Quantitative Methods - Basic concepts Flashcards

Question 1

Q

How much would the following income stream be worth assuming a 12% discount rate?

$100 received today.
$200 received 1 year from today.
$400 received 2 years from today.
$300 received 3 years from today.

A) $721.32.
B) $810.98.
C) $1,112.44.

Question 2

Q

Nortel Industries has a preferred stock outstanding that pays (fixed) annual dividends of $3.75 a share. If an investor wants to earn a rate of return of 8.5%, how much should he be willing to pay for a share of Nortel preferred stock?

A) $31.88.
B) $44.12.
C) $42.10.

Question 3

Q

Perpetuities present value = ?

Answer

A

pmt / interest rate

Question 4

Q

The First State Bank is willing to lend $100,000 for 4 years at a 12% rate of interest, with the loan to be repaid in equal semi-annual payments. Given the payments are to be made at the end of each 6-month period, how much will each loan payment be?

A) $32,925.
B) $16,104.
C) $25,450.

Answer

A

N = 4 × 2 = 8; I/Y = 12/2 = 6; PV = -100,000; FV = 0; CPT → PMT = 16,103.59.

Question 5

Q

Optimal Insurance is offering a deferred annuity that promises to pay 10% per annum with equal annual payments beginning at the end of 10 years and continuing for a total of 10 annual payments. For an initial investment of $100,000, what will be the amount of the annual payments?
A) $42,212.
B) $38,375.
C) $25,937.

Answer

A

B
- To get the PV of the series payments:
Using a financial calculator: N = 10, I = 10, PV = $100,000, PMT = 0, Compute FV = $259,374.25.
- Using a financial calculator and solving for a 10-year annuity due because the payments are made at the beginning of each period (you need to put your calculator in the “begin” mode), with a present value of $259,374.25, a number of payments equal to 10, an interest rate equal to ten percent, and a future value of $0.00, the resultant payment amount is $38,374.51. Alternately, the same payment amount can be determined by taking the future value after nine years of deferral ($235,794.77), and then solving for the amount of an ordinary (payments at the end of each period) annuity payment over 10 years.

!! remember to set the payment to begin!!

Question 6

Q

If 10 equal annual deposits of $1,000 are made into an investment account earning 9% starting today, how much will you have in 20 years?

A) $42,165.
B) $39,204.
C) $35,967.

Answer

A

B
Switch to BGN mode. PMT = -1,000; N = 10, I/Y = 9, PV = 0; CPT → FV = 16,560.29. Remember the answer will be one year after the last payment in annuity due FV problems. Now PV10 = 16,560.29; N = 10; I/Y = 9; PMT = 0; CPT → FV = 39,204.23. Switch back to END mode.

!! remember to set the payment to begin!!

Question 7

Q

What is the maximum an investor should be willing to pay for an annuity that will pay out $10,000 at the beginning of each of the next 10 years, given the investor wants to earn 12.5%, compounded annually?

A) $52,285.
B) $55,364.
C) $62,285.

Answer

A

C
Using END mode, the PV of this annuity due is $10,000 plus the present value of a 9-year ordinary annuity: N=9; I/Y=12.5; PMT=-10,000; FV=0; CPT PV=$52,285; $52,285 + $10,000 = $62,285.

Or set your calculator to BGN mode then N=10; I/Y=12.5; PMT=-10,000; FV=0; CPT PV= $62,285.

Question 8

Q

What is the maximum price an investor should be willing to pay (today) for a 10 year annuity that will generate $500 per quarter (such payments to be made at the end of each quarter), given he wants to earn 12%, compounded quarterly?

A) $6,440.
B) $11,557.
C) $11,300.

Answer

A

B

Using a financial calculator: N = 10 × 4 = 40; I/Y = 12 / 4 = 3; PMT = -500; FV = 0; CPT → PV = 11,557.

Question 9

Q

Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate annual interest rate is 10%.

A) $1000.
B) $683.
C) $751.

Answer

A

C
(first time picked B, draw a timeline will help identify N)
Compute the present value of the perpetuity at (t = 3). Recall, the present value of a perpetuity or annuity is valued one period before the first payment. So, the present value at t = 3 is 100 / 0.10 = 1,000. Now it is necessary to discount this lump sum to t = 0. Therefore, present value at t = 0 is 1,000 / (1.10)3 = 751.

Question 10

Q

A $500 investment offers a 7.5% annual rate of return. How much will it be worth in four years?

A) $668.
B) $650.
C) $892.

Answer

A

A
N = 4; I/Y = 7.5; PV = -500; PMT = 0; CPT → FV = 667.73.

or: 500(1.075)4 = 667.73

Question 11

Q

Wei Zhang has funds on deposit with Iron Range bank. The funds are currently earning 6% interest. If he withdraws $15,000 to purchase an automobile, the 6% interest rate can be best thought of as a(n):

A) financing cost.
B) opportunity cost.
C) discount rate.

Answer

A

B
Since Wei will be foregoing interest on the withdrawn funds, the 6% interest can be best characterized as an opportunity cost - the return he could earn by postponing his auto purchase until the future.

Question 12

Q

A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on this account is:

A) 8.24%.
B) 9.01%.
C) 4.65%.

