Problem Set 5 Time Value of Money
Question 1
Match the formula description to the correct formula.
Future value of an n-period investment
PV x (1 + i)n
Future value with compounding more frequent than annually
PV x (1 + i / m)(m x n)
Future value with continuous compounding
PV x e(i x n)
Present value of a n-period investment
FVn / (1+ i)n
Approximate time for the present value to double
72 / i
Question 2
Future value measures:
what one or more cash flows are worth at the end of a specified period.
what one or more cash flows that is to be received in the future will be worth today.
the value of an investment after subtracting interest earned on it for one or more periods.
the value of an investment’s worth after discounting occurs.
Question 3
Present value measures
what one or more cash flows are worth at the end of a specified period.
what one or more cash flows that is to be received in the future is worth today.
the value of an investment after subtracting interest earned on it for one or more periods.
the value of an investment’s worth after compounding occurs.
Question 4
One way to visualize cash flows, interest rates, and time that is very helpful is to put this information on a:
Timeline.
spaceship.
discount double check.
longitudinal study.
Question 5
All else equal, as you increase the length of time, what happens to the present value of a single cash flow?
it decreases
it increases
it stays the same
it equals the future value
Question 6
All else equal, as you increase the interest rate, what happens to the present value of a single cash flow?
it decreases
it increases
is stays the same
it equals the future value
Question 7
The type of interest that does NOT take into account compounding is called
usury interest.
riba
compound interest.
simple interest.
Question 8
The process of converting an amount given at the present time into a future value is called
annualizing
discounting
compounding.
capital budgeting.
Question 9
Which of the following investments will have the highest future value?
USD 1,000 invested at an annual interest rate of 5% for 5 years
USD 1,000 invested at an annual interest rate of 5% for 10 years
USD 1,000 invested at an annual interest rate of 10% for 5 years
USD 1,000 invested at an annual interest rate of 10% for 10 years
Question 10
Which of the following investments will result in the highest future value?
USD 1,000 invested at 10 percent compounded annually for 5 years.
USD 1,000 invested at 10 percent compounded quarterly for 5 years.
USD 1,000 invested at 10 percent compounded monthly for 5 years.
USD 1,000 invested at 10 percent compounded continuously for 5 years.
Question 11
The process of converting an amount in the future to the present time is called
annualizing.
discounting.
compounding.
capital budgeting.
Question 12
All else equal, when the discount rate
decreases, the present value of the future cash flow does not change.
decreases, the present value of any future cash flow increases.
increases, the present value of any future cash flow increases.
increases, the present value of any future cash flow does not change.
Question 13
All else equal, as you increase the number of compounding periods per year
the smaller the future value
the larger the future value
the larger the present value
this has no effect on the value of the cash flows
Question 14
Suppose there are two identical investments, except for the final payoff amount. Investment A pays off USD
100,000 and investment B pays off USD 125,000. If both investments cost USD 25,000, what accounts for the
difference in the future value of the payoff?
investment A has a higher interest rate
investment B has a higher interest rate
investment B has lower risk
investment A has higher risk
Question 15
Who is the mathematician credited with discovering the number e = 2.71828?
Eve Plumb
Emilio Estevez
Leonhard Euler
James Edgeworth
Question 16
Kate Eden received a graduation present of USD 2,000 that she is planning on investing in a mutual fund that earns
8.5 percent each year. How much money can she collect in 3 years?
N = 3
I/Y = 8.5
PV = -2,000
PMT = 0
FV = ??? = 2,555
Question 17
Your bank pays 5 percent interest semiannually on your savings account. The current balance in the account is USD
3,000. How much money will you have at the end of four years?
N = 4 x 2 = 8
I/Y = 5 / 2 = 2.5
PV = -3,000
PMT = 0
FV = ??? = 3,655
Question 18
Santiago Hernandez is planning to invest USD 25,000 in a money market account for two years. The account pays
interest of 6 percent compounded on a monthly basis. How much money will Santiago Hernandez have at the end
of two years?
