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
Calculate the actual amount of consumption, in nominal dollars, using the stated assumptions.
Total Amount = $1,000,000
Amount left for Kids in today’s equivalent = $100,000
Total Amount for Consumption = $900,000
$900,000 = Value/(.08.03) * (1(1.03/1.08)^20)
Value = $900,000/12.25 = $76,183.63
Yearly consumption (real) = $76,183.63
How much do you need for your kids?
=$100,000*(1+0.03) ^20
=$180,611.12
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?
Year 1 = 1.03^1 = $1.03
Year 2 = 1.03^2 = $1.06
Year 10 = 1.03^10 = $1.34
Year 20 = 1.03^20 = $1.81
iii. How much, in nominal dollars, will $1 of retirement funds earn in year 1? Year 2? Year 10? Year 20?
Year 1 = 1.08^1 = $1.08
Year 2 = 1.08^2 = $1.17
Year 10 = 1.08^10 = $2.16
Year 20 = 1.08^20 = $4.66
In attached excel file.
In attached excel file.
In attached excel file.
At the end of 20 years, the amount of consumption at $76,183.63 will equal $100,000 of purchasing power 20 years from now, or $180,611.
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.
In attached excel file. ($76,183.63)
In attached excel file.
Savings = $1,000,000
Consumption = $76,183.63
Closing balance at the end of 20 years = $100,000
iii. How much, in real dollars, does that leave for your kids?
In attached excel file.
$100,000
(30 marks)
$100,000 (equivalent to $180,611 with inflation rate)
5.2 A. Linus is 18 years old now, and is thinking about taking a 5year 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?
Number of years after university = 100 – 23
= 77 years
FV of investment (FV) = (25,000, 5 years, 5%)
= $138,140.78
PV of first 10 years (PV) = (50,000, 10 years, 5%)
= $386,086.75
PV of second 10 years (PV) = (PV(5%, 20, 1) – PV(5%, 10, 1)) * $75,000
= $355,535.6560
PV of third 10 years (PV) = (PV(5%, 30, 1) – PV(5%, 20, 1)) * $100,000
= $291,024.07
Total PV of salary = $1,032,646.47
After University Investment = $1,032,646.47  $138,140.78
= $894,505.69
Annual Consumption = $894,505.69/PV(5%, 77 years, 1)
= $45,794.93
PV of salary = ($40,000/(0.050.03)) * (1(1+0.03)/(1+0.05))^35
= $979,748.15
Annual Consumption = $979,748.15/PV(5%, 82 years, 1)
= $49,900.64
From a strictly financial point of view, Linus is better off choosing option B, as his annual consumption is higher.
(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:
FV = (400.43, 1%, 47 years)
FV = $639.19
FV = $5*(1+0.01)
FV = $5.05
FV = ($5, 1%, 47 years)
FV = $298.13
FV = ($5, 5%, 47 years)
FV = $890.60
(10 marks)
Bank = $890.60/$298.13
= 2.99 times better rate of return choosing to invest rather than buying the lottery.
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 3year 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%.
PV = $20,880.96
PV = $13,373.95.
= $50,000 – ($20,880.96)
= $29,119.04
Monthly Rate = 0.08/12 = 0.0067
= (1+0.0067)^36
= 1.270237*$29,119.04
Amount of salvage value = $36,988.09
(10 marks)
Lease –
Annual Payment = $650 * 12
= $7,800
Tax @ 40% = $7,800 * 0.40
= $3,120
Purchase –
Annual Payment = $10,000
Tax @ 40% = $10,000 * 0.40
= $4,000
I would prefer to buy the car given the taxdeductible amount is higher than leasing the car.
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.
=200,000/(10,0003,000)
= 28.5714
Break even units = 29 units.
In attached excel file (55 units).
In attached excel file (IRR = 20.6897%).
In attached excel file (Selling Price = $10,608.48).
Year 
0 
1 
2 
3 
4 
5 
Investment 
500,000.0000 

