# End of Chapter Problems

Vertex42 The Excel Nexus

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Q 2.43 What is a perfect market? What were the assumptions made in this chapter that were not part of the perfect market scenario?

Q 2.44 What is the difference between a bond and a loan?

Q 2.45 In the text, I assumed you received the dividend at the end of the period. In the real world, if you received the dividend at the beginning of the period instead of the end of the period, could this change your effective rate of return? Why?

Q2.46 Your stock costs \$100 today, pays \$5 in dividends, and then sells for \$98. What is your rate of return? Q 2.47 The interest rate has just increased from 6% to 8%. How many basis points is this?

Q 2.48 Assume an interest rate of 10% per year. How much would you lose over 5 years if you had to give up interest on the interest—that is, if you received 50% instead of compounded interest?

Q 2.49 Over 20 years, would you prefer 10% per annum, with interest compounding, or 15% per annum but without interest compounding? (That is, you receive the interest, but it is put into an account that earns no interest.)

Q2.50 A project returned +30%, then -30%. Thus, its arithmetic average rate of return was 0%. If you invested \$25,000, how much did you end up with? Is your rate of return positive or negative? How would your overall rate of return have been different if you first earned -30% and then +30%?

Q2.51 A project returned +50%, then -40%. Thus, its arithmetic average rate of return was +5%. Is your rate of return positive or negative?

Q 2.52 An investment for \$50,000 earns a rate of return of 1% in each month of a full year. How much money will you have at year's end?

Q 2.53 There is always disagreement about what stocks are good purchases. The typical degree of disagreement is whether a particular stock is likely to offer, say, a 10% (pessimist) or a 20% (optimist) annualized rate of return. For a \$30 stock today, what does the difference in belief between these two opinions mean for the expected stock price from today to tomorrow? (Assume that there are 365 days in the year. Reflect on your answer for a moment, and recognize that a \$30 stock typically moves about ±\$ 1 on a typical day. This unexplainable up-and-down volatility is often called noise.)

Q 2.54 If the interest rate is 5% per annum, how long will it take to double your money? How long will it take to triple it?

Q 2.55 If the interest rate is 8% per annum, how long will it take to double your money?

Q 2.56 From Fibonacci's Liber Abaci, written in the year 1202: "A certain man gave 1 denaro at interest so that in 5 years he must receive double the denari, and in another 5, he must have double 2 of the denari and thus forever. How many denari from this 1 denaro must he have in 100 years?"

Q 2.57 A bank quotes you a loan interest rate of 14% on your credit card. If you charge \$15,000 at the beginning of the year, how much will you have to repay at the end of the year?

Q 2.58 Go to the website of a bank of your choice. What kind of quote does your bank post for a CD, and what kind of quote does your bank mortgage post for a mortgage? Why?

Q 2.59 What is the one-year discount factor if the interest rate is 33.33%?

Q 2.60 You can choose between the following rent payments:

(a) A lump sum cash payment of \$100,000;

(b) 10 annual payments of \$12,000 each, the first occurring immediately;

(c) 120 monthly payments of \$1,200 each, the first occurring immediately. (Friendly suggestion: This is a lot easier to calculate on a computer spreadsheet.)

Which rental payment scheme would you choose if the interest rate was 5% per year?

(d) Spreadsheet question: At what interest rate would you be indifferent between the first and the second choice above? (Hint: Graph the NPV of the second project as a function of the interest rate.)

Q 2.61 A project has cash flows of \$15,000, \$10,000, and \$5,000 in 1, 2, and 3 years, respectively. If the prevailing interest rate is 15%, would you buy the project if it cost \$25,000?

Q2.62 Consider the same project costing \$25,000 with cash flows of \$15,000, \$10,000, and \$5,000. At what prevailing interest rate would this project be profitable? Try different interest rates, and plot the NPV on the v-axis, the interest rate on the x-axis.

Q2.63 OnApril 12, 2006, Microsoft stock traded for \$27.11 and claimed to pay an annual dividend of \$0.36. Assume that the first dividend will be paid in 1 year, and that it then grows by 5% each year for the next 5 years. Further, assume that the prevailing interest rate is 6% per year. At what price would you have to sell Microsoft stock in 5 years in order to break even?

Q 2.64 Assume you are 25 years old. The LAW insurance company is offering you the following retirement contract (called an annuity): Contribute \$2,000 per year for the next 40 years. When you reach 65 years of age, you will receive \$30,000 per year for as long as you live. Assume that you believe that the chance that you will die is 10% per year after you will have reached 65 years of age. In other words, you will receive the first payment with probability 90%, the second payment with probability 81%, and so on. Assume the prevailing interest rate is 5% per year, all payments occur at year end, and it is January 1 now. Is this annuity a good deal? (Use a spreadsheet.)

Q 2.65 A project has the following cash flows in periods 1 through 4: -\$200, +\$200, -\$200, +\$200. If the prevailing interest rate is 3%, would you accept this project if you were offered an up front payment of \$10 to do so?

Q2.66 Assume you are a real estate broker with an exclusive contract—the condo association rules state that everyone selling their condominiums must go through you or a broker designated by you. A typical condo costs \$500,000 today and sells again every 5 years. This will last for 50 years, and then all bets are off. Your commission will be 3%. Condos appreciate in value at a rate of 2% per year. The interest rate is 10% per annum. What is the value of this exclusivity rule? In other words, at what price should you be willing to sell the privilege of exclusive condo representation to another broker?

Q 2.67 Continued: If free Internet advertising was equally effective and if it could replace all real estate brokers so that buyers' and sellers' agents would no longer earn the traditional 6% (3% each), what would happen to the value gain of the condo?

Q2.68 There is a fable that once upon a time, the Shah of Persia granted a single wish to a craftsman who had designed an ornate chessboard for him. The artist's wish was that he would receive 1 grain of rice on the first square of the chessboard, 2 on the second, 4 on the third, and so on. The craftsman knew that there would be 263 grains on the 64th square, and 264 - 1 grains on all the squares together. The total estimated amount is about 18 trillion grains, which is about 100 billion tons of grains. This is because the number of grains grows exponentially. (Of course, a real shah would have simply solved his problem by reducing the artisan's weight by about one head.) But what would have happened if the shah had simply paid the craftsman wish very slowly over the next 63 years, with only one square paid off every year, and if the prevailing discount rate had been 50% in grains per annum? That is, in today's grain, the second square would have been worth 2/1.5 = 1.33, the third square 4/1.52 = 1.78 and so on. What would the present value of the grain on the final square have been? (Use a spreadsheet.)

Q2.69 If the interest rate is 5%, what would be the equivalent annual cost (see Question 2.38) of a \$2,000 lease payment upfront, followed by \$800 for three more years?

Q 2.70 The prevailing discount rate is 15%/annum. Firm F's cash flows start with \$500 and grow at 20% per annum for 3 years. Firm S's cash flows also start with \$500 but shrink at 20% per annum for 3 years. What are the prices of these two firms? Which one is the better "buy"?