Practice Questions Set 1
FIN 3701 AY 2024-2025
This set of questions is for your practice, and you don’t need to submit a report.
1. Technical Corp. is considering investment between two machines. They can either buy
machine A that costs $100,000, with an annual EBIT of $90,000, that lasts for two years,
or machine B that costs $150,000, with an annual EBIT of $90,000, that lasts for six years.
Both of these investments are expansions. The firm receives the EBIT one-year after the
investment has taken place, uses the straight-line depreciation method over the asset's
life. The firm has an asset beta of 1.5, a negligible debt beta, yield to maturity on firm's
debt is 5%., and it is 30% debt-financed. The market risk premium is 6%, the risk-free rate
is 2%, and the tax rate is 25%.
a. What is the firm’s cost of equity capital? (2.5 points)
βequity = βasset * [1 + (debt/equity)*(1-tax rate)] = 1.5*[1+(0.3/0.7)*(1-0.25)] = 1.98
Cost of equity = rf + β(rm - rf) = 2% + 1.98*(6%) = 0.1389 = 13.9%
b. What is the firm’s weighted average cost of capital? (2.5 points)
WACC = (D/V)*rD*(1 – tax rate) + (E/V)*rE = 30%*5%*(1 – 25%) + 70%*13.89% = 10.8%
c. Assume that the firm can make a one-time investment in either machine A or B. Which
investment is better? (5 points)
A useful formula: 1/(1+r) + 1/(1+r)2+1/(1+r)3+…+1/(1+r)N = 1/r*(1-1/(1+r)N)
Machine A:
Year
0
1
2
Investment cost (100,000)
EBIT
90,000
90,000
Taxes (25%)
(22,500)
(22,500)
Depreciation
50,000
50,000
Free Cash Flow
(100,000)
117,500
117,500
NPV of machine A = -100,000 + 117,500/(1+10.8%) + 117,500/(1+10.8%)2
= $101,623
Machine B:
Year
Investment cost
EBIT
Taxes (25%)
Depreciation
Free Cash Flow
0
(150,000)
(150,000)
1
2
3
4
5
6
90,000
(22,500)
25,000
92,500
90,000
(22,500)
25,000
92,500
90,000
(22,500)
25,000
92,500
90,000
(22,500)
25,000
92,500
90,000
(22,500)
25,000
92,500
90,000
(22,500)
25,000
92,500
Practice Questions Set 1
FIN 3701 AY 2024-2025
NPV of machine B = -150,000 + 92,500/(1+10.8%) + 92,500/(1+10.8%)2 +
92,500/(1+10.8%)3 + 92,500/(1+10.8%)4 + 92,500/(1+10.8%)5 + 92,500/(1+10.8%)6 =
$243,021
If the firm can make a one-time investment in either machine, Machine B would be a
better investment.
2. McGilla Golf is evaluating a new line of golf clubs. The clubs will sell for $970 per set and
have a variable cost of $435 per set. The company has spent $150,000 for a marketing
study that determined the company will sell 49,000 sets per year for seven years. The
marketing study also determined that the company will lose sales of 9,200 sets of its highpriced clubs. The high-priced clubs sell at $1,470 and have variable costs of $600. The
company also will increase sales of its cheap clubs by 11,800 sets. The cheap clubs sell for
$435 and have variable costs of $165 per set. The fixed costs each year will be $9,500,000.
The company has also spent $1,100,000 on research and development for the new clubs.
The plant and equipment required will cost $30,100,000 and will be depreciated on a
straight-line basis to a zero salvage value. The new clubs also will require an increase in
net working capital of $2,440,000 that will be returned at the end of the project. The tax
rate is 24 percent and the cost of capital is 12 percent.
Suppose you feel that the values are accurate to within only ±10 percent. What are the
best-case and worst-case NPVs? For new clubs, price, variable cost, and sales are
uncertain. However, the price and variable costs for the two existing sets of clubs are
known with certainty; only the sales gained or lost are uncertain. (20 points)
Worst case scenario sales volume from new line of clubs = 49,000 * (1-0.1)=44,100
Worst case scenario profit per set from new lines of clubs = 970*0.9-435*1.1=394.5
The rest of the numbers follow a similar logic.
