1)
Future values???For the case shown in the
following? table, calculate the future value of the single cash flow deposited
today at the end of the deposit period if the interest is compounded annually
at the rate specified.???(Click on the icon located on the? top-right corner of
the data table below in order to copy its contents into a? spreadsheet.)
|
Single cash flow |
Interest rate |
Deposit period? (years) |
|
|
?$4 4,000 |
5?% |
3 |
The future value is ?$_________. ?(Round to
the nearest? cent.)
2)
Future value of an annuity Using the values?
below, answer the questions that follow.???(Click on the icon located on the?
top-right corner of the data table below in order to copy its contents into a?
spreadsheet.)
|
Amount of annuity |
Interest rate |
Deposit period? (years) |
|
|
?$1,500 |
4?% |
5 |
a.
Calculate the future value of the? annuity,
assuming that it is
?(1)
An ordinary annuity.
?(2)
An annuity due.
b.?Compare your findings in parts a?(1) and
a?(2). All else being? identical, which
type of annuity—ordinary or annuity due—is preferable as an? investment?
Explain why
a.? (1)
The future value of the ordinary annuity is ?$________ (Round to the
nearest? cent.)
?(2)
The future value of the annuity due is ?$_______.?(Round to the nearest?
cent.)
b.
Compare your findings in parts a?(1) and
a?(2). All else being? identical, which
type of annuity is preferable as an? investment?(Select the best answer?
below.)
Annuity? due, because it yields a greater
future value.
Ordinary? annuity, because it yields a
greater future value.
3)
Present value of an annuity?Consider the
following case.???(Click on the icon located on the? top-right corner of the
data table below in order to copy its contents into a? spreadsheet.)
Amount of annuity Interest rate Period? (years)
$20,000
12?% 6
A)
Calculate the present value of the annuity
assuming that it is
?(1)
An ordinary annuity.
?(2)
An annuity due.
B)
Compare your findings in parts a?(1) and
a?(2). All else being? identical, which
type of annuity—ordinary or annuity—yields a higher present? value? Explain why
The present value of the ordinary annuity is ?$_________Round
to the nearest? cent.)
The present value of the annuity due is ?$__________.???(Round
to the nearest? cent.)
b.?Compare your findings in parts a?(1) and a?(2). All else being? identical, which type of
annuity yields a higher present? value????(Select the best answer? below.)
Annuity? due, because all else being? identical, it will
yield a higher present value.
Ordinary? annuity, because all else being? identical, it
will yield a higher present value.
4) Present value – Mixed streams?Consider the mixed streams
of cash flows shown in the following? table,
|
Cash flow stream |
||||
|
Year |
A |
B |
||
|
1 |
?$52,500 |
?$17,500 |
||
|
2 |
?$43,750 |
?$26,250 |
||
|
3 |
?$35,000 |
?35,000 |
||
|
4 |
?$26,250 |
?$43,750 |
||
|
5 |
$17,500 |
$52,500 |
||
|
Totals |
$175,000 |
$175,000 |
a. Find the present value of each stream
using a 11?% discount rate.
b. Compare the calculated present values and
discuss them in light of the undiscounted cash flows totaling ?$175,000 in each
case
a. The present value of the cash flows of stream A is ?$________. ?(Round to the nearest? dollar.)
The present value of the cash flows of stream B is
?$______. ?(Round to the nearest?
dollar.)
b. Compare the calculated present values and discuss them in
light of the undiscounted cash flows totaling ?$175,000 in each case.???(Select
the best answer? below.)
A. Cash flow stream? A, with a present value of ?$136,075?,
is higher than cash flow stream? B’s present value of ?$122,638 because the
larger cash inflows occur in A in the early years when their present value is?
greater, while the smaller cash flows are received further in the future.
B. Cash flow stream? A, with a present value of ?$136,075?,
is lower than cash flow stream? B’s present value of ?$122,638 because the
smaller cash inflows occur in A in the early years when their present value is?
greater, while the larger cash flows are received further in the future.
C. Cash flow stream? A, with a present value of ?$122,638?,
is higher than cash flow stream? B’s present value of ?$136,075 because the
larger cash inflows occur in A in the early years when their present value is?
greater, while the smaller cash flows are received further in the future.
D. Cash flow stream? A, with a present value of ?$136,075?,
is higher than cash flow stream? B’s present value of ?$122,638 because the
larger cash inflows occur in A in the later years when their present value is?
greater, while the smaller cash flows are received in the earlier years.
5) Changing compounding frequency?Using? annual, semiannual,
and quarterly compounding? periods, (1) calculate the future value if ?$8,000
is deposited initially at 11?% annual interest for 7 ?years, and? (2) determine
the effective annual rate?????(EAR?).
