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FINM1416 Sample Final Exam
Semester 2, 2022
Question 1
What are the five principles underlying all financial decisions Briefly explain
each of them in your own words.
Solutions:
1. Money has a time value: $ 1 today is worth more than $1 tomorrow. We
always can deposit $1 in a bank account to earn an interest rate r > 0.
2. There’s a trade-off between risk and return: Higher (systematic) risk must
be commensurate with higher (expected) return. If a security has higher
risk but offers lower returns, investors would sell it, thereby pushing its
price down and raising its expected return afterwards. Conversely, if a
security has lower risk but offers higher return, investors would rush to
buy it, thereby pushing its price up and driving down its expected returns
afterwards. In equilibrium, you get what you have paid for!
3. Cash flows are the source of value: A firm should create more cash flow
than it uses. The cash flows paid to shareholders and creditors should be
greater than those put into the firm by shareholdres and creditors. A firm
creates value when it buys assets that generate more cash than they cost
and sell claims (bonds/shares/other financial instruments) that raise more
cash than they cost.
4. Market prices reflect information: Market prices aggregate information
about firms’ future prospects. Any relevant information about a firm’s
future cash flows or about any factors that potentially affect its future cash
flows would be factored into its valuation, moving its share price.
5. Individuals respond to incentives: Individual are driven by incentives –
financial or nonfinancial. Market prices send signals that act as incentives
to buyers and sellers in the open market, changing their behavior. When
gasoline prices rise rapidly, many people choose to drive less and use public
transport more. Individuals respond to many different types of incentives,
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some altruistic, but most, not so much. Some people are motivated by a
sense of duty or community in how they live their lives or how they make
choices. In reality, however, the great majority of people and corporations
are driven primarily by financial incentives.
Question 2
Sigma Inc., is considering a new three-year expansion project that requires an
initial fixed asset investment of $1.4 million. The fixed asset will be depreciated
straight-line to zero over its 3-year tax life, after which it will be worthless. The
project is estimated to generate $1,120,000 in annual sales, with costs of $480,000.
The tax rate is 35% and the required return is 12%. What is the project’s NPV
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
Depreciation = 1,400,000 0
3
≈ 466, 666.67
Years 0 1–3
Revenue 1,120,000
Costs 480,000
EBITDA (= Revenue – Costs) 640,000
Less: Depreciation 466,666.67
EBIT 173,333.33
Tax (= EBIT × 35%) 60,666.67
NOPAT 112,666.66
Add: Depreciation 466,666.67
Operating Cash Flows (OCF) 579,333.33
CAPEX 1, 400, 000
After-tax FCF 1, 400, 000 579,333.33
Therefore,
NPV ≡
n∑
i=0
CFi
(1 + r)i
= 1, 400, 000 + 579, 333.33×
[
1 1
(1+0.12)3
0.12
]
= 1, 400, 000 + 1, 391, 460.91
= $8, 539.09
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Question 3
Aqua Corp. has bonds on the market with 11.5 years to maturity, a YTM of 7.6%,
and a current price of $1,060. The bonds make semiannual payments. What must
the coupon rate be on these bonds
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
r = 0.076
2
= 0.038
n = 11.5× 2 = 23
Face value = $1,000
Bond price = $1, 060
C =
Bond price = C ×
[
1 1
(1+r)n
r
]
︸ ︷︷ ︸
PV of Coupons
+
Face Value
(1 + r)n︸ ︷︷ ︸
PV of Face Value
= 1, 060 = C ×
[
1 1
(1+0.038)23
0.038
]
+
1, 000
(1 + 0.038)23
= C × 15.16 + 424.09
= C ≈ 1, 060 424.09
15.16
= $41.95
Since this is the semiannual coupon, we still need to convert it to the annual
coupon payment = The annual coupon payment= 41.95×2 = $83.90 =
Coupon rate = 1,000
83.90
= 8.39%.
