,Solution manual for Basic Finance An Introduction
to Financial Institutions, Investments, and
Management , 13th Edition Herbert B. Mayo
Notes
1- All Chapters are step by step.
2- We have shown you 10 pages.
3- The file contains all Appendix and Excel
sheet if it exists.
4- We have all what you need, we make
update at every time. There are many
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5- If you think you purchased the wrong file
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, Solution and Answer Guide: Chapter 4: Securities Markets
Solution and Answer Guide
Mayo/Lavelle, Basic Finance: An Introduction to Financial
Institutions, Investments, and Management
Chapter 4: Securities Markets
EXERCISE SOLUTIONS
1. You purchase 100 shares for $50 per share ($5,000), and after a year the price rises to $60.
What will be the percentage return on your investment if you bought the stock on margin and the
margin requirement was (a) 25 percent, (b) 50 percent, and (c) 75 percent? (Ignore commissions,
dividends, and interest expense.)
Solution
If the stock rises from $50 to $60, the gain is $1,000 on the purchase of 100 shares. The return
on the individual's investment depends on the amount of margin.
a. If the margin requirement is 25 percent, the amount the investor must put up is $1,250 (0.25 x
$5,000), so the return is $1,000/$1,250 = 80%.
b. If the margin requirement is 50 percent, the return is 40 percent ($1,000/$2,500).
c. If the margin requirement is 75 percent, the required margin is $3,750 and the return is 26.7
percent ($1,000/$3,750).
Be certain to point out the $1,000 capital gain is the same in all three cases but that the
percentage return differs because the amount put up by the investor differs in each case.
2. Repeat Exercise 1 to determine the percentage return on your investment, but in this case
suppose the price of the stock falls to $40 per share. What generalization can be inferred from
your answers to Problems 1 and 2?
Solution
If the stock declines from $50 to $40, the loss is $1,000 on the purchase of 100 shares. The
return on the individual's investment once again depends on the amount of margin.
a. If the margin requirement is 25 percent, the amount the investor must put up is $1,250, and the
return is $1,000/$1,250 = −80%.
b. If the margin requirement is 50 percent, the return is −40 percent ($1,000/$2,500).
c. If the margin requirement is 75 percent, the percentage loss is −26.73 percent ($1,000/$3,750).
The generalization from Problems (1) and (2) is that the percentage return is affected by the
amount of margin and that the lower the margin requirement, the greater is the potential swing in
the return on the investor's funds.
3. A stock is currently selling for $45 per share. What is the gain or loss on the following
transactions?
Solution
a. $41.50 − $45 = −$3.50
b. $45 − $41.50 = $3.50
c. $54 − $45 = $9
d. $45 − $54 = −$9
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 1
website, in whole or in part.
, Solution and Answer Guide: Chapter 4: Securities Markets
In each case, the sale price is subtracted from the purchase price to determine the profit or loss.
Be certain to point out that the sale may occur before the purchase, which is the case in each of
the short sales.
4. A sophisticated investor, B. Graham, sold 500 shares short of Amwell, Inc. at $42 per share. The
price of the stock subsequently fell to $38 before rising to $49 at which time Graham covered the
position (that is, purchased shares to close the short position). What was the percentage gain or
loss on this investment?
Solution
Unfortunately, investor Graham did not cover the short sale after the stock declined but waited
until the price of the stock rose and thus sustained a loss of $7 per share for a total loss of
$3,500.
5. A year ago, Kim Altman purchased 200 shares of BLK, Inc. for $25.50 on margin. At that time the
margin requirement was 40 percent. If the interest rate on borrowed funds was 9 percent and she
sold the stock for $34, what is the percentage return on the funds she invested in the stock?
Solution
Cost of the shares: 200 × $25.50 = $5,100
Margin: $5,100 × 0.40 = $2,040
Funds borrowed: $5,100 − $2,040 = $3,060
Interest paid: $3,060 × 0.09 = $275.40
Profit on the stock: $6,800 − $5,100 = $1,700
Return on the investment: ($1,700 − $275.40)/$2,040 = 69.8%
6. Barbara buys 100 shares of DEM at $35 per share and 200 shares of GOP at $40 per share.
They buy on margin and the broker charges interest of 10 percent on the loan.