N = 2 x 12 = 24
I/Y = 6 / 12 = 0.5
PV = -25,000
PMT = 0
FV = ??? = 28,179
Question 19
You invest USD 1,500 in a mutual fund today that pays 9 percent interest every year. How long will it take to double
your money in years?
N = ??? = 8.04
I/Y = 9
PV = -1,500
PMT = 0
FV = 3,000
OR 72 / 9 = 8
Question 20
What is the future value of USD 10,000 invested at 10 percent for 10 years with continuous compounding?
10,000 x exp(0.10 x 10) = 27,183
Question 21
You bought a corporate bond for USD 863.75 today. In five years the bond will mature and you will receive USD
1,000. What is the annual rate of return on this bond?
N = 5
I/Y = ??? = 2.97
PV = -863.75
PMT = 0
FV = 1,000
Question 22
What is the present value of a USD 10,000 investment received in five years at 10 percent compounded
semiannually?
N = 5 x 2 = 10
I/Y = 10 / 2 = 5
PV = ??? = 6,139
PMT = 0
FV = 10,000
Question 23
What is the present value of USD 10,000 received in five years at 10 percent compounded monthly?
N = 5 x 12 = 60
I/Y = 10 / 12 = 0.83333
PV = ??? = 6,079
PMT = 0
FV = 10,000
Question 24
What is the present value of USD 10,000 received in five years at 10 percent compounded continuously?
10,000 x exp(-0.10 x 5) = 6,065
Question 25
Sam Braxton, the number one draft pick of the Phoenix Cardinals (NFL), and his agent are evaluating the following
contract option. The contract provides for a series of annual payments over the next three years. What is the
present value of these payments if Sam's required rate of return is 10 percent? (Hint: discount each cash flow to
the present and then sum.)
Year 1: USD 1,000,000
Year 2: USD 1,250,000
Year 3: USD 1,500,000
1,000,000 / (1.10)1 = 909,091
1,250,000 / (1.10)2 = 1,033,058
1,500,000 / (1.10)3 = 1,126,972
909,091 + 1,033,058 + 1,126,972 = 3,069,121
Problem set 6: Discounted Cash Flows and Valuation
Question 1
Please match each formula to its description.
Present value of an ordinary annuity (CF / i) x [1 - 1 / (1 + i)n]
Future value of an ordinary annuity (CF / i) x [(1 + i)n - 1]
Present value of a perpetuity CF / i
Value of an annuity due Ordinary annuity value x (1 + i)
Present value of a growing annuity CF1 / (i - g) x [1 - [(1 + g) / (1 + i)]n]
Present value of a growing perpetuity CF1 / (i - g)
Effective annual interest rate (1 + Quoted interest rate / m)m - 1
Question 2
William deposited USD 25,000 today that would earn an interest at the rate of 3 percent for a period of 2 years.
The amount of USD 25,000 represents the:
present value of an annuity
future value of an annuity
present value
future value
Question 3
Anna will receive USD 15,000 from a bank deposit after 2 years which had an interest of 3.5 percent. The amount of
USD 15,000 represents the:
present value of an annuity
future value of an annuity
present value
future value
Question 4
If your investment pays the same amount at the end of each year for a period of six years, the cash flow stream is
called:
a perpetuity.
an ordinary annuity.
an annuity due.
a growing perpetuity.
Question 5
If your investment pays the same amount at the beginning of each year for a period of 10 years, the cash flow
stream is called
a perpetuity.
an ordinary annuity.
an annuity due.
a growing perpetuity.
Question 6
If your investment pays the same amount at the end of each year, forever, the cash flow stream is called
a perpetuity.
an ordinary annuity.
an annuity due.
a growing perpetuity.
Question 7
Your investment in a small business venture will produce cash flows that increase by 15 percent every year for the
next 25 years. This cash flow stream is called
an annuity due.
an ordinary annuity.
a growing annuity.
a growing perpetuity.
