Practice Exam 1
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Exam 1
Practice Exam
1.
What is the relationship between future value and present value?
FV
=
PV
(
1
+
r
)
t
2.
For a given time period and future value – the lower the interest rate, ___________ the present value.
For a given time period and future value – the lower the interest rate, higher
is the present value.
3.
Your best friend from FIN324 invested $3,000 five years ago and earns 2 percent annual interest. By leaving her interest earnings in her account, she increases the amount of interest she earns each year. The way she is handling her interest income is referred to as:
a.
simplifying.
b. compounding.
c.
aggregating.
d. accumulating.
e.
discounting.
Solution: b. compounding
4.
If the monthly interest rate is 1%. What is the annual interest rate?
r
monthly
=
1%
r
annual
=
(
1
+
r
monthly
)
12
−
1
r
annual
=
(
1.01
)
12
−
1
=
12.68%
5.
Calculate the present value of the following cash flows discounted at 10 percent
per year.
a.
$100,000 received 10 years from today.
PV
=
FV
(
1
+
r
)
t
=
100,000
1.1
10
=
$
38,554.33
b.
$100,000 received 2 years from today.
PV
=
¿
100,000
1.1
2
=
$
82,644.63
c.
$100,000 received 20 years from today.
PV
=
¿
100,000
1.1
20
=
$
14,864.36
6.
If you put up $36,000 today in exchange for a 7.00 percent, 18-year annuity, what
will the annual cash flow be?
PV
=
C
r
(
1
−
1
(
1
+
r
)
t
)
36,000
=
C
.07
(
1
−
1
1.07
18
)
C
=
$
3,578.85
7.
You deposit $2,000 at the end of each year into an account paying 10.6 percent
interest.
a.
How much money will you have in the account in 24 years?
FV
=
C
r
[
(
1
+
r
)
t
−
1
]
=
2000
0.106
[
(
1.106
)
24
−
1
]
=
$
192,893.66
b.
How much will you have if you make deposits for 48 years?
FV
=
C
r
[
(
1
+
r
)
t
−
1
]
=
2000
0.106
[
(
1.106
)
48
−
1
]
=
$
2,357,809.41
8.
Shao Professional Basketball Agents issued a 17-year bond 2 years ago at a
coupon rate of 10%. The bond makes semi-annual payments. The bond currently
sells for 102% of par value. If the YTM changes from 9.75% to 12%, where will the
bond be traded?
a) The bond will be traded above par.
b) The bond will be traded at par.
c) The bond will be traded below par.
d) The change in rate will not impact the price at which the bond is traded.
e) The bond could be traded below, at, or above par.
9.
Live Forever Life Insurance Company is selling a perpetuity contract that pays $1,550 monthly. The contract currently sells for $74,000.
a.
What is the monthly interest rate?
We need to find the interest rate that equates the perpetuity cash flows with the PV of
the cash flows. Using the PV of a perpetuity equation:
PV =
C
/
r
$74,000 = $1,550/
r
We can now solve for the interest rate as follows:
r
= $1,550/$74,000
r
= .0209, or 2.09% per month
b.
What is the APR?
The interest rate is 2.09% per month. To find the APR, we multiply this rate by the
number of months in a year, so:
APR = 12(2.09%)
APR = 25.14%
c.
What is the EAR?
Using the equation to find an EAR:
EAR = [1 + (APR/
m
)]
m
− 1
EAR = [1 + 0.0209]
12
− 1
EAR = .2824, or 28.24%
10. Given a market interest rate of 12 percent per year, what is the value at date t
= 4
(i.e., the end of year 4) of a perpetual stream of $50 annual payments that begin at
date t
= 10 (i.e., at the end of year 10 and continue forever)?
We have a perpetuity
r = 12%
C = $50
The payments begin at t=10
At the end of t=9, the value of the perpetuity is:
V
9
=
C
r
=
50
0.12
=
$
416.67
The value at t=4 of a cash flow of $416.67 at t=9 is:
V
4
=
$
416.67
(
1.12
)
5
=
$
236.43
11. The appropriate discount rate for the following cash flows is 7 percent
compounded quarterly.
Year
Cash Flow
1
$ 900
2
900
3
0
4
1,100
What is the present value of the cash flows?
The cash flows are annual and the compounding period is quarterly, so we need to calculate the EAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get:
EAR = [1 + (APR/
m
)]
m
− 1
EAR = [1 + (.07/4)]
4
− 1
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EAR = .0719, or 7.19%
And now we use the EAR to find the PV of each cash flow as a lump sum and add them together:
PV = $900/1.0719 + $900/1.0719
2
+ $1,100/1.0719
4
PV = $2,456.41
12. Your job pays you only once a year for all the work you did over the previous 12
months. Today, December 31, you just received your salary of $46,000 and you
plan to spend all of it. However, you want to start saving for retirement beginning
next year. You have decided that one year from today you will begin depositing 2
percent of your annual salary in an account that will earn 9 percent per year. Your
salary will increase at 6 percent per year throughout your career. How much
money will you have on the date of your retirement 41 years from today?
