University of Toronto
Faculty of Engineering
and
Rotman School of Management
JRE 300H1S – Foundations of Accounting and Finance
Final Examinations, April 17, 2015- SOLUTIONS
Duration: 2.5 hours
Aids allowed: non-programmable calculator
and
2-sided, 8.5" x 11" crib sheet.
Please answer all questions on this exam paper
Please circle your instructor: Scott Douglas
Maureen Stapleton
Fotini Tolias
The exam consists of 12 pages. Answers are to be written on the exam paper.
Last Name: _______________________________________________________
First Name: _______________________________________________________
Student #: ________________________________________________________
Question
1.
2.
3.
4.
5.
Total :
Project Evaluation
Special Case - Leasing
Cost of Capital/Capital Structure
Hedging/Equity Options
Bonds/Time Value of Money
Grade
/20
/20
/20
/20
/20
/100
Page 1 of 11
1. PROJECT VALUATION (20 MARKS)
You are an expert at working with PCs and are considering setting up a software development
business. To set up the enterprise, you anticipate that you will need to acquire computer hardware
costing $ 100,000 (the lifetime of this hardware is 5 years for depreciation purposes, and straight
line depreciation will be used). In addition, you will have to rent an office for $50,000 a year. You
estimate that you will need to hire five software specialists at $ 50,000 each, a year, to work on the
software and that your marketing and selling costs will be $ 100,000 a year for the five year period.
You expect to price the software you produce at $100 per unit and to sell 6000 units in the first year.
The number of units sold is expected to increase 10% a year for the remaining 4 years, and the
revenues and the material costs (only) are expected to increase at 3% a year, reflecting inflation. The
actual cost of materials used to produce each unit is $ 20. You will need to maintain extra working
capital at 10% of incremental revenues (assume that the working capital investment is made at the
beginning of each year). Your tax rate will be 40%, and the after tax cost of capital is 12%.
a. Estimate the after tax free cash flows (ATFCs) each year on this project.
b. Yes accept the project as it has positive NPV
Initial Cost
$ 100,000
Year 1
Year 2
Revenues
2.5 marks
$ 770,213
$ 50,000
$ 250,000
$ 100,000
$ 20,000
$ 154,043
$ 872,652
$ 50,000
$ 250,000
$ 100,000
$ 20,000
$ 174,530
$ 988,714
$ 50,000
$ 250,000
$ 100,000
$ 20,000
$ 197,743
Taxable Income $ 60,000
Taxes (at 40%) $ 24,000
$ 123,840
$ 49,536
$ 196,171
$ 78,468
$ 278,121
$ 111,249
$ 370,972
$ 148,389
$ 36,000 $ 74,304 $ 117,702 $ 166,873
$ 20,000 $ 20,000 $ 20,000 $ 20,000
-$ 7,980 -$ 9,041 -$ 10,244 -$ 11,606
$ 48,020 $ 85,263 $ 127,459 $ 175,267
$ 222,583
$ 20,000
Present Value of ATCF at 12% $ 42,875
NPV $ 350,602
add sum of ATCF and subtract
initial cost of 100,000