Solution
100 shares of DEM at $35 $3,500
200 shares of GOP at $40 $8,000
Total cost of securities $11,500
a. Required margin: 0.55 × $11,500 = $6,325
Amount borrowed: $11,500 − $6,325 = $5,175
b. Interest expense: 0.10 × $5,175 = $517.50
c. Loss on DEM stock: $2,900 − $3,500 = −$600
Loss on GOP stock: $6,400 − $8,000 = −$1,600
Net loss: −$2,200
d. Percentage loss including interest:
−($2,200 + $517.50)/$6,325 = −43%
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 2
website, in whole or in part.
, Solution and Answer Guide: Chapter 4: Securities Markets
7. After an analysis of Lion/Bear, Inc., Karl O’Grady has concluded that the firm will face financial
difficulty within a year. The stock is currently selling for $5 and O’Grady wants to sell it short. His
broker is willing to execute the transaction, but only if O’Grady puts up cash as collateral equal to
the amount of the short sale. If O’Grady does sell the stock short, what is the percentage return
he loses if the price of the stock rises to $7? What would be the percentage return if the firm went
bankrupt and folded?
Solution
Since the stock is sold short, the price increase causes a loss of $2 ($5 − $7) per share. Since
Mr. O'Grady put up 100 percent margin, the percentage loss is
−$2/$5 = −40.0%
If the price of the stock declined to $0, the percentage return is 100 percent.
Be certain to point out that the largest gain to the short seller occurs if the price of the stock
declines to zero, while in a long position there is no limit to the possible price increase. Of course,
in most cases, the price of the stock does not decline to zero, nor does it rise indefinitely.
8. Lisa Lasher buys 400 shares of stock on margin at $18 per share. If the margin requirement is 50
percent, how much must the stock rise for them to realize a
25-percent return on their invested funds? (Ignore dividends, commissions, and interest on
borrowed funds.)
Solution
The initial investment is $18 × 400 × 0.50 = $3,600. To realize a 25 percent return, the value of
the position in the stock must rise by $900 (0.25 × $3,600). The stock must increase by $2.25 per
share ($900/400 shares = $2.25).
9. A broker quotes GameStop stock (GME) with a bid-ask of $93.52–$93.62. You buy 10 shares
and then immediately decide to sell your 10 shares. The stock price has not changed at all, and
there are no commissions or taxes. How much money do you lose?
Solution
You buy at the higher price that the broker is asking: 10 shares × $93.62 = $936.20. You sell at
the lower price that the broker is bidding: 10 shares × $93.52 = $935.20. You receive only
$935.20 after paying $936.20, so you lose $1.00.
10. A broker quotes AMC Entertainment Holdings (AMC), a movie theater chain, at a bid-ask of
$15.94–$16.14 and you decide to buy 100 shares. The next day the stock price has changed,
and the broker quotes a bid-ask of $14.52–$14.72, and you sell your 100 shares. How much have
you gained or lost?
Solution
You buy at the higher ask price on the first day: 100 shares × $16.41 = $1,641. You sell at the
lower bid price the next day: 100 shares × 14.52 = $1,452. $1,452 − $1,641 = a loss of $189.
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 3
website, in whole or in part.
, Solution and Answer Guide: Solution and Answer Guide
Solution and Answer Guide
Mayo/Lavelle Basic Finance: An Introduction to Financial
Institutions, Investments, and Management 13e
Chapter 6: International Currency Flows
EXERCISE SOLUTIONS
1. If the price of a British pound is $1.82, how many pounds are necessary to purchase $1.00?
Solution
The number of pounds necessary to purchase $1 is $1.00/$1.82 = 0.5495 pounds
2. Last year Leather Boot, Inc. had investments in Paris worth 500,000 euros. At that time, the euro
was worth $1.20. Today the euro is trading for $1.30. What is the gain or loss in value of the
inventory expressed in dollars and in euros?
Solution
Value of the inventory:
Initially: 500,000 × $1.20 = $600,000
After the appreciation of the euro:
500,000 × $1.30 = $650,000
Net gain in dollars: $50,000
The value in terms of the euro is not changed.