Annual Compounding
?(1) The future?
value, FV Subscript nFVn?, is ?$___________.
?(Round to the nearest? cent.)
?(2) If the 11?%
annual nominal rate is compounded? annually, the EAR is ____%. ?(Round to two decimal? places.)
Semiannual Compounding
?(1) The future?
value, FV Subscript nFVn?, is $?______.
?(Round to the nearest? cent.)
?(2) If the 11?%
annual nominal rate is compounded? semiannually, the EAR is ______?%. ?(Round to two decimal? places.)
Quarterly Compounding
?(1) The future?
value, FV Subscript nFVn?, is ?$______.
?(Round to the nearest? cent.)
?(2) If the 11?%
annual nominal rate is compounded? quarterly, the EAR is______?%. ?(Round to two decimal? places.)
6) Loan amortization schedule Personal Finance Problem Joan
Messineo borrowed ?$17,000 at a 17?% annual rate of interest to be repaid over
3 years. The loan is amortized into
three? equal, annual,? end-of-year payments.
a. Calculate the? annual, end-of-year loan payment.
b. Prepare a loan amortization schedule showing the interest
and principal breadown of each of the three loan payments.
c. Explain why the interest portion of each payment declines
with the passage of time.
a. The amount of the? equal, annual,? end-of-year loan
payment is ?$__________. ?(Round to the
nearest? cent.)
b. Prepare a loan amortization schedule showing the interest
and principal breakdown of each of the three loan payments. Many financial calculators have an
amortization function which makes this process easy. Once the payment is determined in step a?
above, you can use the AMORT function to calculate the interest? paid,
principal paid and ending loan balance for each payment period. You should consult your calculator
instructions for specific details pertaining to your calculator.
What is the account balance at the beginning of year? 1?
?(Round to the nearest? cent.)
?
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$ |
What is the amount of the loan payment at the end of year?
1??? (Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$ |
What portion of the payment is applied to interest in year?
1????(Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$ |
What portion of the payment is applied to the principal in
year? 1????(Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?2,890.00 |
?$ |
What is the principal balance at the end of year?
1????(Round to the nearest? cent.)
|
|
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$ |
What is the account balance at the beginning of year?
2????(Round to the nearest? cent.)
|
|
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$ |
What is the amount of the loan payment at the end of year?
2????(Round to the nearest? cent.)
|
|
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$ |
What portion of the payment is applied to interest in year?
2????(Round to the nearest? cent.)
|
|
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$7,693.75 |
?$ |
What portion of the payment is applied to the principal in
year? 2????(Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$7,693.75 |
?$2,073.36 |
?$ |
What is the principal balance at the end of year?
2????(Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$7,693.75 |
?$2,073.36 |
?$5,620.39 |
?$ |
What is the account balance at the beginning of year?
3????(Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$7,693.75 |
?$2,073.36 |
?$5,620.39 |
?$6,575.86 |
|
3 |
?$ |
What is the amount of the loan payment at the end of year?
3? ? (Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$7,693.75 |
?$2,073.36 |
?$5,620.39 |
?$6,575.86 |
|
3 |
?$6,575.86 |
?$ |
What portion of the payment is applied to interest in year?
3????(Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$77,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$7,693.75 |
?$2,073.36 |
?$5,620.39 |
?$6,575.86 |
|
3 |
?$6,575.86 |
?$7,693.75 |
?$ |
What portion of the payment is applied to the principal in
year? 3????(Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$7,693.75 |
?$2,073.36 |
?$5,620.39 |
?$6,575.86 |
|
3 |
?$6,575.86 |
?$7,693.75 |
?$1,117.90 |
?$ |
What is the principal balance at the end of year?
3????(Round to the nearest? cent.)
|
?End-of-year |
?Beginning- ?of-year principal |
Loan payment |
Payments |
?End-of-year principal |
|
|
Interest |
Principal |
||||
|
1 |
?$17,000 |
?$7,693.75 |
?$2,890.00 |
?$4,803.75 |
?$12,196.25 |
|
2 |
?$12,196.25 |
?$7,693.75 |
?$2,073.36 |
?$5,620.39 |
?$6,575.86 |
|
3 |
?$6,575.86 |
?$7,693.75 |
?$1,117.90 |
?$6,575.85 |
?$ |
c. Explain why the interest portion of each payment declines
with the passage of time.???(Select the best answer? below.)
A. Through annual? end-of-the-year payments, the interest
balance of the loan is? declining, causing less principal to be accrued on the
balance.
B. Through annual? end-of-the-year payments, the principal
balance of the loan is? declining, causing less interest to be accrued on the
balance.
C. Through annual? end-of-the-year payments, the principal
balance of the loan is? increasing, causing less interest to be accrued on the
balance.