Year
Profits from
new line of
clubs
Sales
volume
Profit per
set
Lost profits
from highpriced clubs
0
1
2
3
4
5
6
7
17,397,4
50
17,397,4
50
17,397,4
50
17,397,4
50
17,397,4
50
17,397,4
50
17,397,4
50
44,100
44,100
44,100
44,100
44,100
44,100
44,100
394.5
394.5
394.5
394.5
394.5
394.5
394.5
(8,804,4
00)
(8,804,4
00)
(8,804,4
00)
(8,804,4
00)
(8,804,4
00)
(8,804,4
00)
(8,804,4
00)
Practice Questions Set 1
Sales
volume loss
Profit per
set
Increased
profits of
low-priced
clubs
Sales
volume inc.
Profit per
set
Yearly fixed
costs
PPE
depreciation
EBIT
Taxes @ 24%
Depreciation
Operating
Cash Flow
PPE cost
Changes in
NWC
Cash flows
Cost of
capital
NPV of cash
flows
(30,100,
000)
(2,440,0
00)
(32,540,
000)
12%
(32,540,
000)
FIN 3701 AY 2024-2025
(10,120)
(10,120)
(10,120)
(10,120)
(10,120)
870
870
870
870
870
870
2,867,40
0
2,867,40
0
2,867,40
0
2,867,40
0
2,867,40
0
2,867,40
0
2,867,40
0
10,620
10,620
10,620
10,620
10,620
10,620
10,620
270
270
270
270
270
270
270
(10,450,
000)
(4,300,0
00)
(3,289,5
50)
789,492
4,300,00
0
1,799,94
2
(10,450,
000)
(4,300,0
00)
(3,289,5
50)
789,492
4,300,00
0
1,799,94
2
(10,450,
000)
(4,300,0
00)
(3,289,5
50)
789,492
4,300,00
0
1,799,94
2
(10,450,
000)
(4,300,0
00)
(3,289,5
50)
789,492
4,300,00
0
1,799,94
2
(10,450,
000)
(4,300,0
00)
(3,289,5
50)
789,492
4,300,00
0
1,799,94
2
(10,450,
000)
(4,300,0
00)
(3,289,5
50)
789,492
4,300,00
0
1,799,94
2
(10,450,
000)
(4,300,0
00)
(3,289,5
50)
789,492
4,300,00
0
1,799,94
2
(10,120)
(10,120)
870
1,799,94
2
1,799,94
2
1,799,94
2
1,799,94
2
1,799,94
2
1,799,94
2
2,440,00
0
4,239,94
2
12%
12%
12%
12%
12%
12%
12%
1,607,09
1
1,434,90
3
1,281,16
3
1,143,89
6
1,021,33
5
911,907
1,917,93
4
2
3
4
5
6
7
Worst case NPV = -$23,221,771
Year
0
1
Practice Questions Set 1
Profits from
new line of
clubs
Sales
volume
Profit per
set
Lost sales
from highpriced clubs
Sales
volume loss
Profit per
set
Increase
sales of
cheap clubs
Sales
volume inc.
Profit per
set
Yearly fixed
costs
PPE
depreciation
EBIT
Depreciation
Operating
Cash Flow
PPE cost
Changes in
NWC
Cash flows
36,409,4
50
36,409,4
50
36,409,4
50
36,409,4
50
36,409,4
50
36,409,4
50
36,409,4
50
53,900
53,900
53,900
53,900
53,900
53,900
53,900
676
676
676
676
676
676
676
(7,203,6
00)
(7,203,6
00)
(7,203,6
00)
(7,203,6
00)
(7,203,6
00)
(7,203,6
00)
(7,203,6
00)
(8,280)
(8,280)
(8,280)
(8,280)
(8,280)
(8,280)
870
870
870
870
870
870
870
3,504,60
0
3,504,60
0
3,504,60
0
3,504,60
0
3,504,60
0
3,504,60
0
3,504,60
0
12,980
12,980
12,980
12,980
12,980
12,980
12,980
270
270
270
270
270
270
270
(8,550,0
00)
(4,300,0
00)
19,860,4
50
(4,766,5
08)
4,300,00
0
19,393,9
42
(8,550,0
00)
(4,300,0
00)
19,860,4
50
(4,766,5
08)
4,300,00
0
19,393,9
42
(8,550,0
00)
(4,300,0
00)
19,860,4
50
(4,766,5
08)
4,300,00
0
19,393,9
42
(8,550,0
00)
(4,300,0
00)
19,860,4
50
(4,766,5
08)
4,300,00
0
19,393,9
42
(8,550,0
00)
(4,300,0
00)
19,860,4
50
(4,766,5
08)
4,300,00
0
19,393,9
42
(8,550,0
00)
(4,300,0
00)
19,860,4
50
(4,766,5
08)
4,300,00
0
19,393,9
42
(8,550,0
00)
(4,300,0
00)
19,860,4
50
(4,766,5
08)
4,300,00
0
19,393,9
42
19,393,9
42
2,440,00
0
21,833,9
42
(8,280)
Taxes @ 24%
(30,100,
000)
(2,440,0
00)
(32,540,
000)
FIN 3701 AY 2024-2025
19,393,9
42
19,393,9
42
19,393,9
42
19,393,9
42
19,393,9
42
Cost of
capital
NPV of cash
flows
12%
(32,540,
000)
Practice Questions Set 1
FIN 3701 AY 2024-2025
12%
12%
12%
12%
12%
12%
12%
17,316,0
20
15,460,7
32
13,804,2
25
12,325,2
01
11,004,6
44
9,825,57
5
9,876,56
7
Best case NPV = $57,072,962
Practice Questions Set 1
FIN 3701 AY 2024-2025
3. “Aviation Biofuel” is considering setting up a shop in Singapore. Their plan can be divided
into 2 stages.