Question 8
A firm receives a cash flow from an investment that will increase by 10 percent annually for an infinite number of
years. This cash flow stream is called
an annuity due.
a growing perpetuity.
an ordinary annuity.
a growing annuity.
Question 9
If the discount rate is positive, the present value of multiple cash flows is
greater than the sum of the cash flows.
equal to the sum of all the cash flows.
less than the sum of the cash flows.
to infinity and beyond.
Question 10
If the interest rate is positive, the future value of a perpetuity is
equal to one million.
less than the sum of the cash flows.
infinity.
less than one million.
Question 11
Which of the following statements is true of loan amortization?
With an amortized loan, the interest portion of each month’s payment remains unchanged.
With an amortized loan, a bigger proportion of each month's payment goes toward interest in the early
periods.
With an amortized loan, a bigger proportion of each month's payment goes toward interest in the later periods.
With an amortized loan, a smaller proportion of each month's payment goes toward interest in the early periods.
Question 12
What is the appropriate interest rate to use when making interest rate comparisons if there is more than one
compounding period per year?
The effective annual interest rate (EAR)
The annual percentage rate (APR)
The quoted interest rate
The simple interest rate
Question 13
Which of the following cash flows has the largest present value if the discount rate is 10 percent?
USD 180,000 received in five years
USD 11,400 forever
USD 19,000 each year for 10 years
USD 6,000 next year and increasing thereafter by 5 percent per year forever
180,000 / (1.10)5 = 111,766
11,400 / 0.10 = 114,000
(N=10, I/Y = 10, PMT=19,000) = 116,747
6,000 / (0.10 - 0.05) = 120,000
Question 14
Dynamics Telecommunications Corporation has made an investment in another company that will guarantee it a
cash flow of USD 22,500 each year for the next five years. If the company uses a discount rate of 15 percent on its
investments, what is the present value of this investment?
N = 5
I/Y = 15
PV = ??? = 75,423
PMT = 22,500
FV = 0
Question 15
Cecelia Thomas is a sales executive at a Baltimore firm. She is 25 years old and plans to invest USD 3,000 every year
in a retirement account, beginning at the end of this year until she turns 65 years old. If the investment will earn
9.75 percent annually, how much will she have in 40 years, when she turns 65?
N = 40
I/Y = 9.75
PV = 0
PMT =3,000
FV = ??? = 1,240,676
Question 16
The Elkridge Bar and Grill has a seven-year loan in the amount of USD 25,000 with Bank of America. It plans to
repay the loan in seven equal installments made at the end of each year. If the rate of interest is 8 percent, how
much will each payment be?
N = 7
I/Y = 8
PV = 25,000
PMT = ??? = 4,802
FV = 0
Question 17
Anna Kashfi is retiring at the end of the year. She would like to make sure she receives payments of USD 10,000 a
year forever, starting when she retires. If she can earn 6.5 percent annually, how much does Anna need to invest
today to produce the desired cash flow?
PV perpetuity= CF / i
10,000 / 0.065 = 153,846
Or
N = 1,000
I/Y = 6.5
PV = ??? = 153,846
PMT = 10,000
FV = 0
Question 18
Anna Kashfi (from above) is retiring at the end of the year. She would like to make sure she receives payments of
USD 10,000 a year forever, starting when she retires, but now she would like these payments to grow by 1.5
percent each year. If she can earn 6.5 percent annually, how much does Anna need to invest today to produce the
desired cash flow?
PV growing perpetuity = CF1 / (i - g)
10,000 (0.065 - 0.015) = 200,000
Question 19
Sharon Kabana won the state lottery and will receive a payment of USD 89,729.45 at the end of each year for the
next 20 years. If the going rate of interest is 7.25 percent, what is the present value of her lottery winnings?
N = 20
I/Y = 7.25
PV = ??? = 932,401
PMT = 89,729.45
FV = 0
Question 20
What is the present value of Sharon Kabana's lottery winnings (from above) if the payments begin today instead of
one year from today?