Answer

A

A
(1 + periodic rate)^m − 1 = (1.02)^4 − 1 = 8.24%.

(first time used the financial calculator, but using the geometric mean method is much faster)

Question 13

Q

Justin Banks just won the lottery and is trying to decide between the annual cash flow payment option or the lump sum option. He can earn 8% at the bank and the annual cash flow option is $100,000/year, beginning today for 15 years. What is the annual cash flow option worth to Banks today?

A) $1,080,000.00.
B) $924,423.70.
C) $855,947.87.

Answer

A

B
First put your calculator in the BGN.

N = 15; I/Y = 8; PMT = 100,000; CPT → PV = 924,423.70.

Alternatively, do not set your calculator to BGN, simply multiply the ordinary annuity (end of the period payments) answer by 1 + I/Y. You get the annuity due answer and you don’t run the risk of forgetting to reset your calculator back to the end of the period setting.

OR N = 14; I/Y = 8; PMT = 100,000; CPT → PV = 824,423.70 + 100,000 = 924,423.70.

Question 14

Q

If $2,000 a year is invested at the end of each of the next 45 years in a retirement account yielding 8.5%, how much will an investor have at retirement 45 years from today?

A) $100,135.
B) $90,106.
C) $901,060.

Answer

A

C

N = 45; PMT = -2,000; PV = 0; I/Y = 8.5%; CPT → FV = $901,060.79.

Question 15

Q

T-bill yields can be thought of as:

A)
nominal risk-free rates because they do not contain an inflation premium.
B)
nominal risk-free rates because they contain an inflation premium.
C)
real risk-free rates because they contain an inflation premium.

Answer

A

B
T-bills are government issued securities and are therefore considered to be default risk free. More precisely, they are nominal risk-free rates rather than real risk-free rates since they contain a premium for expected inflation.

Question 16

Q

The required rate of return on a security = ?

Answer

A

real risk-free rate + expected inflation + default risk premium + liquidity premium + maturity risk premium.

Question 17

Q

Nominal risk-free rate = ?

Answer

A

real risk-free rate + expected inflation rate.

Question 18

Q

_____ = _______ - inflation rate

Answer

A

Real risk-free rate = Nominal risk free rate - inflation rate

Question 19

Q

If an investor puts $5,724 per year, starting at the end of the first year, in an account earning 8% and ends up accumulating $500,000, how many years did it take the investor?

A) 26 years.
B) 27 years.
C) 87 years.

Answer

A

B
I/Y = 8; PMT = -5,724; FV = 500,000; CPT → N = 27.

Remember, you must put the pmt in as a negative (cash out) and the FV in as a positive (cash in) to compute either N or I/Y.

Question 20

Q

As the number of compounding periods increases, what is the effect on the annual percentage rate (APR) and the effective annual rate (EAR)?

A) APR increases, EAR increases.
B) APR increases, EAR remains the same.
C) APR remains the same, EAR increases.

Answer

A

C
The APR remains the same since the APR is computed as (interest per period) × (number of compounding periods in 1 year). As the frequency of compounding increases, the interest rate per period decreases leaving the original APR unchanged. However, the EAR increases with the frequency of compounding.

Question 21

Q

What is the effective annual rate if the stated rate is 12% compounded quarterly?

A) 12.55%.
B) 12.00%.
C) 57.35%.

Answer

A

EAR = (1 + 0.12 / 4)4 - 1 = 12.55%

Question 22

Q

Marc Schmitz borrows $20,000 to be paid back in four equal annual payments at an interest rate of 8%. The interest amount in the second year’s payment would be:

A) $1116.90.
B) $1244.90.
C) $6038.40.

Answer

A

B
With PV = 20,000, N = 4, I/Y = 8, computed Pmt = 6,038.42. Interest (Yr1) = 20,000(0.08) = 1600. Interest (Yr2) = (20,000 − (6038.42 − 1600))(0.08) = 1244.93

Question 23

Q

An investor purchases a 10-year, $1,000 par value bond that pays annual coupons of $100. If the market rate of interest is 12%, what is the current market value of the bond?

A) $950.
B) $1,124.
C) $887.

Answer

A

C
Note that bond problems are just mixed annuity problems. You can solve bond problems directly with your financial calculator using all five of the main TVM keys at once. For bond-types of problems the bond’s price (PV) will be negative, while the coupon payment (PMT) and par value (FV) will be positive. N = 10; I/Y = 12; FV = 1,000; PMT = 100; CPT → PV = -886.99.

Question 24

Q

Steve Hall wants to give his son a new car for his graduation. If the cost of the car is $15,000 and Hall finances 80% of the value of the car for 36 months at 8% annual interest, his monthly payments will be:

A) $376.
B) $413.
C) $289.

Answer

A

PV = 0.8 × 15,000 = -12,000; N = 36; I = 8/12 = 0.667; CPT → PMT = 376.

Question 25

Q

A major brokerage house is currently selling an investment product that offers an 8% rate of return, compounded monthly. Based on this information, it follows that this investment has:

A) an effective annual rate of 8.00%.
B) a periodic interest rate of 0.667%.
C) a stated rate of 0.830%.

Answer

A

B

Periodic rate = 8.0 / 12 = 0.667. Stated rate is 8.0% and effective rate is 8.30%.