Year 5
$ 679,800
$ 50,000
$ 250,000
$ 100,000
$ 20,000
$ 135,960
Net Income:
add back depreciation:
change in working capital
After Tax Free Cash Flows:
0.5 marks
0.5 marks
Year 4
600,000
50,000
250,000
100,000
20,000
120,000
Office Rent
Salaries
marketing & sales
depreciation exp.
material costs
$
$
$
$
$
$
Year 3
$ 67,971
$ 90,723
$ 111,385
$ 242,583
$ 137,648
2.5 marks
3.5 marks total allocated for every year
do not deduct any marks if students used the 1/2 yr rule in year 1 for depreciation (so
$10,000 vs. (20,000)
Page 2 of 11
2. SPECIAL CASE - LEASING (20 MARKS)
a) Your boss provides you with the following specifications for a new machine that she heard about at
a trade show which would reduce operating costs in your department each year. The machine will
cost $500,000 but is estimated to result in a $150,000 pre-tax annual saving for the next 5 years. It
falls into Class 8 for CCA purposes (CCA rate is 20%/year), will have a salvage value of $100,000, and
the asset pool will remain open after the project is complete. An initial investment in inventory and
accounts receivable of $45,000 will be required (recovered at the end of the project’s life), as well
as $4000 in pre-tax annual maintenance costs. Your firm’s tax rate is 30% and its after-tax cost of
debt (the appropriate discount rate in this case) is 12%. She has asked for your evaluation of the
opportunity: should the machine be acquired? Assume all the cash flows are realized at the end of
the year. (10 marks)
Event
Purchase
Work Cap In
PVCCATS***
Salvage Value
Work Cap. Out
Annual Savings
Maintenance
Time Period
T=0
T=0
T=0
T=5
T=5
T=1-5
T=1-5
Cash Flow
PV @12%
-500,000
-500,000 1 mark
-45,000
-45,000 1 mark
78,087
78,087 2 marks
100,000
56,743 1 mark
45,000
25,534 1 mark
150,000*(.70)
378,501 1 mark
4000*(0.7)
-10,093 1 mark
NPV to Acquire:
-16,228 2 marks
since the NPV is negative, we should not acquire the machine
PVCCATS:
***
equals
(-500)*(0.20)*(.30) x (1.06/1.12) - (100)*(0.20)*(0.30)/(0.32) x 1/(1.12)^5
(.20+.12)
=
$78,088
Page 3 of 11
b) Alternately, the machine can be rented as an operating lease for the next five years for yearly
payments of $115,000, paid at the beginning of each year. Although the machine’s maintenance
will be taken care of by the lessor, tax benefits from making the lease payments will not be
realized until the end of each year. Does the option to lease change your decision in part a?
Should you lease or buy the machine? (10 marks)
Students need to compare PV After Tax Lease Payments and consider the incremental cash flows
between the 2 alternatives
Event
Purchase
PV Lease Payments
Tax Savings from Lease
Salvage Value
PVCCATS
Maintenance
Time Period
T=0
T=0-4
T=1-5
T=5
T=0
T=1-5
NPV to Lease:
Cash Flow
PV @12%
500,000
500,000 2 marks for PV lease payments
-115,000
-464,295 ** PV of 115K @12%
115,000*.3
124,365 115 at T=0 2 marks
100,000
-56,743 1 mark
78,087
-78,087 2 marks
4000*(0.7)
10,093 1 mark
35,333 2 marks
Value of acquiring the machine vs leasing the machine = 35,333-16,288=$19,105
Page 4 of 11
3.
COST OF CAPITAL/CAPITAL STRUCTURE (20 marks)
Magna Carta Corp. can issue new 15-year bonds at par that pay a 6.8% annual coupon with a 2.6%
floatation cost, and new preferred shares that pay a $6 annual dividend for a 6.5% floatation cost
(market price for the firm's preferred shares is currently 16 times the dividend). The firm's 1,000,000
common shares currently pay an annual dividend of $2.65 which has grown at a rate of 4% each year.
After a significant rally last year which brought the firm's common share price up to $58, the broad
market is only expected to return 6% this year while government T-Bills are paying a rate of just 1%. The
firm's tax rate is 28%.
a) Assuming a market beta of 1.4 for Magna Carta and a target capital structure of 35% debt, 10%
preferred shares and 55% common shares, estimate the firm's weighted average cost of capital,
assuming the firm would have to raise all new capital. Show both methods to calculate the cost
of equity and take the average of the two returns (10 marks)
Cost of Equity:
Cost of Common Equity :
Div1
P0 
 solvingforKe
Ke  g
Ke 
Cost of New Preferred Shares :
Pp 
Div1
2.65 * (1.04)
g
 .04  8.75%
P0
58
Div
 solvingforKp
Kp
6
 6.25% and
(6 *16)
alternate calc for Ke
6.25%
Ke  rf   * (rm  rf )  .01  1.4 * (.06  .01)  8%
K Pnew 
 6.68%
1  .065
(8.75  8.00)
averageKe 
 8.375%
2
Kp 
2 marks for each : therefore:
Cost of New Debt :
6.8%
Kd 
 6.98% and
(1  .026)
after tax cost of new debt :
6.98% * (1 - .28)  5%





2 marks for cost of common equity
2 marks for alternate. calc for equity
2 marks for prefs
2 marks for debt
2 marks for WACC
WACC  Wd * K dnew  W p * K pnew  We * K e
 (0.35) * (.05)  (.10 * .0668)  (.55) * (8.375%)
WACC  7.02%
Page 5 of 11
b) Falcon Security is a broad-based security contractor working with a number of government
projects. In response to problems which had resulted from inadequate oversight of the
industry during the past few years, the federal government mandated a maximum net profit
margin of 8% after tax for the shareholders of companies involved in this line of work. If the
firm has an asset turnover ratio of 2.1 and its shareholders require a 28% return on their equity,
use the Dupont formula (below) to calculate the firm's Debt / Equity ratio. Hint: the company
has no liabilities other than bonds. (6 marks)
ROE 
Net Income
Revenues
Total Assets
x
x
Revenues
Total Assets
Equity
ROE  Profit margin xAsset turn over x
Total Assets
Equity
Assets
where
Equity
Total Assets  Total Liabilitie s  Shareholde rs' Equity
Total Assets  Debt  Equity
28%  8% x 2.1x