3. Given the following information, determine the balance on the U.S. current account and capital
accounts:
Imports $211.5
Net income from foreign investments 32.3
Foreign investments in the United States 7.7
Government spending abroad 4.6
Exports 182.1
U.S. investments abroad 24.7
Foreign securities bought by the United States 4.9
U.S. securities bought by foreigners 2.8
Purchases of foreign short-term securities 6.5
Foreign purchases of U.S. short-term securities 9.1
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 1
website, in whole or in part.
, Solution and Answer Guide: Solution and Answer Guide
Solution
Current Account Debit Credit Balance
Exports $182.1
Imports $211.5
Net difference −29.4
Government spending abroad 4.6
Net income from foreign investments 32.3
Balance on current account −$1.7
Capital Account
Direct investments abroad 24.7
Foreign investments in the United States 7.7
Purchases of foreign securities 4.9
Foreign purchases of U.S. securities 2.8
Purchases of foreign short-term securities 6.5
Foreign purchases of U.S. short-term securities 9.1
Balance on capital account −$16.5
There is a currency outflow of $1.7 on the current account and $16.5 on the capital account for a
total of $18.2. Point out that the income from previous foreign investments almost offsets the cash
outflow caused by the merchandise trade deficit plus the government spending. However, there
was no offsetting currency inflow to cover the direct foreign investments. Also point out that the
currency that flowed out of the U.S. did not disappear. The currency outflow had to be financed
somehow such as the drawing down of the U.S. holdings of foreign reserves.
4. If 1 Canadian dollar buys U.S. $0.78, and 1 U.S. dollar buys 21 Mexican pesos, how many
Canadian dollars can you buy with 1,000 Mexican pesos?
Solution
1,000 Mexican pesos × (1 U.S. dollar / 21 Mexican pesos) × (1 Canadian dollar / U.S. $0.78) =
1, / 0.78 = 61.05 Canadian dollars.
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 2
website, in whole or in part.
, Solution and Answer Guide: Chapter 7: Financial Tools
Solution and Answer Guide
Mayo/Lavelle, Basic Finance: An Introduction to Financial
Institutions, Investments, and Management 13e
Chapter 7: Financial Tools
EXERCISE SOLUTIONS
1. You invest $1,000 in a certificate of deposit that matures after ten years and pays 5 percent
interest, which is compounded annually until the certificate matures.
a. How much interest will you earn if the interest is left to accumulate?
b. How much interest will you earn if the interest is withdrawn each year?
c. Why are the answers to question 1(a) and question 1(b) different?
Solution
a. $1,000(1 + 0.05)10 = X
X = $1,000(1.629) = $1,629
$1,000 grows to $1,629 at 5% for ten years, of which $629 in interest. The 1.629 is the
interest factor for the future value of $1 for ten years at 5%.
(PV = −1,000; N = 10; I = 5; PMT = 0; and FV = ? = 1,629)
b. If the interest is withdrawn each year, the investor receives $50 annually and $500 over the
lifetime of the investment.
c. The difference in the amount of interest ($629 − $500 = $129) is the result of compounding.
2. A person deposits $3,000 annually in a retirement account that earns 8 percent.
a. How much will be in the account when the individual retires at the age of 65 if the savings
program starts when the person is age 40?
b. How much additional money will be in the account if the saver defers retirement until age 70
and continues the contributions?
c. How much additional money will be in the account if the saver discontinues the contributions
at age 65 but does not retire until age 70?
Solution
a. X = $3,000(73.106) = $219,318
(73.106 is the interest factor for the future sum of an annuity of $1 at 8% for 25 years.)
(PV = 0; N = 25; I = 8; PMT = -3,000; and FV = ? = 219,318)
b. X = $3,000(113.283) = $339,849
(113.283 is the interest factor for the future sum of an annuity of $1 at 8% for 30 years.)
(PV = 0; N = 30; I = 8; PMT = −3,000; and FV = ? = 339,850)
The additional funds:
$339,849 − $219,318 = $120,531
($120,532 if a financial calculator is used.)
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 1
website, in whole or in part.
, Solution and Answer Guide: Chapter 7: Financial Tools
Leaving the funds in the account and continuing the annual contribution for five additional
years increases the retirement funds by over $120,000.
c. In this question the individual stops making the contribution but does not draw on the fund.