Question 26

Q

An investment offers $100 per year forever. If Peter Wallace’s required rate of return on this investment is 10%, how much is this investment worth to him?

A) $10,000.
B) $1,000.
C) $500.

Answer

A

B

For a perpetuity, PV = PMT ÷ I = 100 ÷ 0.10 = 1,000.

Question 27

Q

An individual borrows $200,000 to buy a house with a 30-year mortgage requiring payments to be made at the end of each month. The interest rate is 8%, compounded monthly. What is the monthly mortgage payment?

A) $1,480.46.
B) $1,467.53.
C) $2,142.39.

Answer

A

B

With PV = 200,000; N = 30 × 12 = 360; I/Y = 8/12; CPT → PMT = $1,467.53.

Question 28

Q

What is the present value of a 12-year annuity due that pays $5,000 per year, given a discount rate of 7.5%?

A) $36,577.
B) $41,577.
C) $38,676.

Answer

A

B
Using your calculator: N = 11; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = 36,577 + 5,000 = $41,577. Or set your calculator to BGN mode and N = 12; I/Y = 7.5; PMT = -5,000; FV = 0; CPT → PV = $41,577.
!! annuity due : cash happens at beginning of period

Question 29

Q

Ordinary annuity cash flows occur ____ of each time period. Annuity due cash flows occur ____ of each time period.

Answer

A

at the end; at the beginning

Question 30

Q

____ cash flows occur at the end of each time period. ____ cash flows occur at the beginning of each time period.

Answer

A

Ordinary annuity; Annuity due

Question 31

Q

Concerning an ordinary annuity and an annuity due with the same payments and positive interest rate, which of the following statements is most accurate?

A) The present value of the ordinary annuity is less than an annuity due.
B) The present value of the ordinary annuity is greater than an annuity due.
C) There is no relationship.

Answer

A

A
With a positive interest rate, the present value of an ordinary annuity is less than the present value of an annuity due. The first cash flow in an annuity due is at the beginning of the period, while in an ordinary annuity, the first cash flow occurs at the end of the period. Therefore, each cash flow of the ordinary annuity is discounted one period more.

Question 32

Q

An investor makes 48 monthly payments of $500 each beginning today into an account that will have a value of $29,000 at the end of four years. The stated annual interest rate is closest to:

A) 10.00%.
B) 9.50%.
C) 9.00%.

Answer

A

C
Because this is an annuity due (payments at the start of each period) the calculator must first be set to BGN mode.

N = 48; PMT = 500; FV = -29,000; PV = 0; CPT I/Y = 0.7532

This percentage is a monthly rate because the time periods were entered as 48 months. It must be converted to a stated annual percentage rate (APR) by multiplying by the number of compounding periods per year: 0.7532 × 12 = 9.04%.

Question 33

Q

In 10 years, what is the value of $100 invested today at an interest rate of 8% per year, compounded monthly?

A) $180.
B) $216.
C) $222.

Answer

A

C

N = 10 × 12 = 120; I/Y = 8/12 = 0.666667; PV = -100; PMT = 0; CPT → FV = 221.96.

Question 34

Q

An investor has the choice of two investments. Investment A offers interest at 7.25% compounded quarterly. Investment B offers interest at the annual rate of 7.40%. Which investment offers the higher dollar return on an investment of $50,000 for two years, and by how much?

A) Investment A offers a $122.18 greater return.
B) Investment A offers a $53.18 greater return.
C) Investment B offers a $36.92 greater return.

Answer

A

B
Investment A: I = 7.25 / 4; N = 2 × 4 = 8; PV = $50,000; PMT = 0; CPT → FV = $57,726.98
Investment B: I = 7.40; N = 2; PV = $50,000; PMT = 0; CPT → FV = $57,673.80
Difference = investment A offers a $53.18 greater dollar return.

Question 35

Q

How much should an investor have in a retirement account on his 65th birthday if he wishes to withdraw $40,000 on that birthday and each of the following 14 birthdays, assuming his retirement account is expected to earn 14.5%?

A) $272,977.
B) $234,422.
C) $274,422.

Answer

A

C
This is an annuity due so set your calculator to the BGN mode. N = 15; I/Y = 14.5; PMT = -40,000; FV = 0; CPT → PV = 274,422.50. Switch back to END mode.

Question 36

Q

If $2,500 were put into an account at the end of each of the next 10 years earning 15% annual interest, how much would be in the account at the end of ten years?

A) $27,461.
B) $41,965.
C) $50,759.

Answer

A

C

N = 10; I = 15; PMT = 2,500; CPT → FV = $50,759.

Question 37

Q

Suppose you are going to deposit $1,000 at the start of this year, $1,500 at the start of next year, and $2,000 at the start of the following year in an savings account. How much money will you have at the end of three years if the rate of interest is 10% each year?

A) $4,000.00.
B) $5,750.00.
C) $5,346.00.

Answer

A

C
Future value of $1,000 for 3 periods at 10% = 1,331
Future value of $1,500 for 2 periods at 10% = 1,815
Future value of $2,000 for 1 period at 10% = 2,200
Total = $5,346

N = 3; PV = -$1,000; I/Y = 10%; CPT → FV = $1,331
N = 2; PV = -$1,500; I/Y = 10%; CPT → FV = $1,815
N = 1; PV = -$2,000; I/Y = 10%; CPT → FV = $2,200

Question 38

Q

What’s the effective rate of return on an investment that generates a return of 12%, compounded quarterly?