Stage 1: The project requires a test marketing expense of $20m. This test market is
expected to last 1 year and there is a 60% chance of success.
Stage 2: If the test market is a success, the firm intends to invest $100m in a plant. The
after-tax cash flows will be $66m per year from year 2 to year 5. If the test market is a
failure and the firm goes ahead with the investment, the NPV will be -$20m. Assume a
cost of capital of 17%.
a. Draw the decision tree for this project. (5 points)
NPV1 = -$100 + 66/(1+17%) + 66/(1+17%)2 + 66/(1+17%)3 + 66/(1+17%)4 = 81.053
b. Estimate the NPV of Aviation Biofuel’s plan. (5 points)
(Values are presented in $ millions)
NPV of Aviation Biofuel’s plan – if test market is a success and firm chooses to invest:
NPV0 = -$20 + 0.6*[-100/(1+17%) + 66/(1+17%)2 + 66/(1+17%)3 + 66/(1+17%)4 +
66/(1+17%)5]
+ 0.4*[0/(1+17%)]
= $21.57 million
The NPV of Aviation Biofuel’s plan at Year 0 is estimated to be $21.57 million.
Practice Questions Set 1
FIN 3701 AY 2024-2025
4. James, Inc., has purchased a brand new machine to produce its High Flight line of shoes.
The machine has an economic life of 6 years. The depreciation schedule for the machine
is straight-line with no salvage value. The machine costs $624,000. The sales price per pair
of shoes is $92, while the variable cost is $41. Fixed costs of $320,000 per year are
attributed to the machine. The corporate tax rate is 22 percent and the appropriate
discount rate is 9 percent.
What are the financial break-even points? (10 points)
Given information:
Economic life
6 years
Annual
$104,000
depreciation
Cost of machine
$624,000
Selling price
$92
Variable cost
$41
Fixed cost per year
$320,000
Tax rate
22%
Discount rate
9%
Annual depreciation = 624,000 / 6 = $104,000
Financial break-even point:
EAC of initial investment = (624,000*0.09) / [1 – (1 + 0.09)-6] = $139,101.94
Financial break-even
= [EAC + Fixed costs*(1 – Tax) – Depreciation*Tax] / [(Selling Price – Variable Costs)*(1 – Tax
Rate)]
= [139,101.94 + 320,000*(1 – 22%) – 104,000*22%] / [(92 – 41)*(1 – 22%)]
= 9,196.13
Hence the financial break-even point for the new machine is 9,196 units*.
*Final values are rounded off to their nearest whole number
Practice Questions Set 1
FIN 3701 AY 2024-2025
5. Hickock Mining is evaluating when to open a gold mine. The mine has 33,600 ounces of
gold left that can be mined and mining operations will produce 4,200 ounces per year.
