ENSC 201 Assignment 7 (Required): Model Answers
7.1
You have just started a company, the Soggy Kreme Doughnut Company. You borrow $500,000 from
the bank, to be repaid in three equal annual installments, the first due in a year’s time. The bank
charges an interest rate of 5%. Using the money you’ve borrowed plus $200,000 of the company’s own
money, you buy an Acme Combined Doughnut-Maker-and-Deep-Fat-Fryer for $700,000. According to
Revenue Canada, this depreciates at 25% per year. Your company is taxed at 40%.
Every year for the next three years you purchase $100,000 worth of flour, sugar and fat, and sell
$400,000 worth of doughnuts. At the end of the third year, you sell the Acme Doughnut Maker for
$250,000.
i)
ii)
iii)
iv)
v)
How much of each of your annual payments to the bank is interest?
What is your CCA allowance for the Doughnut-Maker in each of the next three years,
including the terminal loss or gain?
How much do you pay in taxes in each of the next three years?
What are your after-tax cashflows over the three-year period?
What is your after-tax rate of return on your initial investment of $200,000?
i) We first calculate the annual amount owed to the bank.
It’s 500,000(A/P,0.05,3) = 500,000(0.3672) = $183,600
We then build an Excel spreadsheet, “Assignment 7.1”, to calculate the amount of interest
paid every year:
Year
1
2
3
Owed
$500,000
$341,400
$174,870
Interest
$25,000
$17,070
$8,744
RoP
$158,600
$166,530
$174,857
ii) We extend the spreadsheet to calculate the CCA allowances, taking the first-year rule
into account:
Year
1
2
3
UCC
$350,000
$612,500
$459,375
CCA
$87,500
$153,125
$114,844
According to this table, Revenue Canada thought that the machine was worth $459,375$114,844 =$344,531 at the end of the third year, but you only got $250,000 for it, so you’ve
effectively lost an additional $94,531, so the total loss you can claim against taxes at the
end of the third year is $209,375.
iii) Taxes, end of Year One:
You take in $400,000, from which you have to subtract $100,000 in ingredient costs.
This leaves you with $300,000. From this you can subtract $25,000 in interest payments and
$87,500 in CCA, giving a pre-tax cashflow of 300,000-25,000-87,500 = $187,500. So your
taxes are $187,500 × 0.4 = $75,000
Taxes, end of Year Two:
You take in $400,000, from which you have to subtract $100,000 in ingredient costs.
This leaves you with $300,000. From this you can subtract $17,070 in interest payments and
$153,125 in CCA, giving a pre-tax cashflow of 300,000-17,070 -153,125= $129,805. So
your taxes are $129,805× 0.4 = $51,922
Taxes, end of Year Three:
You take in $400,000 (doughnuts), from which you have to subtract $100,000 in ingredient
costs. This leaves you with $300,000. From this you can subtract $8,744 in interest
payments and $209,375 in CCA, giving a pre-tax cashflow of 300,000-8,744 -209,375 =
$81,881. So your taxes are $81,881× 0.4 = $32,752
Comment about the salvage value: you don’t get taxed on the $250,000 salvage, because
this is less than the UCC.
iv) After-tax cashflows: Present
In the present moment, you’ve spent $200,000.
After-tax cashflows: End of Year 1
After taxes you are left with $187,500 × 0.6 = $112,500, plus the CCA allowance of
$87,500, which add up to $200,000. But the $158,600 repayment of principal has to come
out of this, leaving you with $41,400.
After-tax cashflows: End of Year 2
After taxes you are left with $129,805× 0.6 = $77,883, plus the CCA allowance of
$153,125, which add up to $231,008. But the $166,530 repayment of principal has to come
out of this, leaving you with $64,478.