A) 12.55%.
B) 12.00%.
C) 14.34%.

Answer

A

(1 + 0.12 / 4)4 − 1 = 1.1255 − 1 = 0.1255.

Question 39

Q

Paul Kohler inherits $50,000 and deposits it immediately in a bank account that pays 6% interest. No other deposits or withdrawals are made. In two years, what will be the account balance assuming monthly compounding?

A) $53,100.
B) $56,400.
C) $50,500.

Answer

A

B
To compound monthly, remember to divide the interest rate by 12 (6%/12 = 0.50%) and the number of periods will be 2 years times 12 months (2 × 12 = 24 periods). The value after 24 periods is $50,000 × 1.00524 = $56,357.99.

The problem can also be solved using the time value of money functions: N = 24; I/Y = 0.5; PMT = 0; PV = 50,000; CPT FV = $56,357.99.

Question 40

Q

Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.

Year 1:  -2,000
Year 2: -3,000
Year 3:  6,000
Year 4:  25,000
Year 5:  30,000

A) $65,144.33.
B) $58,164.58.
C) $33,004.15.

Answer

A

B (first time calculated NPV on accident…C)
N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04
N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78
N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40
N = 1; I/Y = 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00
N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00

Sum the cash flows: $58,164.58.

Alternative calculation solution: -2,000 × 1.124 − 3,000 × 1.123 + 6,000 × 1.122 + 25,000 × 1.12 + 30,000 = $58,164.58.

Question 41

Q

Given: an 11% annual rate compounded quarterly for 2 years; compute the future value of $8,000 today.

A) $9,939.
B) $8,962.
C) $9,857.

Answer

A

A
Divide the interest rate by the number of compound periods and multiply the number of years by the number of compound periods. I = 11 / 4 = 2.75; N = (2)(4) = 8; PV = 8,000.

Question 42

Q

An investor deposits $4,000 in an account that pays 7.5%, compounded annually. How much will this investment be worth after 12 years?

A) $5,850.
B) $9,358.
C) $9,527.

Answer

A

C

N = 12; I/Y = 7.5; PV = -4,000; PMT = 0; CPT → FV = $9,527.

Question 43

Q

An investor wants to receive $1,000 at the beginning of each of the next ten years with the first payment starting today. If the investor can earn 10 percent interest, what must the investor put into the account today in order to receive this $1,000 cash flow stream?

A) $6,759.
B) $6,145.
C) $7,145.

Answer

A

A
This is an annuity due problem. There are several ways to solve this problem.

Method 1:
PV of first $1,000 = $1,000
PV of next 9 payments at 10% = 5,759.02
Sum of payments = $6,759.02

Method 2:
Put calculator in BGN mode.
N = 10; I = 10; PMT = -1,000; CPT → PV = 6,759.02
Note: make PMT negative to get a positive PV. Don’t forget to take your calculator out of BGN mode.

Method 3:
You can also find the present value of the ordinary annuity $6,144.57 and multiply by 1 + k to add one year of interest to each cash flow. $6,144.57 × 1.1 = $6,759.02.

Question 44

Q

A certain investment product promises to pay $25,458 at the end of 9 years. If an investor feels this investment should produce a rate of return of 14%, compounded annually, what’s the most he should be willing to pay for it?

A) $9,426.
B) $7,618.
C) $7,829.

Answer

A

C
N = 9; I/Y = 14; FV = -25,458; PMT = 0; CPT → PV = $7,828.54.

or: 25,458/1.149 = 7,828.54

Question 45

Q

Which one of the following statements best describes the components of the required interest rate on a security?

A)
The nominal risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
B)
The real risk-free rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.
C)
The real risk-free rate, the expected inflation rate, the default risk premium, a liquidity premium and a premium to reflect the risk associated with the maturity of the security.

Answer

A

C
The required interest rate on a security is made up of the nominal rate which is in turn made up of the real risk-free rate plus the expected inflation rate. It should also contain a liquidity premium as well as a premium related to the maturity of the security.

Question 46

Q

Sarah Parker is buying a new $25,000 car. Her trade-in is worth $5,000 so she needs to borrow $20,000. The loan will be paid in 48 monthly installments and the annual interest rate on the loan is 7.5%. If the first payment is due at the end of the first month, what is Sarah’s monthly car payment?

A) $480.57.
B) $483.58.
C) $416.67.

Answer

A

B

N = 48; I/Y = 7.5 / 12 = 0.625; PV = 20,000; FV = 0; CPT → PMT = 483.58.

Question 47

Q

Given investors require an annual return of 12.5%, a perpetual bond (i.e., a bond with no maturity/due date) that pays $87.50 a year in interest should be valued at:

A) $70.
B) $1,093.
C) $700.

Answer

A

C

87.50 ÷ 0.125 = $700.

Question 48

Q

The real risk-free rate can be thought of as:

A)
approximately the nominal risk-free rate plus the expected inflation rate.
B)
exactly the nominal risk-free rate reduced by the expected inflation rate.
C)
approximately the nominal risk-free rate reduced by the expected inflation rate.

