + (11% - 2%)/2 = 6.5%, and so on. The suitable discount rate for a firm of this riskiness is 12%. (It applies to the $1.2 million cash flow.) What do you believe the value of this firm to be? (Hint: It is common in pro formas to project forward for a given number of years, say 5-10 years, and then to assume that the firm will be sold for a terminal value, assuming that it has steady growth.)

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