Since your salary grows at 6 percent per year, your salary next year will be:
Next year's salary = $46,000 (1 + .06)
Next year's salary = $48,760
This means your deposit next year will be:
Next year's deposit = $48,760(.02)
Next year's deposit = $975
Since your salary grows at 6 percent, you deposit will also grow at 6 percent. We can use
the present value of a growing perpetuity equation to find the value of your deposits
today. Doing so, we find:
PV
=
C
r
−
g
{
1
−
[
1
+
g
1
+
r
]
t
}
PV
=
$
975
.09
−
.06
{
1
−
[
1
+
.06
1
+
.09
]
41
}
PV = $22,154.61
Now, we can find the future value of this lump sum in 41 years. We find:
FV = PV(1 +
r
)
t
FV = $22,154.61(1 + .09)
41
FV = $758,491.28
This is the value of your savings in 41 years.
13. Which of the following cash flows are relevant for capital budgeting analysis?
Sunk Costs: not relevant
Opportunity Costs: relevant
Side effects: relevant
Changes in Net working capital: relevant
Financing Costs: not relevant
Taxes: relevant
14. The internal rate of return is calculated as?
The discount rate which causes the net present value of a project to equal zero
15. Shelton Company purchased a parcel of land six years ago for $873,500. At that
time, the firm invested $145,000 in grading the site so that it would be usable.
Since the firm wasn't ready to use the site itself at that time, it decided to lease the
land for $54,000 a year. The company is now considering building a warehouse on
the site as the rental lease is expiring. The current value of the land is $925,000.
What value should be included in the initial cost of the warehouse project for the
use of this land?
The opportunity cost of the building is what it could be sold for today, or $925,000.
16. Is depreciation a cash-expense? Why is depreciation included in a capital
budgeting analysis?
No, depreciation is not a cash-expense. It is included in a capital budgeting analysis
because it is tax deductible.
17. What are the two types of risk firms face? Which type of risk do we account for
when we calculate the cost of equity using the CAPM? Why?
A firm’s total risk can be decomposed into systematic and unsystematic risk. Using the
CAPM model to calculate cost of equity, we only account for the firm’s systematic risk.
This is because the investor can diversify away the unsystematic risk faced by a specific
firm by holding a carefully selected portfolio of stocks.
18. Bubbly Waters currently sells 300 Class A spas, 450 Class C spas, and 200 deluxe
model spas each year. The firm is considering adding a mid-class spa and expects
that if it does, it can sell 375 units per year. However, if the new spa is added,
Class A sales are expected to decline to 225 units while the Class C sales are
expected to increase to 475. The sales of the deluxe model will not be affected.
Class A spas sell for an average of $12,000 each. Class C spas are priced at $6,000
and the deluxe models sell for $17,000 each. The new mid-range spa will sell for
$8,000. What annual sales figure should you use in your analysis?
Sales = 375($8,000) + (225 − 300)($12,000) + (475 − 450)($6,000)
Sales = $2,250,000
19. McCanless Company recently purchased an asset for $2,500,000 that will be used
in a 3-year project. The asset is in the 4-year MACRS class. The depreciation
percentage each year is 33.33 percent, 44.45 percent, 14.81 percent, and 7.41 percent,
respectively. What is the amount of depreciation in Year 2? Year 2 depreciation = .4445($2,500,000)
Year 2 depreciation = $1,111,250
20. A company purchased an asset for $3,650,000 that will be used in a 3-year project. The asset is in the 3-year MACRS class. The depreciation percentage each year is 33.33 percent, 44.45 percent, and 14.81 percent, respectively. What is the book value of the equipment at the end of the project?
Book value = Initial Investment – Accumulated Depreciation
= $3,650,000 − $3,650,000(.3333 + .4445 + .1481)
= $270,465
21. A company is evaluating a new 4-year project. The equipment necessary for the
project will cost $2,900,000 and can be sold for $655,000 at the end of the project.
The asset is in the 5-year MACRS class. The depreciation percentage each year is
20.00 percent, 32.00 percent, 19.20 percent, 11.52 percent, and 11.52 percent,
respectively. The company's tax rate is 21 percent. What is the after-tax salvage
value of the equipment?
Book value at the end of year 4 = $2,900,000 − $2,900,000(.2 + .32 + .1920 + .1152)
Book value at the end of year 4 = $501,120
Tax paid = ($655,000 - 501,120 )(.21)
Tax paid = $32,315
Aftertax salvage value = $655,000 − 32,315
Aftertax salvage value = $622,685
22. Bi-Lo Traders is considering a project that will produce sales of $40,200 and have
costs of $23,300. Taxes will be $4,100 and the depreciation expense will be $2,350.