Value of annuity due = Value of ordinary annuity x (1 + i)
932,401 x (1.0725) = 1,000,000
Question 21
If the APR is 9.65 percent, what is the effective annual interest rate (EAR), in percent, if the compounding is
quarterly?
EAR = (1 + i / m)m - 1
EAR = (1 + 0.0965 / 4)4 - 1
EAR = 10
Question 22
You're hoping to buy a new house that costs USD 300,000. The bank requires a 10 percent down payment, meaning
you can borrow USD 270,000. If the interest rate is six percent, what is the monthly payment on a 30-year
mortgage loan?
N = 30 x 12 =360
I/Y = 6 / 12 = 0.50
PV = -270,000
PMT = ??? = 1,619
FV = 0
Question 23
You're hoping to buy a new house that costs USD 300,000. The bank requires a 10 percent down payment, meaning
you can borrow USD 270,000, with an interest rate of six percent. If you make monthly payments of USD 2,138.77,
how many months will it take to pay off the loan in full?
N = ??? = 200
I/Y = 6 / 12 = 0.50
PV = -270,000
PMT = 2,138.77
FV = 0
Question 24
You're hoping to buy a new house that costs USD 300,000. The bank requires a 10 percent down payment, meaning
you can borrow USD 270,000, with an interest rate of six percent. What is the amount of interest in the first
monthly payment?
(0.06 / 12) x 270,000 = 1,350
Question 25
Assume you will start working as soon as you graduate from college. You plan to start saving for your retirement on
your 25th birthday and retire on your 65th birthday. After retirement, you expect to live until you are at least 85.
You wish to be able to withdraw USD 50,000 every year from the time of your retirement until you are 85 years old
(i.e., for 20 years). What is the dollar amount you need to invest every year, starting at age 26 and ending at age 65
(i.e., for 40 years), to be able to accomplish this plan if the interest rate is 10 percent?
This needs to be solved in two steps.
First you need a big pot of money sitting in the account when you retire.
N = 20
I/Y = 10
PV = ??? = 425,678
PMT = 50,000
FV = 0
Then ask how much you need to save each year to accumulate that amount of money.
N = 40
I/Y = 10
PV = 0
PMT = ??? = 962
FV = 425,678
Problem Set 7: Risk and Return
Question 1
Robert paid USD 100 for a stock one year ago. The total return on the stock was 10 percent. Therefore, the stock
must be selling for USD 110 today.
True
False
Stocks pay dividends. The 10 percent return could be from a USD 10 dividend payment, which means the stock
would still be trading for USD 100 today.
Question 2
The capital gains yield plus the dividend yield on a security is called the
geometric return.
variance of returns.
current yield.
total return.
Question 3
A capital gain occurs when
the purchase price is less than the selling price.
the selling price is less than the purchase price.
the selling price is the same as the dividend.
there is no dividend paid.
Question 4
The Zolo Company just declared that it is increasing its annual dividend from USD 1.00 per share to USD 1.25 per
share. If the stock price remains constant, then
the capital gains yield will decrease.
the capital gains yield will increase.
the dividend yield will increase.
the dividend yield will decrease.
Question 5
A symmetric, bell-shaped frequency distribution that is completely defined by its mean and standard deviation is
the ____________ distribution.
gamma
uniform
bi-modal
normal
Question 6
Which of the following statements is false?
Variance is equal to the square root of standard deviation.
Standard deviation is equal to the square root of the variance.
Variance can never be negative.
Standard deviation is a measure of risk.
Question 7
Which of the following investment classes had the greatest average return in the historical data?
Short term government bonds
Long term government bonds
Large US stocks
Small US stocks
Question 8
Which of the following investment classes had the greatest variability in returns in the historical data?
Short term government bonds
Long term government bonds
Large US stocks
Small US stocks
Question 9
Which of the following statements is correct if investors are risk averse?
The greater the risk associated with an investment, the lower the return investors expect from it.