Answer

A

C
The approximate relationship between nominal rates, real rates and expected inflation rates can be written as:

Nominal risk-free rate = real risk-free rate + expected inflation rate.

Therefore we can rewrite this equation in terms of the real risk-free rate as:

Real risk-free rate = Nominal risk-free rate - expected inflation rate

The exact relation is: (1 + real)(1 + expected inflation) = (1 + nominal)

Question 49

Q

An investor deposits $10,000 in a bank account paying 5% interest compounded annually. Rounded to the nearest dollar, in 5 years the investor will have:

A) $12,500.
B) $10,210.
C) $12,763.

Answer

A

C
PV = 10,000; I/Y = 5; N = 5; CPT → FV = 12,763.

or: 10,000(1.05)5 = 12,763.

Question 50

Q

What will $10,000 become in 5 years if the annual interest rate is 8%, compounded monthly?

A) $14,693.28.
B) $14,802.44.
C) $14,898.46.

Answer

A

C
FV(t=5) = $10,000 × (1 + 0.08 / 12)^60 = $14,898.46

N = 60 (12 × 5); PV = -$10,000; I/Y = 0.66667 (8% / 12months); CPT → FV = $14,898.46

Question 51

Q

A 10% coupon bond was purchased for $1,000. One year later the bond was sold for $915 to yield 11%. The investor’s holding period yield on this bond is closest to:

A) 1.5%.
B) 9.0%.
C) 18.5%.

Answer

A

A
HPY = [(interest + ending value) / beginning value] − 1
= [(100 + 915) / 1,000] − 1
= 1.015 − 1 = 1.5%

Question 52

Q

Given a $1,000 T-bill with 100 days to maturity and a discount of $10 (price of $990):

What is bank discount yield? (formula is fine)

Answer

A

bank discount yield = discount/coupon value * 360/days to maturity
10/1000 * 360/100 = 3.6%

Question 53

Q

Given a $1,000 T-bill with 100 days to maturity and a discount of $10 (price of $990):

What is holding period yield? (formula is fine)

Answer

A

HPY = [(interest + ending value) / beginning value] − 1

(1000-990)/990 = 1.01%

Question 54

Q

Given a $1,000 T-bill with 100 days to maturity and a discount of $10 (price of $990):

What is effective annual yield? (formula is fine)

Answer

A

EAY = (1 + holding period yield)^365/t − 1.

1.0101^(365/100)-1 = 3.74%

Question 55

Q

Given a $1,000 T-bill with 100 days to maturity and a discount of $10 (price of $990):

What is money market yield? (formula is fine)

Answer

A

holding period yield * 365/holding period

1.01% x 360/100 = 3.636%

Question 56

Q

An investment with a cost of $5,000 is expected to have cash inflows of $3,000 in year 1, and $4,000 in year 2. The internal rate of return (IRR) for this investment is closest to:

A) 25%.
B) 15%.
C) 30%.

Answer

A

A
The IRR is the discount rate that makes the net present value of the investment equal to 0.

This means -$5,000 + $3,000 / (1 + IRR) + $4,000 / (1 + IRR)2 = 0

One way to compute this problem is to use trial and error with the existing answer choices and choose the discount rate that makes the PV of the cash flows closest to 5,000.

$3,000 / (1.25) + $4,000 / (1.25)2 = 4,960.

Alternatively: CFO = -5,000; CF1 = 3,000; CF2 = 4,000; CPT → IRR = 24.3%. **this is what i used

Question 57

Q

Sarah Kelley, CFA, is analyzing two mutually exclusive investment projects. Kelley has calculated the net present value (NPV) and internal rate of return (IRR) for each project:

Project 1: NPV = $230; IRR = 15%

Project 2: NPV = $4,000; IRR = 6%

Kelley should make which of the following recommendations concerning the two projects?

A) Accept Project 2 only.
B) Accept both projects.
C) Accept Project 1 only.

Answer

A

A
(this question is similar to the ones in capital budgeting)
Because the investment projects are mutually exclusive, only one project can be chosen. The NPV and IRR criteria are giving conflicting project rankings. When decision criteria conflict, always use the NPV criteria because NPV evaluates projects using an appropriate discount rate, the weighted average cost of capital. The IRR may not be a market rate, therefore future cash flows associated with the project may not be capable of earning a rate of return equal to the IRR.

Question 58

Q

A stock is currently worth $75. If the stock was purchased one year ago for $60, and the stock paid a $1.50 dividend over the course of the year, what is the holding period return?

A) 24.0%.
B) 22.0%.
C) 27.5%.

Answer

A

C
HPY = [(interest + ending value) / beginning value] − 1
(75 − 60 + 1.50) / 60 = 27.5%.

Question 59

Q

A Treasury bill has 40 days to maturity, a par value of $10,000, and is currently selling for $9,900. Its effective annual yield is closest to:

A) 9.00%.
B) 1.00%.
C) 9.60%.

Answer

A

C
The effective annual yield (EAY) is based on a 365-day year and accounts for compound interest. EAY = (1 + holding period yield)^365/t − 1. The holding period yield formula is (price received at maturity − initial price + interest payments) / (initial price) = (10,000 − 9,900 + 0) / (9,900) = 1.01%. EAY = (1.0101)365/40 − 1 = 9.60%.