An initial cash outlay of $1,900 is required for net working capital. What is the
project's operating cash flow?
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OCF = $40,200 − 23,300 − 4,100
OCF = $12,800
23. You have calculated the pro forma net income for a new project to be $46,440. The
incremental taxes are $23,450 and incremental depreciation is $17,510. What is the
operating cash flow?
OCF = $46,440 + 17,510
OCF = $63,950
24.
Smathers Corporation stock has a beta of .91. The market risk premium is 7.40 percent and
the risk-free rate is 2.97 percent annually. What is the company's cost of equity?
R
E
= .0297 + .91(.0740)
R
E
= .0970, or 9.70%
25.
Kim's Bridal Shoppe has 10,200 shares of common stock outstanding at a price of $36 per
share. There are 520 bonds outstanding that have a coupon rate of 5.5 percent paid
semiannually. The bonds mature in 17 years, have a face value of $1,000, and sell at 93 percent
of par. What is the capital structure weight of the common stock?
Common stock:
10,200 × $36 =
$ 367,200
Debt:
520 × $1,000 × .93 =
483,600
Total value:
$ 850,800
W
E
= $367,200/$850,800
W
E
= .4223
26.
Bermuda Cruises issues only common stock and coupon bonds. The firm has a debt-equity
ratio of 1.35. The cost of equity is 13.2 percent and the pretax cost of debt is 7.5 percent. What
is the capital structure weight of the firm's equity if the firm's tax rate is 21 percent? W
E
= 1/(1 + 1.35)
W
E
= .4255
27.
The Two Dollar Store has a cost of equity of 11.6 percent, the YTM on the company's bonds is
6.2 percent, and the tax rate is 21 percent. If the company's debt-equity ratio is .51, what is the
weighted average cost of capital?
WACC = (1/1.51)(11.6%) + (.51/1.51)(6.2%)(1 − .21)
WACC = 9.34%
28. Michael's, Incorporated, just paid $2.45 to its shareholders as the annual dividend.
Simultaneously, the company announced that future dividends will be increasing by 5.3
percent. If you require a rate of return of 9.5 percent, how much are you willing to pay today
to purchase one share of the company's stock?
P
0
=
[
$
2.45
×
(
1
+
.053
)
]
.095
–
.053
=
$
61.43
29.
A stock just paid a dividend of $5.45 and is expected to maintain a constant dividend growth
rate of 4.5 percent indefinitely. If the current stock price is $79, what is the required return on
the stock?
Dividend yield = [$5.45(1 + .045)]/$79 = .0721, or 7.21%
Required return = 4.5% + 7.21% = 11.71%
30. Shares of common stock of the Samson Company offer an expected total return of 12.80
percent. The dividend is increasing at a constant 5.10 percent per year. The dividend yield
must be:
Dividend yield = 12.80% – 5.10% = 7.70%
31.
NU YU announced today that it will begin paying annual dividends. The first dividend will
be paid next year in the amount of $.33 a share. The following dividends will be $.38, $.53,
and $.83 a share annually for the following three years, respectively. After that, dividends are
projected to increase by 2.6 percent per year. How much are you willing to pay today to buy
one share of this stock if your desired rate of return is 9 percent?
P
4
=
$
.83
×
1.026
.09
–
.026
=
$
13.31
P
0
=
$.
33
1.09
+
$.
38
1.09
2
+
$ .
53
1.09
3
+
$.
83
1.09
4
+
$
13.31
1.09
4
=
$
11.05
32.
Santa Klaus Toys just paid a dividend of $3.20 per share. The required return is 9.4 percent
and the perpetual dividend growth rate is 4.1 percent. What price should this stock sell for
five years from today?
P
=
[
$
3.20
(
1
+
.041
)
6
]
.094
−
.041
Capital Budgeting I
Jen and Berry are considering investing in a new frozen yogurt mixer to replace an old
machine. The old machine was expected to last for 8 years. We are already three years
into the life of the old machine. The old machine was bought at $1600 and straight-line
depreciated for 8 years. It has been generating an EBIT of $100 per year during its
lifetime. If the new machine is purchased the old machine will be sold today at $400.
The old machine has no salvage value at the end of the next five years. The EBIT from
the old machine for the next five years would be lost if the new machine is installed.
On the other hand, the new machine is expected to generate $500 dollars of sales per
year for the next five years with COGS of $100 per year. The new machine costs $900
and will be depreciated in five years using the MACRS depreciation method (sheet
attached). The salvage value (SV) of the new machine in year 5 is equal to $200. There
will be no changes in the NWC.
Jen and Berry already paid $100 to J&S for the feasibility study. Tax rate is 45%. The cost
of capital is 10%.