When choosing between two investments that have the same level of risk, investors prefer the investment with
the higher return.
If two investments have the same expected return, investors prefer the riskier alternative.
When choosing between two investments that have the same level of risk, investors prefer the investment with the
lower return.
Question 10
Common stock portfolios that offer the highest expected return for a given level of risk are known as
efficient portfolios.
inefficient portfolios.
unusual portfolios.
empty portfolios.
Question 11
The excess return you earn by moving from a relatively risk-free investment to a risky investment is called the
geometric average return.
arithmetic average return.
time premium.
risk premium.
Question 12
Which of the following risks is considered a "non-diversifiable" risk in common stock returns?
the company CEO becomes ill
the company receives a new contract for a large purchase of its products
the US Congress eliminates the corporate income tax
the company loses a lawsuit filed by its employees
Question 13
The statistic calculated as the weighted average of the squared deviations from the mean is known as
standard deviation
standard weight
standard fit
variance
Question 14
The standard deviation of the stock returns can be calculated as the
square root of the average return.
average squared difference between the actual return and the average return.
square root of the variance.
variance squared.
Question 15
If a random variable follows a normal distribution, what is the probability that the random variable is larger than
+1.96 standard deviations from the mean?
1.25 percent
2.50 percent
3.75 percent
5.00 percent
Question 16
If we assume investors a risk-averse and they must choose between two stocks with the same expected return,
which stock will they choose?
the stock with the larger variance
the stock with the larger standard deviation
the stock with the smaller Sharpe Ratio
the stock with the larger Sharpe Ratio
Question 17
Friendly Airlines stock is currently selling for USD 37.50 per share. If the stock pays a dividend of USD 1.25 and the
stock price in one year is USD 40.00, what is the total return on the stock?
change in price: 40.00 - 37.50 = 2.50 (known as a capital gain)
(2.50 + 1.25) / 37.50 = 10 percent
Question 18
In a game of chance, the probability of winning USD 50 is 60 percent and the probability of losing USD 50 is 40
percent. What is the expected value of the game?
(0.60 x 50) + (0.40 x -50) = 10
Question 19
Barbara is considering investing in a stock and the return on that investment is sensitive to economic conditions.
Her analysis suggests that there will be four possible economic states as follows. What is the expected return on
the stock?
STATE PROBABILITY RETURN %
Boom 0.10 20
Good 0.40 15
Level 0.30 10
Slump 0.20 -5
0.10 x 20 = 2
+ 0.40 x 15 = 6
+ 0.30 x 10 = 3
+ 0.20 x -5 = -1
Solve for E[R]: 2 + 6 + 3 - 1 = 10
Question 20
Using the information in the question above, what is the standard deviation of the return on Barbara's stock?
0.10 x (20 - 10)2 = 10
+ 0.40 x (15 - 10)2 = 10
+ 0.30 x (10 - 10)2 = 0
+ 0.20 x (-5 - 10)2 = 45
Solve for variance: 10 + 10 + 0 + 45 = 65
Solve for standard deviation: SQRT(65) = 8.06
Question 21
What is the expected return on a portfolio comprised of USD 3,000 in stock A and USD 5,000 in stock B?
STATE PROBABILITY RETURN % (A) RETURN % (B)
Boom 0.20 30 50
Normal 0.80 10 10
E[RA] = (0.20 x 30) + (0.80 x 10) = 14
E[RB] = (0.20 x 50) + (0.80 x 10) = 18
E[RP] = (3/8 x 14) + (5/8 x 18) = 16.50
Question 22
Suppose you invest USD 4,500 in Stock A and USD 5,500 in Stock B. The variance of Stock A is 10 percent, the
variance of Stock B is 20 percent, and the covariance between the two stocks is 1.87 percent. What is the standard
deviation of your portfolio?
Solve for variance: 0.452 x 10 + 0.552 x 20 + 2 x 0.45 x 0.55 x 1.87 = 9
Solve for standard deviation: SQRT(9) = 3
Question 23
Suppose the risk free interest rate is 4.20 percent, the market risk premium is 6.00 percent and the beta for AAPL
stock is 1.30. What is the expected return on AAPL stock?