Debt 

28%  8% x 2.1x 1 
 Equity 
Debt
Ratio  0.67 or 67%
Equity
3 marks for setting up the equation
correctly
2 marks for recalling and using
basic equation
1 marks
c) What is the benefit of adding debt to the capital structure? Why is it important that firms
maintain a reasonable amount of debt in the capital structure (rather than 100% debt )?(4
points)
Some key points:




Benefit of tax savings because coupon payments are tax deductible
Adding debt to an all-equity firm usually lowers the WACC and increases its firm value.
As more debt is added, the cost of financial distress (possibility of bankruptcy) also
increases and starts to outweigh the benefits of tax savings
A firm with nearly 100% debt will usually have an extremely high WACC, which will
lower its firm value
Page 6 of 11
4.
HEDGING/EQUITY OPTIONS (20 marks)
Part A (8 marks)
Use the American option pricing information shown below to answer the questions that follow. The
underlying stock is currently selling for $114.
Expiration Date
Strike/Exercise Price
Call Option Price
Put Option Price
February
$110.00
$7.60
$0.60
March
$110.00
$8.80
$1.55
May
$110.00
$10.25
$2.85
August
$110.00
$13.05
$4.70
a) It is now January and the February calls are trading at a premium of $7.60 (see table above).
What is the intrinsic and time value of the call option? (2 marks)
Call premium = TV + IV, therefore the intrinsic value of the option is $114-$110 = $4 and the time value is
equal to $7.60 - 4 = $3.60.
b) Suppose you buy 10 contracts of the February call option. What is your net profit or loss (i.e.
after deducting the original investment) on the 10 contracts immediately before expiration
when the underlying stock is selling for $140? (3 marks)
Each contract is for 100 shares. As $140 is higher than the exercise price of $110, you will exercise the call
option.
Thus, the net profit upon exercise is: 10 contracts * 100 shares * [($140 - $110) - $7.60] = $22,400.
c) Suppose you buy 10 contracts of the August put option. What is your net profit or loss (i.e. after
deducting the original investment) on the 10 contracts immediately before expiration when the
underlying stock is selling for $104? (3 marks)
Each contract is for 100 shares. As $104 is lower than the exercise price of $110, you will exercise the put
option.
Thus, the net profit upon exercise is: 10 contracts * 100 shares * [($110 - $104) - $4.70] = $1,300.
Page 7 of 11
Part B (12 marks)
Silver Lining Mining Corporation (SLMC) is a Canadian corporation listed on the TSX. The majority of
SLMC’s operations are based in Canada, but the firm also has silver mining operations in Mexico and
Russia. The annual operating costs in Mexico are 29,500,000 pesos (“MP”), and annual operating costs
in Russia are 93,768,000 rubles (“RR”). Output from the Mexican site is expected to be 265,000 ounces
of silver per year, while output from the Russian site is expected to be 290,000 ounces of silver per year.
Spot contracts for silver are currently $16.80 US/ounce. Management at SLMC is risk averse and would
like to hedge against all potential currency and commodity risk. Assume all cash flows occur at the end
of each year and that the following one-year forward rates are being widely offered in the market:
CAD / MP = 0.083
CAD / RR = 0.029
CAD / USD = 0.965
USD / Silver Oz = $18
a) With storage costs of 2.75% of the value (spot price) of the silver, what is the implied annual
financing cost (%) for 1 year (in US/oz)? (4 marks)
•
Buy spot and store gold:
– Spot cost:
– Interest on purchase
– Storage of commodity:
– Cost: buying spot-delivering forward
$16.80
?
2.75% of 16.80 or $.46
$ 18
solving for interest costs: $.74, or
1  k domestic 
F  S
  $16.801  cost of storage  financing cost   $18
 1  k foreign 
(1  Costs)  1.0714  1
Costs  7.14%
Therefore, if storage costs are equal to 2.75% then storage costs equal to 7.14-2.75 =4.39%
(3 marks to lay out equation) (1 mark for getting the right answer!)
b) If PGC hedges all of its currency and gold price risks using the one year forward rates (above), what
are the Canadian dollar cash flow results from the two mining operations? (4 marks)
1) Total revenues: (265,000+290,000) oz of silver x $18USD per oz x 0.965 =$9,640,350 (1 mark)
2) Costs in Mexico: 29,500,000 x 0.083 = $2,448,500 CAD (1 mark)
3) Costs in Russia: 93,768,000 x 0.029 = $2,719,272 CAD (1 mark)
profit: 1-(2+3) = $4,472,578 CAD (1 mark)
Page 8 of 11
c) Assume that, one year in the future, the following spot rates are being offered:
CAD / MP = 0.097
CAD / RR = 0.047
CAD / USD = 0.945
USD / Silver oz = $17.70
How much profit or loss (in CAD) was avoided by being perfectly hedged? (4 marks)
1) Total revenues (no hedge): (265,000 + 290,000) oz of silver x $17.70USD per oz x 0.945 =$9,283,208
(1 mark)
2) Costs in Mexico (no hedge): 29,500,000 x 0.097 = $2,861,500 CAD (1 mark)
3) Costs in Russia (no hedge): 93,768,000 x 0.047 = $4,407,096 CAD (1 mark)
Profit: 1-(2+3) = $2,014,612
Therefore a loss of ($4,472,568-$2,014,612) = $2,457,957 million was avoided (1 mark)
Page 9 of 11
5.
TIME VALUE OF MONEY, BONDS, MORTGAGES (20 MARKS)
On April 1, 2015, Finning International borrowed money by issuing $100 million par value of bonds
with 10 year term to maturity and coupon rate of 3.8%. The selling price of the bond was $98.35 so
the yield to maturity was 4%. Finning’s corporate tax rate is 40%. Assume no flotation costs.
a)
What is the total amount of interest that Finning must pay annually to investors who purchased
these bonds? (2 marks)
$100 million *3.8%=$3.8 million
b)
What is Finning’s after tax cost of debt? (2 marks)
After tax interest rate /proceeds = 3.8(1-0.4)/98.35=2.32%
c)
Toromont having observed the success of the Finning bond issue is now also interested in
issuing a bond with a 5 year term to maturity. The issue date is set for April 17th, 2015. The
underlying government benchmark bond yield is 2.15% and the credit spread for Toromont is
185 basis points.
i.
What is the expected coupon on the new bond issue and what is the bond's yield to
maturity (in the primary market) if the bond is priced to sell at par? (3 marks)
coupon = 2.15%+1.85% = 4%(1 mark)
bond's price = 100 when c = YTM, therefore YTM = 4%(2 marks)
ii.
It is now April 17th, 2016, a year later, and the Toromont bond is trading in the
market at a yield to maturity of 5%. What is the market price of the bond? Assume
semi-annual compounding and each bond has a par value of $1,000. (5 marks)
1 mark each calculation (3 marks) + (2 marks for semi-annual adjustments)
PV of the Coupon Payments : 
1