After-tax cashflows: End of Year 3
After taxes you are left with $81,881× 0.6 = $49,129, plus the CCA allowance of $209,375,
plus the $250,000 salvage, which add up to $508,504. But the $174,857 repayment of
principal has to come out of this, leaving you with $333,647.
v)
After-tax rate of return
The equation we have to solve is:
-200,000 + 41,400(P/F,i,1) + 64,478(P/F,i,2) + 333,647(P/F,i,3) = 0
We plot this in the spreadsheet “Assignment 7.1”, and see that the IRR is about 35.4%
7.2
Take the same scenario as in the previous question, but assume there is 10% inflation every year. As a
result, your doughnut ingredients cost $100,000, $110,000 and $121,000 (actual dollars) in the three
years, respectively. You put up your prices so that you sell $400,000, $440,000 and $484,000 worth of
doughnuts (actual dollars) in the three years, respectively. When you sell the Doughnut-Maker at the
end of the third year, you receive $300,000 (actual dollars). Your annual payments to the bank are the
same as they were in Question 7.1, and these payments are in actual dollars. Your payments to Revenue
Canada (which are not necessarily the same as they were in Question 7.1) are also in actual dollars.
What is your real after-tax rate of return on your investment?
To answer this apparently simple question, we have to redo most of Question 7.1, modifying
it to take inflation into account:
The values we calculated for interest payments are still correct:
Year
1
2
3
Owed
$500,000
$341,400
$174,870
Interest
$25,000
$17,070
$8,744
RoP
$158,600
$166,530
$174,857
The CCA allowances we calculated are also still correct:
Year
1
2
3
UCC
$350,000
$612,500
$459,375
CCA
$87,500
$153,125
$114,844
According to this table, Revenue Canada thought that the machine was worth $459,375$114,844 =$344,531 at the end of the third year, but you only got $300,000 for it, so you’ve
effectively lost an additional $44,531, so the total loss you can claim against taxes at the
end of the third year is $159,375.
i) Taxes, end of Year One:
You take in $400,000, from which you have to subtract $100,000 in ingredient costs.
This leaves you with $300,000. From this you can subtract $25,000 in interest payments and
$87,500 in CCA, giving a pre-tax cashflow of 300,000-25,000-87,500 = $187,500. So your
taxes are $187,500 × 0.4 = $75,000
Taxes, end of Year Two:
You take in $440,000, from which you have to subtract $110,000 in ingredient costs.
This leaves you with $330,000. From this you can subtract $17,070 in interest payments and
$153,125 in CCA, giving a pre-tax cashflow of 330,000-17,070 -153,125= $159,805. So
your taxes are $159,805× 0.4 = $63,922
Taxes, end of Year Three:
You take in $484,000, from which you have to subtract $121,000 in ingredient costs. This
leaves you with $363,000. From this you can subtract $8,744 in interest payments and
$159,375 in CCA, giving a pre-tax cashflow of 363,000-8,744 -159,375 = $194,881. So
your taxes are $194,881× 0.4 = $77,952
ii) Actual After-tax cashflows: Present
In the present moment, you’ve spent $200,000.
Actual After-tax cashflows: End of Year 1
After taxes you are left with $187,500 × 0.6 = $112,500, plus the CCA allowance of
$87,500, which add up to $200,000. But the $158,600 repayment of principal has to come
out of this, leaving you with $41,400.
Actual After-tax cashflows: End of Year 2
After taxes you are left with $159,805× 0.6 = $95,883, plus the CCA allowance of
$153,125, which add up to $249,008. But the $166,530 repayment of principal has to come
out of this, leaving you with $82,478.
Actual After-tax cashflows: End of Year 3
After taxes you are left with $194,881× 0.6 = $116,929, plus the terminal loss of $159,375,
plus the salvage income of $300,000, which add up to $576,304. But the $174,857
repayment of principal has to come out of this, leaving you with $401,447.
iii) Real After-tax cashflows: Present
In the present moment, you’ve spent $200,000, and at the present moment, an actual dollar
has the same value as a real dollar.
Real After-tax cashflows: End of Year 1
You have an actual after-tax cashflow of $41,400, which corresponds to a real after-tax
cashflow of 41,400(P/F,0.1,1) =$37,636.
