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.xls” 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 using straight-line depreciation (depreciated to expected salvage value) and assuming your tax rate is 40%, would you prefer to buy or lease the car?

**(10 marks)**

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