Question 60

Q

Which of the following is NOT a problem with the internal rate of return (IRR)?

A) Sometimes the IRR exceeds the cost of capital.
B) A higher IRR does not necessarily indicate a more-profitable project.
C) Non-normal cash flow patterns may result in multiple IRRs.

Answer

A

A
If the IRR exceeds the cost of capital, that merely indicates that the project is acceptable-this is not a problem associated with IRR. Non-normal cash flow patterns such as cash outflows during the project’s life can result in multiple IRRs, leaving open the question as to which one is valid. A higher IRR will only be realized if the project’s cash flows can be reinvested at the IRR, and the true profitability of a project also depends on project size, not just IRR.

Question 61

Q

The ______ rate of return is the IRR calculated using periodic cash flows into and out of an account and is the discount rate that makes the PV of cash inflows equal to the PV of cash outflows.

Answer

A

money-weighted

Question 62

Q

The money-weighted rate of return is the IRR calculated using periodic cash flows into and out of an account and is the discount rate that makes the ______ equal to the ____.

Answer

A

PV of cash inflows; PV of cash outflows

Question 63

Q

The ______ of return measures compound growth.

Answer

A

time-weighted rate

Question 64

Q

_____ is the rate at which $1 compounds over a specified performance horizon.

Answer

A

time-weighted rate of return

Answer 63

A

time-weighted; money-weighted

Answer 64

A

the manager controls the money flows into and out of an account

Answer 65

A

just before a period of poor performance; just prior to a period of high returns

Answer 66

A

lower; higher

Answer 67

A

The holding period yield is the return the investor will earn if the T-bill is held to maturity. HPY = (100,000 - 98,000) / 98,000 = 0.0204, or 2.04%.

Answer 68

A

C
The present value of the current lease is $508,766.38, while the present value of the lease being offered is $459,177.59; a savings of 49,589. Alternatively, the present value of the extra $40,000 at the beginning of each of the next 4 years is $129,589 which is $49,589 more than the extra $80,000 added to the payment today.

Answer 69

A

B (first time picked A, that’s when you don’t calculate the actual discount first)

The actual discount is 1.3%, 1.3% × (360 / 45) = 10.4%

The bank discount yield is computed by the following formula, r = (dollar discount / face value) × (360 / number of days until maturity) = [(1,000,000 − 987,000) / (1,000,000)] × (360 / 45) = 10.40%.

Answer 70

A

C
To calculate the EAY from the HPY, the formula is: (1 + HPY)^(365/t) − 1. Therefore, the EAY is: (1.0107)^(365/197) − 1 = 0.0199, or 1.99%.

Answer 71

A

A
($21,000 / 1,000,000) × (360 / 135) = 5.6%.
bank discount yield = discount/coupon value * 360/days to maturity
**coupon, not selling price

Answer 72

A

possible mutually exclusive events;

greater than 1 or less than 0.

Answer 73

A

Empirical

Answer 74

A

Subjective

Answer 75

A

predetermined probabilities; well-defined inputs

Answer 76

A

observations or experiments

Answer 77

A

an informed guess.

Answer 78

A

B
The formula for the standard deviation of a 2-stock portfolio is:

s = [WA^2sA^2 + WB^2sB^2 + 2WAWBsAsB(rA,B)]^1/2

s = [(0.8^2 × 0.34^2) + (0.2^2 × 0.16^2) + (2 × 0.8 × 0.2 × 0.34 × 0.16 × 0.67)]^1/2 = [0.073984 + 0.001024 + 0.0116634]^1/2 = 0.0866714^1/2 = 0.2944, or approximately 29.4%.

Answer 79

A

A
A joint probability is the probability that two events occur when neither is certain or a given. Joint probability is calculated by multiplying the probability of each event together. (0.75) × (0.80) = 0.60 or 60%.

Answer 80

A

B
A random variable must be a number. Sometimes there is an obvious method for assigning a number, such as when the random variable is a number itself, like a P/E ratio. A stock symbol of a randomly selected stock could have a number assigned to it like the number of letters in the symbol. The symbol itself cannot be a random variable.

Answer 81

A

B (not C, C did not do 1/2次方)
[W1^2 σ1^2 + W2^2 σ2^2 + 2W1W2σ1σ2r1,2]^0.5
= [(0.75)2(0.102)2 + (0.25)^2(0.139)^2 + (2)(0.75)(0.25)(0.102)(0.139)(-1.0)]^0.5
= 0.0418, or 4.18%.

Answer 82

A

B
This is a choose four from six problem where order is important. Thus, it requires the permutation formula: n! / (n − r)! = 6! / (6 − 4)! = 360.

With TI calculator: 6 [2nd][nPr] 4 = 360.

Answer 83

A

B
A conditional probability involves two events. One of the events is a given, and the probability of the other event depends upon that given.

Answer 84

A

C
This is a joint probability. From the information: P(beta > 1) = 0.500 and P(comp. stock | beta > 1) = 0.333. Thus, the joint probability is the product of these two probabilities: (0.500) × (0.333) = 0.167.