The amount grows to:
$219,318(1 + 0.08)5 = $219,318(1.469) = $322,178
(1.469 is the interest factor for the future value of $1 at 8% for five years.)
(PV = −219,318; N = 5; I = 8; PMT = 0; and FV = ? = 322,250)
The difference in (b) and (c) is
$339,849 − $322,178 = $17,671
3. A 45-year-old woman decides to put funds into a retirement plan. She can save $2,000 a year
and earn 6 percent on this savings. How much will she have accumulated if she retires at age
65? At retirement how much can she withdraw each year for 20 years from the accumulated
savings if the savings continue to earn 6 percent?
Solution
$2,000(36.786) = $73,572
(36.786 is the interest factor for the future value of an annuity of $1 at 6% for
20 years.)
(PV = 0; N = 20; I = 6; PMT = −2,000; and FV = ? = 73,571)
The individual has accumulated $73,571. This will permit withdrawals of $6,414 a year for twenty
years:
$73,571 = X(11.470)
X = $6,414
(PV = 73,571; N = 20; I = 6; FV = 0; and PMT = ? = 6,414)
4. You annually invest $1,500 in an individual retirement account (IRA) starting at the age of 20 and
make the contributions for 10 years. Your twin sister does the same starting at age 30 and makes
the contributions for 30 years. Both of you earn 7 percent annually on your investment. Who has
the larger amount at age 60?
(Exercises 2 through 4 illustrate the basic elements of pension plans. A sum of money is
systematically set aside. It earns interest so that by retirement a considerable amount has been
accumulated. Then the retired person draws on the fund until it is exhausted, or until death
occurs, in which case the remainder of the fund becomes part of the estate. Of course, while the
retired person draws on the fund, the remaining principal continues to earn interest.)
Solution
Your account:
$1,500(FVAIF) = $1,500(13.816) = $20,724
(PV = 0; N = 10; I = 7; PMT = -1,500, and FV = ? = 20,725)
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 2
website, in whole or in part.
, Solution and Answer Guide: Chapter 7: Financial Tools
$20,724(FVAIF) = $20,724(7.612) = $157,751
(PV = −20,724; N = 30; I = 7; PMT = 0; and FV = ? = 157,757)
Your sister's account:
$1,500(FVAIF) = $1,500(94.461) = $141,692
(PV = 0; N = 30; I = 7; PMT = -1500, and FV = ? = 141,692)
This Exercise illustrates the importance of starting contributions to a retirement account as early
as possible.
5. Holly wants to have $200,000 to send a recently born child to college. She sets up a 529 plan and
wants to know how much she must invest at the end of each year for the next 18 years if the
funds can earn 5 percent. If she can earn 7 percent, how much less will she have to invest each
year?
Solution
This Exercise also illustrates the future value of an annuity except the future value is known and
the amount of the annual contribution (PMT) is the unknown.
X(28.132) = $200,000
X = $200,000/28.132 = $7,109
(28.132 is the interest factor for the future sum of an annuity of $1 at 5% for 18 years.)
(PV = 0; N = 18; I = 5; FV = 200,000; and PMT = ? = −7,109)
If Holly starts saving for college expenses early, the required annual amount may be modest. You
may wish to use this Exercise to start a discussion of tax-advantaged plans for saving for college.
In addition, since college costs are continuing to rise, the $200,000 may be inadequate 18 years
from now.
If Holly can increase the return to 7 percent, the required annual contribution decreases by
$7,109 – 5,883 = $1,226.
X(33.999) = $200,000
X = $200,000/33.999 = $5,883
(33.999 is the interest factor for the future sum of an annuity of $1 at 5% for 18 years.)
(PV = 0; N = 18; I = 7; FV = 200,000; and PMT = ? = −5,883)
6. A widow currently has a $93,000 investment that yields 6 percent annually. Can she withdraw
$14,000 for the next ten years? Would your answer be different if the yield were 9 percent?
Solution
To answer this question, determine the amount that can be withdrawn:
$93,000 = X(PVAIF)
$93,000 = X(7.360)
X = $12,636
(PV = 93,000; N = 10; I = 6; FV = 0; and PMT = ? = −12,636)
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 3
website, in whole or in part.
to Financial Institutions, Investments, and
Management , 13th Edition Herbert B. Mayo
Notes
1- All Chapters are step by step.