(RM - Rf) is known as the "market risk premium."
(RM - Rf) = 6.00.
use the CAPM: Ri = Rf + B x (RM - Rf)
Ri = 4.20 + 1.30 x 6.00 = 12
Ri = 12
Question 24
A stock has a mean return of 3.25 percent with a standard deviation of 20 percent. Based on this information, what
is the 95 percent probability range for the return in any one given year assuming the normal distribution?
-16.25 to 22.65
-24.50 to 34.25
-35.95 to 42.45
-54.75 to 61.50
3.25 - 1.96 x 20 = -35.95
3.25 + 1.96 x 20 = 42.45
Question 25
A stock has an expected rate of return of 8.3 percent and a standard deviation of 6.4 percent. Which one of the
following best describes the probability that this stock will lose 11 percent or more in any one given year?
less than 0.5 percent
less than 1.0 percent
less than 1.5 percent
less than 2.5 percent
-11 percent is more than 3 standard deviations from the mean
8.3 - (3 x 6.4) = -10.9
Problem Set 8: Bond Valuation and Structure of Interest Rates
Question 1
The stated interest payment, in dollars, made on a bond each period is called the bond's
coupon.
face value.
yield to maturity.
coupon rate.
Question 2
The principal amount of a bond that is repaid at the end of the loan term is called the bond's
coupon.
face value.
yield to maturity.
coupon rate.
Question 3
The rate of return required by investors in the market for owning a bond is called the
coupon.
face value.
yield to maturity.
coupon rate.
Question 4
The most common purchasers of bonds are
life insurance companies and pension funds.
speculators.
The US Government
James Bond.
Question 5
Which one of the following statements about vanilla bonds is false?
They have fixed coupon payments.
The face value, or par value, for most corporate bonds is $1,000.
Coupon payments are usually made quarterly.
The bond's coupon rate is calculated as the annual coupon payment divided by the bond's face value.
Question 6
Which one of the following statements is true?
All else equal long-term bonds have lower price volatility than short-term bonds.
There is an inverse relation between bond prices and market interest rates.
All else equal short-term bonds are more risky than long-term bonds.
All else equal US government bonds are more risky than corporate bonds.
Question 7
If the bond's coupon rate is equal to the market rate then the bond will sell at a price
equal to its face value
greater than its face value
less than its face value
equal to its foreign currency value, e.g., its price in British pounds
Question 8
A bond with a face value of 1,000 USD that sells for less than 1,000 USD in the market is called a _____________
bond.
par
discount
premium
zero coupon
Question 9
Bonds sell at a premium when the market rate of interest is
equal to the risk-free rate.
less than the bond's coupon rate
greater than the bond's coupon rate.
equal to the bond's coupon rate.
Question 10
Bonds sell at a discount when the market rate of interest is
equal to the risk-free rate.
greater than the bond's coupon rate
less than the bond's coupon rate.
equal to the bond's coupon rate.
Question 11
When calculating the price of a bond that pays a semiannual coupon one needs to
use double the number of years until maturity for the number of payments
use half the annual coupon payment
use half the annual rate of return as the discount rate
all of the above
Question 12
The yield to maturity of a bond is the discount rate that makes the present value of the coupon and principal
payments
more than the price of the bond
equal to zero
equal to the price of the bond
less than the price of the bond
Question 13
An investor owns a 10-year US government bond with a 9 percent coupon rate. If the yield-to-maturity on the bond
is 8 percent then this bond is selling for
its par value.
a discount.
a premium.
its face value.
Question 14
Which of the following statements is true?
For a given change in market interest rates, the prices of higher-coupon bonds change more than the prices of
lower-coupon bonds.
If market interest rates rise, a 1-year bond will fall in value more than a 10-year bond.
If market interest rates rise, a 10-year bond will fall in value more than a 1-year bond.