Answer 85

A

C
For event “E,” the probability stated as odds is: P(E) / [1 - P(E)]. Here, the probability that a poultry research assistant received a salary increase in excess of 2.5% = 2,000 / 10,000 = 0.20, or 1/5 and the odds are (1/5) / [1 - (1/5)] = 1/4, or 1 to 4.

Answer 86

A

C
Joint probability is the probability that both events, in this case a car being red and having a radio, happen at the same time. Joint probability is computed by multiplying the individual event probabilities together: P(red and radio) = (P(red)) × (P(radio)) = (0.4) × (0.7) = 0.28 or 28%.

Answer 87

A

C

This is a conditional expectation. The analyst indicates how an expected value will change given another event.

Answer 88

A

!!! C
According to Bayes’ formula: P(B | default) = P(default and B) / P(default).

P(default and B )= P(default | B) × P(B) = 0.250 × 0.300 = 0.075

P(default and CCC) = P(default | CCC) × P(CCC) = 0.400 × 0.700 = 0.280

P(default) = P(default and B) + P(default and CCC) = 0.355

P(B | default) = P(default and B) / P(default) = 0.075 / 0.355 = 0.211

Answer 89

A

B
Stating a probability does not require defining a mutually exclusive and exhaustive set of events. The two defining properties of probability are that the probability of an event is greater than or equal to zero and less than or equal to one, and if a set of events is mutually exclusive and exhaustive, their probabilities sum to one.

Answer 90

A

A
For the four independent events where the probability is the same for each, the probability of all defaulting is (0.24)^4. The probability of all not defaulting is (1 − 0.24)^4.

Answer 91

A

A
For the four independent events defined here, the probability of the specified outcome is 0.5000 × 0.5000 × 0.1667 × 0.1667 = 0.0069.

Answer 92

A

B
The addition rule for probabilities is used to determine the probability of at least one event among two or more events occurring. The probability of each event is added and the joint probability (if the events are not mutually exclusive) is subtracted to arrive at the solution. P(air bags or bucket seats) = P(air bags) + P(bucket seats) − P(air bags and bucket seats) = (125 / 220) + (110 / 220) − (75 / 220) = 0.57 + 0.50 − 0.34 = 0.73 or 73%.

Alternative: 1 − P(no airbag and no bucket seats) = 1 − (60 / 220) = 72.7%
**mine = (75+35+50)/220

Answer 93

A

balls are put back after each draw, so it is independent.

Answer 94

A

C
Because a good economy and a bad economy are mutually exclusive, the probability of a bull market is the sum of the joint probabilities of (good economy and bull market) and (bad economy and bull market): (0.40 × 0.50) + (0.60 × 0.20) = 0.32 or 32%.

*diagram is helpful in this case

Answer 95

A

If the outcome of one event does not influence the outcome of another, then the events are independent.

Answer 96

A

C
We calculate the probability that at least one of the options will fall below the strike price using the addition rule for probabilities (A represents AlphaDog, O represents OmegaWolf):

P(A or O) = P(A) + P(O) − P(A and O), where P(A and O) = P(A) × P(O)
P(A or O) = 0.65 + 0.47 − (0.65 × 0.47) = approximately 0.81

Answer 97

A

A
The standard deviation of the portfolio is found by:

[W1^2 σ1^2 + W2^2 σ2^2 + 2W1W2σ1σ2r1,2]^0.5, or [(0.30)^2(0.046)^2 + (0.70)^2(0.078)^2 + (2)(0.30)(0.70)(0.046)(0.078)(0.45)]^0.5 = 0.0620, or 6.20%.
*remember to do 1/2 at the end!!

Answer 98

A

A
If the probability against the event occurring is twelve to one, this means that in thirteen occurrences of the event, it is expected that it will occur once and not occur twelve times. The probability that the event will occur is then: 1/13 = 0.0769.

Answer 99

A

Covariance

Answer 100

A

Sum of Probability x (A-mean of A)(B-mean of B)

Answer 101

A

r = Cov (A,B)/SDa*SDb

Answer 102

A

C
E(RA) =11.65%, E(RB) =12.55%

[RA - E(RA)]x [RB - E(RB)] x P(S):
0.000614
0.000583
0.000041
0.000660
Thus, Cov(RA,RB) =0.001898

Answer 103

A

A
A positive covariance indicates a positive linear relationship but nothing else. The magnitude of the covariance by itself is not informative with respect to the strength of the relationship.

Answer 104

A

negative infinity to positive infinity

thus a big positive cov doesn’t mean it’s strong, since it could go all the way to infinity

Answer 105

A

B
The joint probability of independent events is obtained by multiplying the probabilities of the individual events together: (0.40) × (0.40) = 0.16 or 16%.

Answer 106

A

A
Find the weighted average return (0.10)(−5) + (0.30)(−2) + (0.50)(10) + (0.10)(31) = 7%.

Next, take differences, square them, multiply by the probability of the event and add them up. That is the variance. Take the square root of the variance for Std. Dev. (0.1)(−5 − 7)^2 + (0.3)(−2 − 7)^2 + (0.5)(10 − 7)^2 + (0.1)(31 − 7)^2 = 100.8 = variance.

100.8^0.5 = 10.04%.