2- We have shown you 10 pages.
3- The file contains all Appendix and Excel
sheet if it exists.
4- We have all what you need, we make
update at every time. There are many
new editions waiting you.
5- If you think you purchased the wrong file
You can contact us at every time, we can
replace it with true one.
Our email:
, Solution and Answer Guide: Chapter 4: Securities Markets
Solution and Answer Guide
Mayo/Lavelle, Basic Finance: An Introduction to Financial
Institutions, Investments, and Management
Chapter 4: Securities Markets
EXERCISE SOLUTIONS
1. You purchase 100 shares for $50 per share ($5,000), and after a year the price rises to $60.
What will be the percentage return on your investment if you bought the stock on margin and the
margin requirement was (a) 25 percent, (b) 50 percent, and (c) 75 percent? (Ignore commissions,
dividends, and interest expense.)
Solution
If the stock rises from $50 to $60, the gain is $1,000 on the purchase of 100 shares. The return
on the individual's investment depends on the amount of margin.
a. If the margin requirement is 25 percent, the amount the investor must put up is $1,250 (0.25 x
$5,000), so the return is $1,000/$1,250 = 80%.
b. If the margin requirement is 50 percent, the return is 40 percent ($1,000/$2,500).
c. If the margin requirement is 75 percent, the required margin is $3,750 and the return is 26.7
percent ($1,000/$3,750).
Be certain to point out the $1,000 capital gain is the same in all three cases but that the
percentage return differs because the amount put up by the investor differs in each case.
2. Repeat Exercise 1 to determine the percentage return on your investment, but in this case
suppose the price of the stock falls to $40 per share. What generalization can be inferred from
your answers to Problems 1 and 2?
Solution
If the stock declines from $50 to $40, the loss is $1,000 on the purchase of 100 shares. The
return on the individual's investment once again depends on the amount of margin.
a. If the margin requirement is 25 percent, the amount the investor must put up is $1,250, and the
return is $1,000/$1,250 = −80%.
b. If the margin requirement is 50 percent, the return is −40 percent ($1,000/$2,500).
c. If the margin requirement is 75 percent, the percentage loss is −26.73 percent ($1,000/$3,750).
The generalization from Problems (1) and (2) is that the percentage return is affected by the
amount of margin and that the lower the margin requirement, the greater is the potential swing in
the return on the investor's funds.
3. A stock is currently selling for $45 per share. What is the gain or loss on the following
transactions?
Solution
a. $41.50 − $45 = −$3.50
b. $45 − $41.50 = $3.50
c. $54 − $45 = $9
d. $45 − $54 = −$9
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 1
website, in whole or in part.
, Solution and Answer Guide: Chapter 4: Securities Markets
In each case, the sale price is subtracted from the purchase price to determine the profit or loss.
Be certain to point out that the sale may occur before the purchase, which is the case in each of
the short sales.
4. A sophisticated investor, B. Graham, sold 500 shares short of Amwell, Inc. at $42 per share. The
price of the stock subsequently fell to $38 before rising to $49 at which time Graham covered the
position (that is, purchased shares to close the short position). What was the percentage gain or
loss on this investment?
Solution
Unfortunately, investor Graham did not cover the short sale after the stock declined but waited
until the price of the stock rose and thus sustained a loss of $7 per share for a total loss of
$3,500.
5. A year ago, Kim Altman purchased 200 shares of BLK, Inc. for $25.50 on margin. At that time the
margin requirement was 40 percent. If the interest rate on borrowed funds was 9 percent and she
sold the stock for $34, what is the percentage return on the funds she invested in the stock?
Solution
Cost of the shares: 200 × $25.50 = $5,100
Margin: $5,100 × 0.40 = $2,040
Funds borrowed: $5,100 − $2,040 = $3,060
Interest paid: $3,060 × 0.09 = $275.40
Profit on the stock: $6,800 − $5,100 = $1,700
Return on the investment: ($1,700 − $275.40)/$2,040 = 69.8%
6. Barbara buys 100 shares of DEM at $35 per share and 200 shares of GOP at $40 per share.
They buy on margin and the broker charges interest of 10 percent on the loan.