1

1 

 .05  
1


1 
 
 1  y    4%
2  
 
Cpn
*1000
 $143.403

.05

y


  2




2


Present Value of the Maturity Value :


1
 1 


Pr incipal
  $1,000 1  .025   $820.75


 1  y  
add the principal and coupon payments: 820.75+143.03=$964.15
8
n
n
8
Page 10 of 11
d) You just decided to purchase a condo to take advantage of the low interest rates available
today. To buy the condo, you must borrow $200,000. Your bank offered you a mortgage loan
with a 20 year amortization period at a quoted rate of 3.5% and monthly mortgage payments.
Recall that Canadian mortgages are based on semi-annual (i.e., 2 times per year) compounding.
i.
What is the effective monthly interest rate on this mortgage loan? (2 marks)
m
f
r
per
period
Where
ii.
2
12
 r 
 .035 
 1    1  1 
  0.002896 or 0.2896%
2 

 m
s
Rs
m
f
is the quoted rate (3.5% annually)
is the compounding frequency (2 times per year)
is the payment frequency (12 times per year)
What will be your monthly payment on the mortgage? (2 marks)
𝑃𝑉
𝑃𝑀𝑇 =
[
Where
PV
n
1−(1+𝑘𝑚𝑜𝑛𝑡ℎ𝑙𝑦 )
𝑘𝑚𝑜𝑛𝑡ℎ𝑙𝑦
−𝑛
]
is the present value of the mortgage ($200,000)
is the number of periods (20 years x 12 periods/year = 240)
𝑷𝑴𝑻 =
$𝟐𝟎𝟎, 𝟎𝟎𝟎
𝟏−(𝟏+𝟎.𝟎𝟎𝟐𝟖𝟗𝟔)−𝟐𝟒𝟎
= $𝟏, 𝟏𝟓𝟕. 𝟑𝟎
𝟎.
iii.
Now, assume that 5 years have passed since you purchased your condo and obtained the
mortgage loan. What is the balance of the principal amount outstanding on the loan? (i.e.
how much do you owe after making monthly mortgage payments for 5 years) (4 marks)
The principal outstanding is the PV of loan payments not yet made. After 5 years, 15 of the 20
year amortization period remains so the number of monthly payments to be made is
15*12=180.
1 − (1 + 0.0028960−180
𝑃𝑉 = $1,157.30 [
] = $162,170
0.002896
Page 11 of 11