Answer 107

A

sum of
(each value - expected value)^2 x probability
SD is ^.5 of variance

Answer 108

A

Expected value

Answer 109

A

A
Odds are the number of successful possibilities to the number of unsuccessful possibilities:

P(E)/[1 − P(E)] or 0.6 / 0.4 or 3/2.

Answer 110

A

The correlations and standard deviations cannot give a measure of central tendency, such as the expected value.

Answer 111

A

B
(tree diagram helps!)

E(r) = (0.70 × 0.12) + (0.30 × 0.40 × 0.30) + (0.30 × 0.60 × 0.25) = 0.165.

Answer 112

A

C
The standard deviation is the positive square root of the variance. The variance is the expected value of the squared deviations around the expected value, weighted by the probability of each observation. The expected value is: (0.5) × (0.12) + (0.3) × (0.1) + (0.2) × (0.15) = 0.12. The variance is: (0.5) × (0.12 − 0.12)2 + (0.3) × (0.1 − 0.12)2 + (0.2) × (0.15 − 0.12)2 = 0.0003. The standard deviation is the square root of 0.0003 = 0.017 or 1.7%.

Answer 113

A

B
The probability of being a nonsmoker is 240 / 300 = 0.80. The probability of not suffering from allergies is 210 / 300 = 0.70. The probability of being a nonsmoker and not suffering from allergies is 185 / 300 = 0.62. Since the question asks for the probability of being either a nonsmoker or not suffering from allergies we have to take the probability of being a nonsmoker plus the probability of not suffering from allergies and subtract the probability of being both: 0.80 + 0.70 − 0.62 = 0.88.

Alternatively: 1 − P(Smoker & Allergies) = 1 − (35 / 300) = 88.3%.

Answer 114

A

C

This is the definition of the expected value. It is the long-run average of all outcomes.

Answer 115

A

C
The expected values are: E(X) = (0.4 × 20) + (0.6 × 30) = 26, and E(Y) = (0.4 × 0) + (0.6 × 50) = 30.
The covariance is COV(XY) = (0.4 × ((20 − 26) × (0 − 30))) + ((0.6 × (30 − 26) × (50 − 30))) = 120.

Answer 116

A

A
Note that events being independent means that they have no influence on each other. It does not necessarily mean that they are mutually exclusive. Accordingly, P(X or Y) = P(X) + P(Y) − P(X and Y). By the definition of independent events, P(X|Y) = P(X).

Answer 117

A

B
Using the addition rule, the probability of being accepted at Harvard or Yale is equal to: P(Harvard) + P(Yale) − P(Harvard and Yale) = 0.25 + 0.42 − 0.028 = 0.642 or 64.2%.

Answer 118

A

P(X) + P(Y) - P (X and Y)

Answer 119

A

C

A set of probabilities must sum to one.

Answer 120

A

A
Given a set of prior probabilities for an event of interest, Bayes’ formula is used to update the probability of the event, in this case that the company we have already selected will experience a decline in earnings next year. Bayes’ formula says to divide the Probability of New Information given Event by the Unconditional Probability of New Information and multiply that result by the Prior Probability of the Event. In this case, P(company having a decline in earnings next year) = 0.20 is divided by 0.26 (which is the Unconditional Probability that a company having an earnings decline will have a negative ratio (90% have negative ratios of the 20% which have earnings declines) plus (10% have negative ratios of the 80% which do not have earnings declines) or ((0.90) × (0.20)) + ((0.10) × (0.80)) = 0.26.) This result is then multiplied by the Prior Probability of the ratio being negative, 0.90. The result is (0.20 / 0.26) × (0.90) = 0.69 or 69%.

Answer 121

A

C

The correlation coefficient = Cov (X,Y) / [(Std Dev. X)(Std. Dev. Y)] = 18.17 / 28 = 0.65

Answer 122

A

B
This is a joint probability. From the information: P(Bear Market given inverted yield curve) = 0.75 and P(inverted yield curve) = 0.20. The joint probability is the product of these two probabilities: (0.75)(0.20) = 0.15.

Answer 123

A

70 analysts / 200 individuals = 0.35.

Answer 124

A

A
The multiplication rule of probability is stated as: P(AB) = P(A|B) × P(B), where P(AB) is the joint probability of events A and B.

Answer 125

A

C

P(A) = 0.40, P(B|A) = 0.60. Therefore, P(AB) = P(A)P(B|A) = 0.40(0.60) = 0.24.

Answer 126

A

B
Expected return = .315%+.73% = 0.066
SD = [0.30 × (0.15 − 0.066)^2 + 0.70 × (0.03 − 0.066)^2]^1/2 = 5.5%.

Answer 127

A

the joint probability of two events

P(AB) = P(A | B) × P(B)

Answer 128

A

P(AB) = P(A | B) × P(B)

Answer 129

A

the probability that at least one of two events will occur

P(A or B) = P(A) + P(B) − P(AB)

Answer 130

A

at least one of two events will occur

Answer 131

A

the unconditional probability of an event, given conditional probabilities:
P(A) = P(A | B1)P(B1) + P(A | B2)P(B2) +…+ P(A | BN)P(BN)

where B1, B2,…BN is a mutually exclusive and exhaustive set of outcomes.

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