Solution
100 shares of DEM at $35 $3,500
200 shares of GOP at $40 $8,000
Total cost of securities $11,500
a. Required margin: 0.55 × $11,500 = $6,325
Amount borrowed: $11,500 − $6,325 = $5,175
b. Interest expense: 0.10 × $5,175 = $517.50
c. Loss on DEM stock: $2,900 − $3,500 = −$600
Loss on GOP stock: $6,400 − $8,000 = −$1,600
Net loss: −$2,200
d. Percentage loss including interest:
−($2,200 + $517.50)/$6,325 = −43%
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 2
website, in whole or in part.
, Solution and Answer Guide: Chapter 4: Securities Markets
7. After an analysis of Lion/Bear, Inc., Karl O’Grady has concluded that the firm will face financial
difficulty within a year. The stock is currently selling for $5 and O’Grady wants to sell it short. His
broker is willing to execute the transaction, but only if O’Grady puts up cash as collateral equal to
the amount of the short sale. If O’Grady does sell the stock short, what is the percentage return
he loses if the price of the stock rises to $7? What would be the percentage return if the firm went
bankrupt and folded?
Solution
Since the stock is sold short, the price increase causes a loss of $2 ($5 − $7) per share. Since
Mr. O'Grady put up 100 percent margin, the percentage loss is
−$2/$5 = −40.0%
If the price of the stock declined to $0, the percentage return is 100 percent.
Be certain to point out that the largest gain to the short seller occurs if the price of the stock
declines to zero, while in a long position there is no limit to the possible price increase. Of course,
in most cases, the price of the stock does not decline to zero, nor does it rise indefinitely.
8. Lisa Lasher buys 400 shares of stock on margin at $18 per share. If the margin requirement is 50
percent, how much must the stock rise for them to realize a
25-percent return on their invested funds? (Ignore dividends, commissions, and interest on
borrowed funds.)
Solution
The initial investment is $18 × 400 × 0.50 = $3,600. To realize a 25 percent return, the value of
the position in the stock must rise by $900 (0.25 × $3,600). The stock must increase by $2.25 per
share ($900/400 shares = $2.25).
9. A broker quotes GameStop stock (GME) with a bid-ask of $93.52–$93.62. You buy 10 shares
and then immediately decide to sell your 10 shares. The stock price has not changed at all, and
there are no commissions or taxes. How much money do you lose?
Solution
You buy at the higher price that the broker is asking: 10 shares × $93.62 = $936.20. You sell at
the lower price that the broker is bidding: 10 shares × $93.52 = $935.20. You receive only
$935.20 after paying $936.20, so you lose $1.00.
10. A broker quotes AMC Entertainment Holdings (AMC), a movie theater chain, at a bid-ask of
$15.94–$16.14 and you decide to buy 100 shares. The next day the stock price has changed,
and the broker quotes a bid-ask of $14.52–$14.72, and you sell your 100 shares. How much have
you gained or lost?
Solution
You buy at the higher ask price on the first day: 100 shares × $16.41 = $1,641. You sell at the
lower bid price the next day: 100 shares × 14.52 = $1,452. $1,452 − $1,641 = a loss of $189.
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 3
website, in whole or in part.
, Solution and Answer Guide: Solution and Answer Guide
Solution and Answer Guide
Mayo/Lavelle Basic Finance: An Introduction to Financial
Institutions, Investments, and Management 13e
Chapter 6: International Currency Flows
EXERCISE SOLUTIONS
1. If the price of a British pound is $1.82, how many pounds are necessary to purchase $1.00?
Solution
The number of pounds necessary to purchase $1 is $1.00/$1.82 = 0.5495 pounds
2. Last year Leather Boot, Inc. had investments in Paris worth 500,000 euros. At that time, the euro
was worth $1.20. Today the euro is trading for $1.30. What is the gain or loss in value of the
inventory expressed in dollars and in euros?
Solution
Value of the inventory:
Initially: 500,000 × $1.20 = $600,000
After the appreciation of the euro:
500,000 × $1.30 = $650,000
Net gain in dollars: $50,000
The value in terms of the euro is not changed.