Revenue Impact 
0.0000 
600,000.0000 
630,000.0000 
661,500.0000 
694,575.0000 
729,303.7500 
Variable Cost Impact 
0.0000 
180,000.0000 
189,000.0000 
198,450.0000 
208,372.5000 
218,791.1250 
Fixed Cost Impact 
0.0000 
200,000.0000 
200,000.0000 
200,000.0000 
200,000.0000 
200,000.0000 
Income Impact Before tax 
0.0000 
220,000.0000 
241,000.0000 
263,050.0000 
286,202.5000 
310,512.6250 
Tax 
0.0000 
88,000.0000 
96,400.0000 
105,220.0000 
114,481.0000 
124,205.0500 
Depreciation (SL) 
100,000.0000 
100,000.0000 
100,000.0000 
100,000.0000 
100,000.0000 

Tax Shield on Dep'n 
40,000.0000 
40,000.0000 
40,000.0000 
40,000.0000 
40,000.0000 

Net Working Capital 

Salvage 
0.0000 
0.0000 
0.0000 
0.0000 

Sum (Undiscounted) 
500,000.0000 
172,000.0000 
184,600.0000 
197,830.0000 
211,721.5000 
226,307.5750 
Discounted 
500,000.0000 
149,565.2174 
139,584.1210 
130,076.4363 
121,052.4548 
112,514.8613 
Total Present Value 
152,793.0907 
(20 marks)
The inclusion of working capital means that net present value would decrease.
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.
Year 
Nominal cash flow 
Real cash flow 
0 
–100,000 
–100,000 
1 
+ 12,000 
11,765 
2 
+22,000 
21,569 
3 
+15,000 
14,706 
4 
+10,000 
9,804 
Net present value 
47,502 
46,079 
(10 marks)
Year 1 Real Cash Flow =
12,000/(1+0.02)
= $11,764.7059
Year 2 Real Cash Flow =
22,000/(1+0.02)
= $21,568.6274
Year 3 Real Cash Flow =
15,000/(1+0.02)
= $14,705.8824
Year 4 Real Cash Flow =
10,000/(1+0.02)
= $9,803.9216
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.
Using xe.com, yes the GBP is shown.
The exchange rate between the Canadian dollar and US dollar is 1 CAN dollar is equal to 0.79935 US (or 1.25119 US to Canadian).
One ounce of gold is worth $1,563.38 CAN dollars. One ounce of gold is worth $1,249.97 in US dollars. This conversion implies that the exchange rate between Canadian dollars and US dollars is almost exactly equal to the answer found in part B, as $1,249.97 US dollars is equal to $1,563.95 in Canadian dollars.
Seeing that the price of gold is one dollar less than the price soon, I could use this information to purchase the gold at a lower price, and then selling at the price shown to earn a profit.
(10 marks)
7.2 A. Fill in the following table using xe.com or a similar foreigncurrency 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 0.85861 1.25102 111.888
European €1 1.16468 1 1.45709 130.309
Canadian $1 0.79935 0.68634 1 89.4273
Japanese ¥1 0.00894 0.00767 0.01118 1
The Japanese Yen is so inflated compared to the other currencies in the table because of Japan’s economic success has led to a steady appreciation of the Yen.
(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.
iii. A 1year Tbill? 1.22
iiv. A 30year Tbond? 2.89
iiiv. On what date did you look up these yields? July 28, 2017
https://www.treasury.gov/resourcecenter/datachartcenter/interestrates/Pages/TextView.aspx?data=yield
B. Is this yield curve flat, rising, or inverted?
This yield curve is rising.
For introductory finance students to “assume the yield curve is flat” reduces the confusion that may come if interest rates were to change sporadically in the years leading up to the maturity date. With a flat yield curve, interest rates remain constant throughout the years leading to the maturity date, and reduces the need to calculate multiple YTM rates in multiple years, had the curve suddenly began to rise or become inverted.
(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)
Bond # 
1 
2 
3 
4 
1year 
2year 
2year 6% coupon bond 
2year 7% coupon bond 

