Assignment 2

Assignment 2 is due after you complete Lessons 5 to 8. It is worth 20% of your final grade.

Prepare your responses to these assignment problems in a word processing file; put financial data in a spreadsheet file. As you complete the assignment problems for each lesson, add your responses to these files.

Do not submit your answers for grading until you have completed all parts of Assignment 2.

Note: In assignments, show all calculations to 4 decimal places.

Spreadsheets are provided on the Assignment 2 page of the course website to help you complete Assignment 2.

Lesson 5: Assignment Problems

5.1   Assume you have $1 million now, and you have just retired from your job. You expect to live for 20 years, and you want to have the same level of consumption (i.e., purchasing power) for each of these 20 years, after adjusting for inflation. You also wish to leave the purchasing power equivalent of $100,000 today to your kids at the end of the 20 years as a bequest (or to pay them to take care of you).
You expect inflation to be 3% per year for the next 20 years, and nominal interest rates are expected to stay around 8% per year.

       A.   Calculate the actual amount of consumption, in nominal dollars, using the stated assumptions.

             i.     How much do you need for your kids?

             ii.    If you plan to consume $1.03 in year 1, how much will you need to have to keep the same real consumption in year 2? In year 10? In year 20?

             iii.    How much, in nominal dollars, will $1 of retirement funds earn in year 1? Year 2? Year 10? Year 20?

             iv.   In an Excel spreadsheet (or in a manual table), calculate the following:

                   a.   annual investment earnings for each year

                   b.   total savings after investment earnings for each year

                   c.   subtract annual consumption from total savings each year

                   d.   by trial and error, or with the Goal Seek command, determine the amount of consumption that will give you exactly $100,000, in today's purchasing power, at the end of 20 years

Hint: You will need to make your annual consumption column dependent on the inflation rate, your investment earnings will grow at the nominal rate, and the bequest of $100,000 will grow at the inflation rate.

       B.   Do the calculation again using real rates, and setting inflation to equal 0. If you set up your Excel spreadsheet carefully, you should be able to set the inflation rate to equal 0 and enter the real rate of return as the investment earning rate.

Feel free to use a spreadsheet called "5.1template" (link is provided on the Assignment 2 page) to help you answer this question.

             i.     What is the amount of real consumption in year 1? In year 2? In year 10? In year 20?

             ii.    Show that this is consistent with your calculation using normal rates.

             iii.    How much, in real dollars, does that leave for your kids?

             iv.   Show that your bequest is consistent with the nominal rate results above.

                                                                                                                                   (30 marks)

5.2   A.   Linus is 18 years old now, and is thinking about taking a 5-year university degree. The degree will cost him $25,000 each year. After he's finished, he expects to make $50,000 per year for 10 years, $75,000 per year for another 10 years, and $100,000 per year for the final 10 years of his working career. If Linus lives to be 100, and if real interest rates stay at 5% per year throughout his life, what is the equal annual consumption he could enjoy until that date?

       B.   Linus is also considering another option. If he takes a job at the local grocery store, his starting wage will be $40,000 per year, and he will get a 3% raise, in real terms, each year until he retires at the age of 53. If Linus lives to be 100, what is the equal annual consumption he could enjoy until that date?

        C.   From strictly a financial point of view, is Linus better off choosing option A or B?

                                                                                                                                     (10 marks)

5.3   Are you better off playing the lottery or saving the money? Assume you can buy one ticket for $5, draws are made monthly, and a winning ticket correctly matches 6 different numbers of a total of 49 possible numbers.

The probabilities: In order to win, you must pick all the numbers correctly. Your number has a 1 in 49 chance of being correct. Your second number, a 1 in 48 chance, and so on. There are exactly 49 x 48 x 47 x 46 x 45 x 44 = 10,068,347,520 ways to pick 6 numbers from 49 options.

But the order in which you pick them does not matter, so you actually have a few more ways to win. You can pick 6 different numbers in exactly 6 x 5 x 4 x 3 x 2 x 1 = 720 orders of choice. Any one of those orders would still win the lottery.

Putting this all together, your ticket has 720/10,068,347,520 = 1/13,983,816 chance of winning. This equates to a .000000071 percentage chance.

If you played one ticket every month from age 18 to age 65, you would have 47 x 12 = 564 plays. Your odds of not ever winning would be calculated using a binomial distribution to be .9999599568, meaning your chances of winning would be 1 - .9999599568 = .0000400432.