3. Given the following information, determine the balance on the U.S. current account and capital
accounts:
Imports $211.5
Net income from foreign investments 32.3
Foreign investments in the United States 7.7
Government spending abroad 4.6
Exports 182.1
U.S. investments abroad 24.7
Foreign securities bought by the United States 4.9
U.S. securities bought by foreigners 2.8
Purchases of foreign short-term securities 6.5
Foreign purchases of U.S. short-term securities 9.1
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website, in whole or in part.
, Solution and Answer Guide: Solution and Answer Guide
Solution
Current Account Debit Credit Balance
Exports $182.1
Imports $211.5
Net difference −29.4
Government spending abroad 4.6
Net income from foreign investments 32.3
Balance on current account −$1.7
Capital Account
Direct investments abroad 24.7
Foreign investments in the United States 7.7
Purchases of foreign securities 4.9
Foreign purchases of U.S. securities 2.8
Purchases of foreign short-term securities 6.5
Foreign purchases of U.S. short-term securities 9.1
Balance on capital account −$16.5
There is a currency outflow of $1.7 on the current account and $16.5 on the capital account for a
total of $18.2. Point out that the income from previous foreign investments almost offsets the cash
outflow caused by the merchandise trade deficit plus the government spending. However, there
was no offsetting currency inflow to cover the direct foreign investments. Also point out that the
currency that flowed out of the U.S. did not disappear. The currency outflow had to be financed
somehow such as the drawing down of the U.S. holdings of foreign reserves.
4. If 1 Canadian dollar buys U.S. $0.78, and 1 U.S. dollar buys 21 Mexican pesos, how many
Canadian dollars can you buy with 1,000 Mexican pesos?
Solution
1,000 Mexican pesos × (1 U.S. dollar / 21 Mexican pesos) × (1 Canadian dollar / U.S. $0.78) =
1, / 0.78 = 61.05 Canadian dollars.
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, Solution and Answer Guide: Chapter 7: Financial Tools
Solution and Answer Guide
Mayo/Lavelle, Basic Finance: An Introduction to Financial
Institutions, Investments, and Management 13e
Chapter 7: Financial Tools
EXERCISE SOLUTIONS
1. You invest $1,000 in a certificate of deposit that matures after ten years and pays 5 percent
interest, which is compounded annually until the certificate matures.
a. How much interest will you earn if the interest is left to accumulate?
b. How much interest will you earn if the interest is withdrawn each year?
c. Why are the answers to question 1(a) and question 1(b) different?
Solution
a. $1,000(1 + 0.05)10 = X
X = $1,000(1.629) = $1,629
$1,000 grows to $1,629 at 5% for ten years, of which $629 in interest. The 1.629 is the
interest factor for the future value of $1 for ten years at 5%.
(PV = −1,000; N = 10; I = 5; PMT = 0; and FV = ? = 1,629)
b. If the interest is withdrawn each year, the investor receives $50 annually and $500 over the
lifetime of the investment.
c. The difference in the amount of interest ($629 − $500 = $129) is the result of compounding.
2. A person deposits $3,000 annually in a retirement account that earns 8 percent.
a. How much will be in the account when the individual retires at the age of 65 if the savings
program starts when the person is age 40?
b. How much additional money will be in the account if the saver defers retirement until age 70
and continues the contributions?
c. How much additional money will be in the account if the saver discontinues the contributions
at age 65 but does not retire until age 70?
Solution
a. X = $3,000(73.106) = $219,318
(73.106 is the interest factor for the future sum of an annuity of $1 at 8% for 25 years.)
(PV = 0; N = 25; I = 8; PMT = -3,000; and FV = ? = 219,318)
b. X = $3,000(113.283) = $339,849
(113.283 is the interest factor for the future sum of an annuity of $1 at 8% for 30 years.)
(PV = 0; N = 30; I = 8; PMT = −3,000; and FV = ? = 339,850)
The additional funds:
$339,849 − $219,318 = $120,531
($120,532 if a financial calculator is used.)
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website, in whole or in part.
, Solution and Answer Guide: Chapter 7: Financial Tools
Leaving the funds in the account and continuing the annual contribution for five additional
years increases the retirement funds by over $120,000.
c. In this question the individual stops making the contribution but does not draw on the fund.