Real After-tax cashflows: End of Year 2
You have an actual after-tax cashflow of $82,478, which corresponds to a real after-tax
cashflow of $82,478(P/F,0.1,2) =$68,163
Real After-tax cashflows: End of Year 3
You have an actual after-tax cashflow of $401,447, which corresponds to a real after-tax
cashflow of $401,447 (P/F,0.1,3) =$301,613
iv) Real After-tax rate of return
The equation we have to solve is:
-200,000 + 37,636 (P/F,i,1) + 68,163 (P/F,i,2) + 301,613 (P/F,i,3) = 0
We plot this in the spreadsheet “Assignment 7.1”, and see that the real after-tax IRR is
about 31.6%.
7.3
Just as you are about to go into the Doughnut-making business, you are offered the opportunity to rent
an Ajax Combined Deep-Fat-Fryer-and-Doughnut-Maker for $190,000 a year, payable at the beginning
of the year. The rental contract fixes this rental fee for the next three years. If you rent the Ajax
machine, you will not need to borrow any money from the bank and you will not need to buy the Acme
machine.
i)
If there is no inflation, what is your after-tax rate of return on your initial investment of
$190,000 over the first three years of doughnut-making, assuming that every year you
purchase $100,000 worth of flour, sugar and fat, and sell $400,000 worth of doughnuts?
ii)
If there is 10% inflation, what is your real after-tax rate of return on your initial investment
of $190,000 over the first three years of doughnut-making, assuming that your doughnut
ingredients cost $100,000, $110,000 and $121,000 (actual dollars) in the three years,
respectively, and that you put up your prices so that you sell $400,000, $440,000 and
$484,000 worth of doughnuts (actual dollars) in the three years, respectively?
This question is thankfully a bit easier than the previous ones.
i)
You have to spend $190,000 right away.
At the end of the first year, you have taken in $400,000 and spent $100,000 in ingredients
and $190,000 on the second instalment of the rental payments. So your pre-tax cashflow is
$110,000; you pay $44,000 in taxes and are left with an after-tax cashflow of $66,000.
At the end of the second year, you have taken in $400,000 and spent $100,000 in ingredients
and $190,000 on the third instalment of the rental payments. So your pre-tax cashflow is
again $110,000, and you again pay $44,000 in taxes and are left with an after-tax cashflow
of $66,000.
At the end of the third year, you have taken in $400,000 and spent $100,000 in ingredients.
So your pre-tax cashflow is $300,000, and you pay $120,000 in taxes and are left with an
after-tax cashflow of $180,000.
So to find your IRR you have to solve the equation
PW = -190,000 + 66,000(P/F,i,1) + 66,000(P/F,i,2) + 180,000(P/F,i,3)
This is solved in the accompanying spreadsheet and gives an IRR of 24.15%
ii)
You have to spend $190,000 right away.
At the end of the first year, you have taken in $400,000 and spent $100,000 in ingredients
and $190,000 on the second instalment of the rental payments. So your pre-tax cashflow is
$110,000; you pay $44,000 in taxes and are left with an after-tax cashflow of $66,000
(actual dollars). This is equivalent to a real after-tax cashflow of 66,000(P/F,0.1,1) =
$60,000.
At the end of the second year, you have taken in $440,000 and spent $110,000 in ingredients
and $190,000 on the third instalment of the rental payments. So your pre-tax cashflow is
$140,000, and you pay $56,000 in taxes and are left with an after-tax cashflow of $84,000
(actual dollars). This is equivalent to a real after-tax cashflow of 84,000(P/F,0.1,2) =
$69,421.
At the end of the third year, you have taken in $484,000 and spent $121,000 in ingredients.
So your pre-tax cashflow is $363,000, and you pay $145,200 in taxes and are left with an
after-tax cashflow of $217,800 (actual dollars). This is equivalent to a real after-tax
cashflow of 217,800(P/F,0.1,3) = $163,636.
So to find your real after-tax IRR you have to solve the equation
PW = -190,000 + 60,000(P/F,i,1) + 69,421(P/F,i,2) + 163,636(P/F,i,3)
This is solved in the accompanying spreadsheet and gives an IRR of 20.8%