The required return on the gold mine is 12 percent and it will cost $17.4 million to open
the mine. When the mine is opened the company will sign a contract that will guarantee
the price of gold of the remaining life of the mine. If the mine is opened today each ounce
of gold will guarantee an after-tax cashflow of $900 per ounce. If the company waits one
year, there is a 60 percent probability that the contract price will generate an after-tax
cashflow of $1,150 per ounce and a 40 percent probability that the after-tax cashflow will
be $700 per ounce. The company will know whether the after tax cashflow will be high or
low in year one. What is the value of option to wait? (10 points)
Remaining life of the mine = Gold left / Gold produced per year = 33,600 / 4,200 = 8 years
In order to determine the value of option to wait, we will have to take the difference between
the NPV of project with the option to wait and the NPV without the option to wait (Value of
option = Project value with the option to wait – Project value without the option to wait).
Project 1 (option without waiting):
Cash flow per ounce = $900
Cash flow per year (after tax) = $900 * 4,200
= $3,780,000
Project 1 cash flows:
Year
0
1
FCF
($17,400,000
)
$3,780,000
2
$3,780,000
3
$3,780,000
4
$3,780,000
5
$3,780,000
6
$3,780,000
7
$3,780,000
8
$3,780,000
PV at Year 0
$3,780,000/(1+12%) =
$3,375,000
$3,780,000/(1+12%)2 =
$3,013,393
$3,780,000/(1+12%)3 =
$2,690,529
$3,780,000/(1+12%)4 =
$2,402,258
$3,780,000/(1+12%)5 =
$2,144,874
$3,780,000/(1+12%)6 =
$1,915,066
$3,780,000/(1+12%)7 =
$1,709,880
($3,780,000/(1+12%)8 =
$1,526,679
Practice Questions Set 1
FIN 3701 AY 2024-2025
NPV at year 0 = -17,400,000 + 3,375,000 + 3,013,393 + 2,690,529 + 2,402,258 + 2,144,874 +
1,915,066 +
1,709,880 + 1,526,679
= $1,377,678
Project 2 (option to wait one year):
If you open the mine in one year, the cash flow will be either:
CFUp = 4,200($1,150) = $4,830,000 per year
CFDown = 4,200($700) = $2,940,000 per year
The PV of these cash flows is:
Price increase CF = $4,830,000 *(1/1.12 + 1/1.122 +1/1.123 + 1/1.124 + 1/1.125 + 1/1.126 +
1/1.127 + 1/1.128) = $23,993,700.07
Price decrease CF = $2,940,000*(1/1.12 + 1/1.122 +1/1.123 + 1/1.124 + 1/1.125 + 1/1.126 +
1/1.127 + 1/1.128) = $14,604,860.91
So, the NPV is one year will be:
NPVUp = –$17,400,000 + 23,993,700.07 = $6,593,700.07
NPVDown = –$17,400,000 + 14,604,860.91 = -$2,795,139.09
If the price goes down, it is a negative NPV project, and it will not be undertaken. Thus, the
payoff if price goes down is zero, and not -$2,795,139.09.
NPV = 0.6* NPVUp + 0.4*0 = $3,956,220.04
And the NPV today is:
NPV today = $3,956,220.04/1.12
NPV today = $3,532,339.32
So, the value of the option to wait is:
Option value of waiting = $3,532,339.32– 1,377,678.32
Option value of waiting = $2,154,661
One key takeaway from this exercise is that by waiting, we can avoid the unprofitable outcome.
Practice Questions Set 1
FIN 3701 AY 2024-2025
6. Kapitan Properties (KP) is evaluating six real estate investments. Management plans to
buy the properties today and sell them five years from today. The following table
summarizes the initial cost and the expected sale price for each property, as well as the
appropriate discount rate based on the risk of each venture.
Project
Cost Today
Mountain Ridge
Ocean Park
Lakeview
Seabreeze
Green Hills
West Ranch
3,000,000
15,000,000
9,000,000
6,000,000
3,000,000
9,000,000
Discount
Rate
15%
15%
15%
8%
8%
8%
Expected Sale Price in Year
5
18,000,000
75,500,000
50,000,000
35,500,000
10,000,000
46,500,000
a. What is the NPV of each investment? (5 points)
b. KP has a total capital budget of $18,000,000 to invest in properties. Which properties
should KP choose? (5 points)
Assuming each property can only be bought once, we will invest in the combination of
properties that will maximize our NPV. Hence by elimination, we will determine the NPV
of various feasible combinations and choose the combination that yields the highest NPV.