The amount grows to:
$219,318(1 + 0.08)5 = $219,318(1.469) = $322,178
(1.469 is the interest factor for the future value of $1 at 8% for five years.)
(PV = −219,318; N = 5; I = 8; PMT = 0; and FV = ? = 322,250)
The difference in (b) and (c) is
$339,849 − $322,178 = $17,671
3. A 45-year-old woman decides to put funds into a retirement plan. She can save $2,000 a year
and earn 6 percent on this savings. How much will she have accumulated if she retires at age
65? At retirement how much can she withdraw each year for 20 years from the accumulated
savings if the savings continue to earn 6 percent?
Solution
$2,000(36.786) = $73,572
(36.786 is the interest factor for the future value of an annuity of $1 at 6% for
20 years.)
(PV = 0; N = 20; I = 6; PMT = −2,000; and FV = ? = 73,571)
The individual has accumulated $73,571. This will permit withdrawals of $6,414 a year for twenty
years:
$73,571 = X(11.470)
X = $6,414
(PV = 73,571; N = 20; I = 6; FV = 0; and PMT = ? = 6,414)
4. You annually invest $1,500 in an individual retirement account (IRA) starting at the age of 20 and
make the contributions for 10 years. Your twin sister does the same starting at age 30 and makes
the contributions for 30 years. Both of you earn 7 percent annually on your investment. Who has
the larger amount at age 60?
(Exercises 2 through 4 illustrate the basic elements of pension plans. A sum of money is
systematically set aside. It earns interest so that by retirement a considerable amount has been
accumulated. Then the retired person draws on the fund until it is exhausted, or until death
occurs, in which case the remainder of the fund becomes part of the estate. Of course, while the
retired person draws on the fund, the remaining principal continues to earn interest.)
Solution
Your account:
$1,500(FVAIF) = $1,500(13.816) = $20,724
(PV = 0; N = 10; I = 7; PMT = -1,500, and FV = ? = 20,725)
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website, in whole or in part.
, Solution and Answer Guide: Chapter 7: Financial Tools
$20,724(FVAIF) = $20,724(7.612) = $157,751
(PV = −20,724; N = 30; I = 7; PMT = 0; and FV = ? = 157,757)
Your sister's account:
$1,500(FVAIF) = $1,500(94.461) = $141,692
(PV = 0; N = 30; I = 7; PMT = -1500, and FV = ? = 141,692)
This Exercise illustrates the importance of starting contributions to a retirement account as early
as possible.
5. Holly wants to have $200,000 to send a recently born child to college. She sets up a 529 plan and
wants to know how much she must invest at the end of each year for the next 18 years if the
funds can earn 5 percent. If she can earn 7 percent, how much less will she have to invest each
year?
Solution
This Exercise also illustrates the future value of an annuity except the future value is known and
the amount of the annual contribution (PMT) is the unknown.
X(28.132) = $200,000
X = $200,000/28.132 = $7,109
(28.132 is the interest factor for the future sum of an annuity of $1 at 5% for 18 years.)
(PV = 0; N = 18; I = 5; FV = 200,000; and PMT = ? = −7,109)
If Holly starts saving for college expenses early, the required annual amount may be modest. You
may wish to use this Exercise to start a discussion of tax-advantaged plans for saving for college.
In addition, since college costs are continuing to rise, the $200,000 may be inadequate 18 years
from now.
If Holly can increase the return to 7 percent, the required annual contribution decreases by
$7,109 – 5,883 = $1,226.
X(33.999) = $200,000
X = $200,000/33.999 = $5,883
(33.999 is the interest factor for the future sum of an annuity of $1 at 5% for 18 years.)
(PV = 0; N = 18; I = 7; FV = 200,000; and PMT = ? = −5,883)
6. A widow currently has a $93,000 investment that yields 6 percent annually. Can she withdraw
$14,000 for the next ten years? Would your answer be different if the yield were 9 percent?
Solution
To answer this question, determine the amount that can be withdrawn:
$93,000 = X(PVAIF)
$93,000 = X(7.360)
X = $12,636
(PV = 93,000; N = 10; I = 6; FV = 0; and PMT = ? = −12,636)
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