So, if the lottery winnings averaged $10 million over this time period, your expected return would be less than .0000400432 x $10 million = $400.43.

(It's less than $400.43 because your 564 plays are spread out over the next 47 years, so the present value of these future plays would be significantly less than if you were able to play all 564 immediately. The $400.43 assumes you play all 564 plays today, which makes it the highest possible expected value.)

REQUIRED:

       A.   What would your $400.43 be worth if you invested it at 1% real interest for 47 years?

       B.   If, instead, you wrote down your 6 numbers on a piece of paper, and deposited your $5 in a bank at 1% real interest, how much would you have at the end of the first year?

       C.   If you did this every year for 47 years, how much would you have at age 65?

       D.   If you earned 5% real interest on your deposits, how much would you have at age 65?

E.    Which option would make you better off at age 65? How many times better off?

                                                                                                                                    (10 marks)

5.4   Use the Excel spreadsheet named"LeasevsBuyCCA"(link is on the Assignment 2 page) to answer the following question. You may choose to answer the question without using the spreadsheet, but be very careful to show all work, so your marker can follow your calculation and award part marks as necessary.

You want to buy a new car, but you're not sure whether you should lease it or buy it. You can buy it for $50,000, and you expect that it will be worth $20,000 after you use it for 3 years. Alternatively, you could lease it for payments of $650 per month for the 3-year term, with the first payment due immediately. The lease company did not tell you what interest rate they're using to calculate the monthly payments, but you know you could borrow money from your banker at an annual percentage rate (APR) of 8%.

       A.   Calculate the present value of the lease payments, assuming monthly compounding at the given APR of 8%.

       B.   Calculate the present value of the $20,000 salvage value, again using monthly compounding and the given APR of 8%. Which option do you prefer, lease or buy?

       C.   Calculate the amount of the salvage value which would make you indifferent between leasing and buying.

D.   If you were able to use this car 100% for business, rendering the lease payments tax-deductible, or alternatively, allowing you to deduct depreciation, and assuming your tax rate is 40%, would you prefer to buy or lease the car? 

                                                                                                                                    (10 marks)

Do not submit these questions for grading until you have completed all parts of Assignment 2, which is due after Lesson 8.

Lesson 6: Assignment Problems

You may find it helpful to use the Excel file named"Chapter 6 template"(link is on the Assignment 2 page) to answer the following questions. You may choose to answer the questions without using the spreadsheet, but be very careful to show all work, so your marker can follow your calculation and award part marks as necessary.

In order to ensure that you know how the spreadsheet works, it is recommended that you replicate table 6.5 from page 182 of your textbook before proceeding to answer the following questions. (Note that a completed spreadsheet for Table 6.5 is included with the Excel file as a separate worksheet, so you can check your work.)

6.1   You and your friends are thinking about starting a motorcycle company named Apple Valley Choppers. Your initial investment would be $500,000 for depreciable equipment, which should last 5 years, and your tax rate would be 40%. You could sell a chopper for $10,000, assuming your average variable cost per chopper is $3000, and assuming fixed costs, such as rent, utilities and salaries, would be $200,000 per year.

       A.   Accounting breakeven: How many choppers would you have to sell to break even, ignoring the costs of financing?

       B.   Financial breakeven: How many choppers would you have to sell to break even, if you required a 15% return? (Hint: Use the 15% as the discount rate and calculate net present value. In Excel, you may want to use the Goal Seek command, or simply use trial and error to find the correct amount.)

       C.   Assuming you could sell 60 choppers per year, what would be your IRR?

       D.   Assuming you could sell 60 choppers per year, what would your selling price have to be to generate a net present value of $150,000 at a 15% discount rate?

       E.    If you could sell 60 choppers in the first year, and your sales volume increased by 5% each year until the end of year 5, what would the net present value be at a 15% discount rate?

       F.     If you need to invest working capital equal to 10% of the next (coming) year's sales revenue, what would be the effect on the net present value of the project? Do you think that working capital investments always reduce the net present value of projects?

(Assume a 15% discount rate, and sales volume increases by 5% each year.)

                 (20 marks)

6.2    Fill in the missing items in the following table. Assume that the real interest rate is 3% per year, and inflation is expected to be constant at 2% per year.

                                                                                                                                    (10 marks)

Do not submit these questions for grading until you have completed all parts of Assignment 2, which is due after Lesson 8.