Should Jen and Berry replace the old frozen yogurt mixer with the new one?
Yes, NPV>0
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Capital Investment Analysis
0
1
2
3
4
5
D
Sales
500
500
500
500
500
D
Cost
(100)
(100)
(100)
(100)
(100)
D
DP
(180)
(288)
(172.8)
(103.68)
(103.68)
D
DP (old)
200 200 200 200 200 D
EBIT
420 312 427 496 496 DEBIT (
old
)
(100)
(100)
(100)
(100)
(100)
DEBIT (
total
)
320 212 327 396 396 D
EBIT ´
(1-t)
176
116.6
179.96
217.98
217.98
D
DP
(20)
88 (27)
(96)
(96)
CX (900)
D
NWC
Δ
SV
200
T(SV-BV)
(67)
Δ
SV (old)
400 T(SV-BV) (old)
270 Δ
CF
(230)
156 205 153 122 255 (1+r)^t
1
1.1000
1.2100
1.3310
1.4641
1.6105
= PV
D
CF
(230)
142 169 115 83 158 NPV
437
MACRS Tax Depreciation
Schedules
YEAR(S)
3-YEAR
5-YEAR
7-YEAR
10-YEAR
15-YEAR
20-YEAR
1
.3333
.2000
.1429
.1000
.0500
.0375
2
.4445
.3200
.2449
.1800
.0950
.0722
3
.1481
.1920
.1749
.1440
.0855
.0668
4
.0741
.1152
.1249
.1152
.0770
.0618
5
.1152
.0893
.0922
.0693
.0571
6
.0576
.0893
.0737
.0623
.0528
7
.0893
.0655
.0590
.0489
8
.0445
.0655
.0590
.0452
9
.0655
.0590
.0446
10
.0655
.0590
.0446
11
.0329
.0590
.0446
12
.0590
.0446
13
.0590
.0446
14
.0590
.0446
15
.0590
.0446
16
.0299
.0446
17
.0446
18
.0446
19
.0446
20
.0446
21
.0225
Note: U.S. tax depreciation allowed for various MACRS asset classes. Figures represent the fraction of asset value depreciable in each year.
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- 5. You decide to invest $100 into a savings account with an interest rate of 2% annually in2015. The amount of money in your savings account in a given year can be modeled by the following function. P(t)=100(10)^.009 a. Evaluate P(0) and explain what it means in this context. b. Approximately how many years will it take for the amount of money in your bank account to reach $120? c. What year will you have $120 in your savings account?arrow_forwardQuestions: 1. Using simple interest computations, find the future value of $3,620 at 2 38%/2 38% 2. Now, using compound interest computations, find the future value of $3,620 at 2 38%/2 38% Time Value of Money Solver). Show what you put into the calculator for your work. 3. Now, using compound interest computations, find the future value of $3,620 at 2 38%/2 38% Time Value of Money Solver). Show what you put into the calculator for your work. 4. Explain why the future values are different in questions 1-3. Explain who would benefit from more frequent compounding. Who would be at a disadvantage from more frequent compounding.arrow_forwardInterest Rate? Problem 2 In 4 years, you plan to buy a new car and will need a down payment. How much would you need to invest today in order to have $8,000 in 4 years? Assume interest rates are 4%. Which table will you use for the above calculation? Number of periods? Factor? hapter What is the amount of investment? Problom 3 value of money and Бопа X A P Q S Yarrow_forward
- Question 1. Suppose that you invest P dollars at the beginning of every week. However, your crazy banker decides to compound interest at a rate r at the end of Week 5, Week 9, Week 12, Week 14, and Week 15. What is the value of the account at the end of Week 15? At the end of the Week 15, you need to spend $15, 000 on a bandersnatch. How much money must you invest weekly to ensure you have exactly $15, 000 after Week 15 if the weekly interest rate is 10%?arrow_forwardA ALEKS - Harley Biltoc - Learn O Exponential and Logarithmic Functions Finding the present value of an investment earning compound interest Explanation Check X www-awu.aleks.com S myPascoConnect C To help with his retirement savings, Pablo has decided to invest. Assuming an interest rate of 3.43% compounded quarterly, how much would he have to invest to have $128,900 after 16 years? Do not round any intermediate computations, and round your final answer to the nearest dollar. If necessary, refer to the list of financial formulas. MacBook Air 3/5 Portal Harley Ⓒ2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Acces.arrow_forwardThe present value represents the amount of money you would have to deposit today in order to match what you would get from the income stream at the future date. The formula is Time = M = i Future value represents the total amount of money you would have if you deposit the income stream until a future date. The formula is To start our problem we need to identify the variables. Rate =r= i Income Stream S(t) = i Present Value = years % M 1. 0 S (t) et dt. Future Value = Present Value* erM dollars/yeararrow_forward
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