Time 0 cash flow (i.e., Purchase Price for the bond) 
–950 
1,000/ (1+5.5%)^2 = 898.45 
(+60/(1+5.5%) +1,060/(1+5.5%)^2) =1,009.36 
(+70/(1+5.5%) +1,070/(1+5.5%)^2) =1,027.84 
Time 1 cash flow 
+1000 
0 
+60 
+70 
Time 2 cash flow 
0 
+1000 
+1060 
+1070 
Yield 
(1000950)/950 =0.0526 5.26% 
5.50% 
5.50% 
5.50% 
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.
1000*60= 60,000
1000*1060 = 1,060,000
60,000 + 1,060,000 = 1,120,000
1120*1000 = 1,120,000
For replicating bond 4, there is a requirement for $70 for first year investment and $1,070 for the second year. In other words, 70 units of bond 1 will provide $70 and buy 1,070 units of bond 2 will result in $1,070 in year 2. Bond 4 can be replicated.
1000 * $1,009.36 = $1,009,360
60 * $950 = $57,000
iii. From part A. above, infer the value of 1060 units of Bond #2.
1,060 * $898.45 = $952,357
$898.45, yield is 5.50%
$1,027.84, yield is 5.50%
As per the Law of One Price, bonds that are identical will have the same price. Bonds that have the same year to maturity with different coupon rates will have the same yield to maturity rate. Arbitrage opportunity will arise if the YTM is different that takes short position with lower YTM and take a long position with higher YTM. Part A calculation of YTM and bond price indicates that there are differences in the price but the payment during maturity remains the same and thus, YTM are equal.
(10 marks)
8.4 Assume the yield curve on "plain vanilla" defaultfree bonds is flat at 5%, and you are thinking of buying a defaultfree bond. Specifically, you're thinking of buying a bond issued by Risklessco, a company considered to be defaultfree by all major bond rating firms.
You will select one of the following three bonds, all identical except for the special features listed:
Face Value 
Maturity 
Coupon Rate (Paid Annually) 
Yield to Maturity 
Special Features 
Price 

A 
1000 
20 years 
5.5% 
5% 
None 
? 
B 
1000 
20 years 
5.5% 
5% 
Callable 
Par 
C 
1000 
20 years 
5.5% 
3.5% 
Callable and Convertible into Risklessco Stock 
? 
Both bond A and B has a YTM of 5% indicating the growth in market demand. The investor will not make an investment in bond lower than 5% YTM. Bond C has lower YTM due to the incremental features that are callable and convertible feature motivated investor to purchase them resulting in pulling down the YTM of the bond.
N = 20, I/Y (YTM) = 5%, PV =?, PMT = $55, FV = $1,000
PV = $1,062.31 (negative, as the priced amount to pay).
Price of bond C =
N = 20, I/Y (YTM) = 3.5%, PV =?, PMT = $55, FV = $1,000
PV = 1,284.25
Price of bond A = $1,062.31.
$1,284.25  $1,062.31
= $221.94 is the additional price paid for the callable and convertible features for bond C. The conversion privilege benefits the bondholder, as the bond is more attractive. This raises its price and lowers the yield to maturity. This is consistent with the price calculated for bond C because the price of bond C is $221.94 more than that of bond A. Bond C also has a lower yield to maturity of 3.5% compared to 5% of bond A and B.
The callability provision benefits the issuer, as the bond is more attractive from an issuer standpoint. The callability benefit lowers the price of the bond, while it has a higher yield to maturity. This is consistent with the price calculated for bond A, because the price of bond A is $221.94 less than that of bond C, while bond A has a higher yield of maturity of 5% compared to 3.5% for bond C.
(10 marks)
Once you complete these questions, check to see that Assignment 2 is complete, and submit it for grading.
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