D. Through annual? end-of-the-year payments, the principal
balance of the loan is? declining, causing more interest to be accrued on the
balance.
7) Bond interest payments before and after taxes Charter
Corp. has issued 2,986 debentures with a total principal value of
?$2,986,000. The bonds have a coupon
interest rate of 5?%.
a. What dollar amount of interest per bond can an investor
expect to receive each year from? Charter?
b. What is? Charter’s total interest expense per year
associated with this bond? issue???
c. Assuming that Charter is in a 35?% corporate tax?
bracket, what is the? company’s net? after-tax interest cost associated with
this bond? issue??
a. The dollar amount of interest per bond an investor can
expect to receive each year from Charter is ?$______?(Round to the nearest?
dollar.)
b. Charter’s total interest expense per year associated with
this bond issue is ?$_________. ?(Round
to the nearest? dollar.)
c. Assuming that Charter is in a 35?% corporate tax?
bracket, the? company’s net? after-tax interest cost associated with this bond
issue is ?$________. ?(Round to the
nearest? dollar.)
8) Valuation of assets
Using the information provided in the following? table, find the value
of each? asset:
|
|
||||
|
Asset |
End of Year |
Amount |
Appropriate required return |
|
|
A |
1 |
?$ |
3,000 |
17?% |
|
2 |
3,000 |
|||
|
3 |
3,000 |
|||
|
B |
1 through infinity? |
?$ |
200 |
14?% |
|
C |
1 |
?$ |
0 |
16?% |
|
2 |
0 |
|||
|
3 |
0 |
|||
|
4 |
0 |
|||
|
5 |
33,000 |
|||
|
D |
1 through 5 |
?$ |
1,900 |
11?% |
|
6 |
8,400 |
|||
|
E |
1 |
?$ |
3,000 |
14?% |
|
2 |
4,000 |
|||
|
3 |
6,000 |
|||
|
4 |
8,000 |
|||
|
5 |
5,000 |
|||
|
6 |
2,000 |
The value of Asset A is ?$_________(Round to the nearest? cent.)
The value of Asset B is ?$__________. ?(Round to the nearest? cent.)
The value of Asset C is ?$_________. ?(Round to the nearest? cent.)
The value of Asset D is ?$___________. ?(Round to the nearest? cent.)
The value of Asset E is ?$___________.?(Round to the
nearest? cent.)
9) Bond value and time—Constant required returns Pecos
Manufacturing has just issued a 15?-year, 15?% coupon interest? rate,
?$1,000?-par bond that pays interest annually. The required return is currently
18?%, and the company is certain it will remain at 18?% until the bond matures
in 15 years.
a. Assuming that the required return does remain at 18?%
until? maturity, find the value of the bond with? (1) 15 ?years, (2) 12? years,
(3) 9? years, (4) 6? years, (5) 3? years, (6) 1 year to maturity.
b. All else remaining the? same, when the required return
differs from the coupon interest rate and is assumed to be constant to?
maturity, what happens to the bond value as time moves toward? maturity? Explain in light of the following? graph:
a. ? (1) The value of the bond with 1515 years to maturity
is ?$_____. ?(Round to the nearest?
cent.)
?(2) The value of the bond with 12 years to maturity is
?$____. ?(Round to the nearest? cent.)
?(3) The value of the bond with 9 years to maturity is
?$________. ?(Round to the nearest?
cent.)
?(4) The value of the bond with 6 years to maturity is
?$__________. ?(Round to the nearest?
cent.)
?(5) The value of the bond with 3 years to maturity is ?$________. ?(Round to the nearest? cent.)
?(6) The value of the bond with 1 year to maturity is
?$________. ? (Round to the nearest? cent.)
b. All else remaining the? same, when the required return
differs from the coupon interest rate and is assumed to be constant to?
maturity, what happens to the bond value as time moves toward?
maturity????(Select the best answer? below.)
A. The bond value approaches the amount of the last interest
payment.
B. The bond value approaches the par value.
C. The bond value approaches zero.
D. The bond value approaches infinity.
10) Bond valuation—Semiannual interest. Calculate the value
of each of the bonds shown in the following? table, all of which pay interest
semiannually.???(Click on the icon located on the? top-right corner of the data
table below in order to copy its contents into a? spreadsheet.)
|
|
Par Value |
Coupon interest rate |
Years to maturity |
Required stated annual return |
||||
|
A |
$1,000 |
8 |
?% |
10 |
10 |
?% |
||
|
B |
1,000 |
13 |
15 |
12 |
||||
|
C |
500 |
12 |
6 |
15 |
The value of bond A is ?$________ ? (Round to the nearest?
cent.)
The value of bond B is ?$_____. ?(Round to the nearest? cent.)
The value of bond C is ?$_______. ?(Round to the nearest?
cent.)