Practice Questions Set 1
FIN 3701 AY 2024-2025
List of possible project combinations
Combinations
NPV
Mountain Ridge, Ocean Park
$5,949,181 + $22,536,844 = $28,486,025
Ocean Park, Green Hills
$22,536,844 + $3,805,832 = $26,342,676
Lakeview, West Ranch
$15,858,837 + $22,647,119 = $38,505,956
Lakeview, Seabreeze, Mountain Ridge
$15,858,837 + $18,160,703 + $5,949,181 =
$39,968,721
Lakeview, Seabreeze, Green Hills
$15,858,837 + $18,160,703 + $3,805,832 =
$37,825,372
West Ranch, Seabreeze, Mountain Ridge
$22,647,119 + $18,160,703 + $5,949,181 =
$46,747,003
West Ranch, Seabreeze, Green Hills
$22,647,119 + $18,160,703 + $3,805,832 =
$44,613,654
Mountain Ridge, Seabreeze, Green Hills
$5,949,181 + $18,160,703 + $3,805,832 =
$27,915,716
Based on the NPV criteria, we should invest in West Ranch, Seabreeze and Mountain
Ridge since they give the highest combined NPV.
c. If KP’s budget were $12,000,000, which properties should KP choose? (5 points)
Given the budget constraint of $12,000,000, we will use the same method in (d) to
determine the combination of projects that yields the highest NPV.
List of possible project combinations
Combinations
NPV
Mountain Ridge, Lakeview
$5,949,181 + $15,858,837 = $21,808,018
Mountain Ridge, West Ranch
$5,949,181 + $22,647,119 = $28,596,300
Lakeview, Green Hills
$15,858,837 + $3,805,832 = $19,664,669
West Ranch, Green Hills
$22,647,119 + $3,805,832 = $26,452,951
Mountain Ridge, Seabreeze, Green Hills
$5,949,181 + $18,160,703 + $3,805,832 =
$27,915,716
Based on NPV criteria, we should invest in both Mountain Ridge and West Ranch.
Practice Questions Set 1
FIN 3701 AY 2024-2025
7. AirPay company is deciding to invest between projects A and B. They hire you to evaluate
the company. They give you the following information about the projects:
Project A
Initial
Investment Cost
Revenue
Cost
Year 0
6,000
Project B
Initial
Investment Cost
Revenue
Cost
Year 0
3,000
Year 1
Year 2
Year 3
Year 4
20,000
6,000
15,000
4,000
30,000
25,000
1,000
18,000
Year 1
Year 2
Year 3
Year 4
10,000
8,000
12,000
7,000
40,000
18,000
1,000
18,000
Assume that change in net working capital is 25% of the change in sales incurred at the
beginning of the year, a tax rate of 20%. Assume that both projects are fully depreciated
with the straight-line method after four years, and both have no salvage value. Both
projects have a required rate of return of 10%.
a. Calculate the NPVof both projects. (25 points)
For Project A
NPV method
Initial Investment
Revenue
Cost
Depreciation
Profit before
taxes
Taxes
Profit after taxes
Depreciation
Change in NWC
FCF
PV of FCF
NPV = $4,777
For Project B
(6,000)
(5,000)
(11,000)
(11,000)
20,000
(6,000)
(1,500)
12,500
15,000
(4,000)
(1,500)
9,500
30,000
(25,000)
(1,500)
3,500
1,000
(18,000)
(1,500)
(18,500)
(2,500)
10,000
1,500
1,250
12,750
11,591
(1,900)
7,600
1,500
(3,750)
5,350
4,421
(700)
2,800
1,500
7,250
11,550
8,678
3,700
(14,800)
1,500
250
(13,050)
(8,913)
NPV method
Initial Investment
Revenue
Cost
Depreciation
Profit before
taxes
Taxes
Profit after taxes
Depreciation
Change in NWC
FCF
PV of FCF
NPV = $4,926
Practice Questions Set 1
FIN 3701 AY 2024-2025
10,000
(8,000)
(750)
1,250
12,000
(7,000)
(750)
4,250
40,000
(18,000)
(750)
21,250
1,000
(18,000)
(750)
(17,750)
(250)
1,000
750
(500)
1,250
1,136
(850)
3,400
750
(7,000)
(2,850)
(2,355)
(4,250)
17,000
750
9,750
27,500
20,661
3,550
(14,200)
750
250
(13,200)
(9,016)
(3,000)
(2,500)
(5,500)
(5,500)
b. Which project is a better choice? (5 points)
Using the NPV criteria, we will select Project B since it has a higher NPV than Project A.
NPV
Project A
$4,777
Project B
$4,926