Lesson 7: Assignment Problems

7.1   Find a Web site that shows exchange rates for all major international currencies. At the time of writing, xe.com and oanda.com are examples of such sites.

       A.    Is the British Pound shown? If not, why not? (You might have to do some investigation online if you're not familiar with the history of European currency.)

       B.   What is the exchange rate between the Canadian dollar and the US dollar?

       C.   xe.com also allows you to see exchange rates for gold ounces (under "more currencies available"). What does xe.com(or a similar site) say 1 ounce of gold is worth in Canadian dollars? In US dollars? What does this imply is the exchange rate between Canadian dollars in US dollars? Is this the same as your answer to part B?

        D.   If you saw that the US dollar price of gold was one dollar less than the price shown, how could you use that information to make an arbitrage profit?

                                                                                                                                    (10 marks)

7.2    A.   Fill in the following table using xe.com or a similar foreign-currency quote Web site. In each cell, record the number of units of the currency stated in the first cell of the row that would be required to buy one unit of currency as stated in the column heading.

For example, if you sold US$1, how many European Euros could you buy? Enter that amount in the third column, second row. Continue until the table is filled completely.

sell/buy                       US $1           European €1   Canadian $1        Japanese ¥1

US $1                                1                                           

European €1                                          1                       

Canadian $1                                                              1     

Japanese ¥1                                                                                        1

       B. Why are the numbers in the Japanese ¥ column so much higher than the numbers in the other rows?

              (10 marks)

Do not submit these questions for grading until you have completed all parts of Assignment 2, which is due after Lesson 8.

Lesson 8: Assignment Problems

8.1   A.   Look up the US Treasury yield curve online.

             i.     What is the promised yield for a 1-month T-bill?

             ii.    For a 6-month T-bill?

             iii.     A 1-year T-bill?

             iv.     A 5-year T-bond?

             v.     A 10-year T-bond?

             iv.     A 20-year T-bond?

             iiv.    A 30-year T-bond?

             iiiv.    On what date did you look up these yields?

             ix.     On what Web site did you find these yields?

       B.   Is this yield curve flat, rising, or inverted?

       C.    Many introductory finance textbooks say, at the beginning of bond valuation problems, "Assume the yield curve is flat." Another way of putting this is "Assume the term structure of interest rates is flat." How would this assumption make the questions easier for students of introductory finance to solve?

                                                                                                                                     (10 marks)

8.2     Fill in the missing items in the following table, using the Law of One Price. Assume all these bonds have the same risk, the yield curve is flat, and any coupon payments are paid annually.                                                                         (10 marks)

8.3   A.   You are considering two investments from the bonds listed in question 8.2. Show that the cash flows from the following two investments would be identical.

             i.      60 units of Bond #1 + 1060 units of Bond #2, and

             ii.      1000 units of Bond #3.

       B.   How many units of Bond #1 and #2 would you need to replicate the cash flows of 1000 units of Bond #4?

       C.   i.      If the yield of Bond #3 is 5.5%, what would it cost to buy 1000 units of Bond #3?

             ii.      What would it cost to buy 60 units of Bond #1?

             iii.     From part A. above, infer the value of 1060 units of Bond #2.

             iv.     What is the value of one unit of Bond #2? Yield of Bond #2?

       D.   What's the value of 1000 units of Bond #4? Yield?

        E.   What have you learned about the Law of One Price from questions 8.2 and 8.3?

                                                                                                                                     (10 marks)

8.4    Assume the yield curve on "plain vanilla" default-free bonds is flat at 5%, and you are thinking of buying a default-free bond. Specifically, you're thinking of buying a bond issued by Risklessco, a company considered to be default-free by all major bond rating firms.

You will select one of the following three bonds, all identical except for the special features listed:   

     
A.   Why is the yield on bonds A and B 5%? Why is the yield on bond C different?

       B.   What would be the price of Bond A?

       C.   If bond C is considered identical to bond B except for the conversion privilege, what is the value of the conversion privilege? Does the conversion privilege benefit the issuer of the bond or the purchaser? Is this consistent with the price you calculated for bond C?

       D.    Who does the callability provision benefit, the issuer or the purchaser? Is this consistent with the price you calculated for bond A?

                                                                                                                                     (10 marks)

Once you complete these questions, check to see that Assignment 2 is complete, and submit it for grading.