Question 4
The Beta Corporation’s common stock has a beta of 1.21. If the risk-free rate is
3.5% and the expected return on the market is 11%, what is Beta’s cost of equity
capital
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
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By CAPM,
E[Ri] = rf + βi (E[rm] rf )
= 0.035 + 1.21× (0.11 0.035)
= 0.1258 = 12.58%
Question 5
Goala Co. is expected to pay the following dividends over the next four years:
$10, $7, $6, and $2.75. Afterwards, the company pledges to maintain a constant
5% growth rate in dividends forever. If the required return on the stock is 13%,
what is the current share price
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
P4 ≡ D5
r g =
D4 × (1 + g)
r g =
2.75× (1 + 0.05)
0.13 0.05 = $36.09
Hence,
P0 =
10
(1 + 0.13)
+
7
(1 + 0.13)2
+
6
(1 + 0.13)3
+
2.75
(1 + 0.13)4
+
36.09
(1 + 0.13)4
= 8.85 + 5.48 + 4.16 + 1.69 + 22.13
= $42.31
Question 6
A stock has a beta of 1.15, the expected return on the market is 11%, and the
risk-free rate is 5%. What must the expected return on this stock be
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
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By CAPM, the expected return on an asset i is
E[Ri] = rf + βi (E[rm] rf )
= 0.05 + 1.15× (0.11 0.05) = 0.1190 = 11.90%
Question 7
Gamma Corp. has a target debt–equity ratio of 0.55. Its cost of equity is 14%, and
its cost of debt is 7%. If the tax rate is 35%, what is Gamma’s WACC
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
Since D
E
= 0.55, we have D = 0.55E = V = D + E = 1.55E. Therefore,
WACC = E
V
×Re + D
V
×Rd × (1 Tax Rate)
=
1
1.55
× 0.14 + 0.55
1.55
× 0.07× (1 0.35)
= 0.09032 + 0.01615 ≈ 0.10645 = 10.64%
Question 8
Calculate the expected return and standard deviation based on the following in-
formation:
State of Probability of Rate of Return
Economy State of Economy if State Occurs
Depression 0.10 0.105
Recession 0.25 0.059
Normal 0.45 0.130
Boom 0.20 0.211
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
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Expected return:
E[Ri] =
n∑
k=1
pkRi,k = 0.10× ( 0.105) + 0.25× 0.059 + 0.45× 0.130 + 0.20× 0.211
= 0.1050 = 10.50%
Standard deviation:
σ2Ri =E (Ri E[Ri])2
= 0.10× ( 0.105 0.1050)2 + 0.25× (0.059 0.1050)2 + 0.45× (0.130 0.1050)2
+ 0.20× (0.211 0.1050)2
≈ 0.00441 + 0.00053 + 0.00028 + 0.00225
= 0.00747
= σRi =
√
σ2Ri =
√
0.00747 ≈ 0.08641 = 8.64%
Question 9
Hawken Co. will pay a $2.65 per share dividend next year. The company pledges
to increase its dividend by 4.75% per year, indefinitely. If you require a return of
11 percent on your investment, how much will you pay for the company’s stock
today
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
P0 =
D1
r g =
2.65
0.11 0.0475 = $42.40
Question 10
Alpha has issued a bond with the following characteristics:
Par value: $1,000
Time to maturity: 15 years
Coupon rate: 7%
Semiannual payments
Calculate the price of this bond if the YTM is:
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a) 7%
b) 9%
c) 5%
Show your workings and round your final answers to 2 decimal places.
Total marks: 10 marks
Solutions:
Bond price = C ×
[
1 1
(1+r)n
r
]
︸ ︷︷ ︸
PV of Coupons
+
Face Value
(1 + r)n︸ ︷︷ ︸
PV of Face Value
C = 0.07×1,000
2
= 35
n = 15× 2 = 30
Face value = $1,000
Bond price =
a) Since YTM = 7% = coupon rate, the bond price is equal to par, that is, $1,000.
Alternatively,
r = 0.07
2
= 0.035
Bond price = 35×
[
1 1
(1+0.035)30
0.035
]
+
1, 000
(1 + 0.035)30
≈ 643.72 + 356.28 = $1, 000
b)
r = 0.09
2
= 0.045
Bond price = 35×
[
1 1
(1+0.045)30
0.045
]
+
1, 000
(1 + 0.045)30
≈ 570.11 + 267.00 = $837.11
c)
r = 0.05
2
= 0.025
Bond price = 35×
[
1 1
(1+0.025)30
0.025
]
+
1, 000
(1 + 0.025)30
≈ 732.56 + 476.74 = $1, 209.30