If market interest rates rise, bond prices will rise.
Question 15
The three economic factors that affect the shape of the yield curve are
the real rate of interest, the expected rate of inflation, and marketability.
the real rate of interest, the expected rate of inflation, and interest rate risk.
the nominal rate of interest, the expected rate of inflation, and default risk.
the real rate of interest, the nominal rate of interest, and currency risk.
Question 16
Downward-slopping yield curves are usually observed
before the beginning of a recession.
always.
never.
when the economy is growing quickly.
Question 17
BA Corp is issuing a 10 year bond with a coupon rate of 8 percent and a par value of 1,000 USD. The market interest
rate on similar bonds is currently 6 percent. If the coupon payments are made annually, what is the value of this
bond?
N = 10
I = 6
PV = ??? = 1,147
PMT = 80
FV = 1,000
Question 18
Knight, Inc. has issued a 3 year bond with a 1,000 USD par value and an annual coupon rate of 6 percent. The
current market rate of interest is 5 percent. What is the value of this bond if the coupon payments are made
semiannually?
N = 3 x 2 = 6
I = 5 / 2 = 2.50
PV = ??? = 1,028
PMT = 60 / 2 = 30
FV = 1,000
Question 19
Regatta, Inc., has bonds outstanding that pay an 8.250 percent coupon rate on a 1,000 USD face value. Investors
buying the bond today can expect to earn a yield to maturity of 6.875 percent. How many years until the bonds
mature if the current value of the bonds is 1,056.57 USD and payments are made annually?
N= ??? = 5
I/Y = 6.875
PV = -1,056.57
PMT = 82.50
FV = 1,000
Question 20
Diane Carter is interested in buying a five year zero coupon bond with a face value of 5,000 USD.If the market
interest rate on these types of bonds is currently 9 percent, what is the current price of this bond?
N = 5
I = 9
PV = ??? = 3,250
PMT = 0
FV = 5,000
Question 21
Diane Carter is interested in buying a five year zero coupon bond with a face value of 5,000 USD. If the current
market value of the bond is 3,104.61 USD, what is the bond's yield to maturity?
N = 5
I/Y = ??? = 10
PV = -3,104.61
PMT = 0
FV = 5,000
Question 22
Rudy Sandberg wants to invest in five year bonds that are currently priced at 850.00 USD. The bonds have a coupon
rate of 10 percent and semiannual coupon payments. If the par value of the bonds is 1,000 USD, what is the bond's
effective annual yield (EAY)?
N = 5 x 2 = 10
I = ??? =7.15, semiannual
PV = -850
PMT = 100 / 2 = 50
FV = 1,000
7.15 is a semiannual rate
Solve for EAY: (1.0715)2 - 1 = 14.81 percent
Question 23
Kafki Co. offers a zero coupon bond with an 10 percent yield to maturity. The bond matures in 15 years with annual
compounding. What is the current price of a 1,000 USD face value bond?
1,000 / (1.10)15 = 239.39
Or
N = 15
I/Y = 10
PV = ??? = 239.39
PMT = 0
FV = 1,000
Question 24
Kafki Co. offers a zero coupon bond with an 10 percent yield to maturity. The bond matures in 15 years with
monthly compounding. What is the current price of a 1,000 USD face value bond?
1,000 / (1 + 0.10/12)15 x 12 = 224.52
Or
N = 15 x 12 = 180
I/Y = 10 / 12 = 0.833333
PV = ??? = 224.52
PMT = 0
FV = 1,000
Question 25
You own a five year bond with a face value of 1,000 USD and a coupon rate of five percent with annual payments.
The bond is currently worth 810.46 USD. If market interest rates remain unchanged, what will be the value of the
bond next year when there are four years left until maturity?
Step 1
N = 5
I = ??? =10
PV = -810.46
PMT = 50
FV = 1,000
Step 2
N = 4
I = 10
PV = ??? =842
PMT = 50
FV = 1,000
