Intermediate
14. This stock has a constant growth rate of dividends, but the required return changes twice. To find the
value of the stock today, we will begin by finding the price of the stock at Year 6, when both the
dividend growth rate and the require
So, the number of shares you need to purchase is:
Number of shares to purchase = (400,000 .20) + 1
Number of shares to purchase = 80,001
And the total cost to you will be the shares needed times the price per share, or:
Total cost = 80,001 $48
Total cost
We can solve for the dividend that was just paid:
$3.25 = D0(1 + .055)
D0 = $3.25 / 1.055 = $3.08
7.
The price of any financial instrument is the PV of the future cash flows. The future dividends of this
stock are an annuity for 11 years, so the price of
5.
Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing
equation and solve for the coupon payment as follows:
P = $948 = C(PVIFA5.90%,9) + $1,000(PVIF5.90%,9)
Solving for the coupon payment, we get:
C = $51.39
NOTE: Most problems do not explicitly list a par value for bonds. Even though a bond can have any par
value, in general, corporate bonds in the United States will have a par value of $1,000. We will use this
par value in all problems unless a different pa
Note that this is the PV of this annuity exactly seven years from today. Now we can discount this
lump sum to today. The value of this cash flow today is:
PV = $133,166.63 / [1 + (.10/12)]84 = $66,320.68
Now we need to find the PV of the annuity for the f
Using the PVA equation:
PVA = $2,720,000 = $17,500[cfw_1 [1 / (1 + r)360]/ r]
Unfortunately this equation cannot be solved to find the interest rate using algebra. To find the
interest rate, we need to solve this equation on a financial calculator, using
42.
The amount of principal paid on the loan is the PV of the monthly payments you make. So, the
present value of the $1,300 monthly payments is:
PVA = $1,300[(1 cfw_1 / [1 + (.0585/12)]360) / (.0585/12)] = $220,361.04
The monthly payments of $1,300 will
FVA rises as r increases, and FVA falls as r decreases
The present values of $7,500 per year for 20 years at the various interest rates given are:
[email protected]% = $7,500cfw_[1 (1/1.10)20] / .10 = $63,851.73
[email protected]% = $7,500cfw_[1 (1/1.05)20] / .05 = $93,466.58
P
35. Since we are looking to quadruple our money, the PV and FV are irrelevant as long as the FV is four
times as large as the PV. The number of periods is four, the number of quarters per year. So:
FV = $4 = $1(1 + r)(12/3)
r = .4142, or 41.42%
36. Here w
So, the total amount saved at retirement is:
$1,808,390.34 + 401,806.02 = $2,210,196.36
Solving for the withdrawal amount in retirement using the PVA equation gives us:
PVA = $2,210,196.36 = $C[1 cfw_1 / [1 + (.07/12)]300 / (.07/12)]
C = $2,210,196.36 / 1
19.
Enter
6
N
7.10%
I/Y
$15,000
PV
PMT
11%
I/Y
$15,000
PV
PMT
Solve for
20.
Enter
Solve for
N
16.62
FV
$22,637.48
$85,000
FV
From now, youll wait 2 + 16.62 = 18.62 years
Chapter 6
30. Here we need to convert an EAR into interest rates for different compou
13.
Enter
115
N
Solve for
Enter
30
N
I/Y
8.24%
8.24%
I/Y
$150
PV
PMT
$1,350,000
PV
PMT
$1
PV
PMT
$125,000
FV
$12,377,500
PV
PMT
$10,311,500
FV
PMT
$100,000
FV
PMT
$42,380
FV
PMT
$100,000
FV
PMT
$190,000
FV
Solve for
14.
Enter
115
N
Solve for
15.
Enter
4
N
Enter
Solve for
6.
Enter
N
21.44
18
N
Solve for
7.
Enter
Solve for
N
11.01
Enter
Solve for
8.
Enter
N
22.01
10
N
Solve for
9.
Enter
Solve for
10.
Enter
N
33.23
$21,500
PV
PMT
$430,258
FV
$65,000
PV
PMT
$300,000
FV
6.5%
I/Y
$1
PV
PMT
$2
FV
6.5%
I/Y
$1
PV
P
Enter
4
N
13%
I/Y
29
N
14%
I/Y
40
N
9%
I/Y
Solve for
Enter
Solve for
Enter
Solve for
4.
Enter
4
N
Solve for
Enter
18
N
Solve for
Enter
19
N
Solve for
Enter
25
N
Solve for
5.
Enter
Solve for
N
10.54
Enter
Solve for
N
8.50
Enter
Solve for
N
17.56
I/Y
5.47%
20.
To answer this question, we can use either the FV or the PV formula. Both will give the same
answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 + r)t
Solving for t, we get:
t = ln(FV / PV) / ln(1 + r)
t = l
Intermediate
16. To answer this question, we can use either the FV or the PV formula. Both will give the same
answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 + r)t
Solving for r, we get:
r = (FV / PV)1 / t 1
11.
To find the PV of a lump sum, we use:
PV = FV / (1 + r)t
PV = $1,000,000 / (1.09)80 = $1,013.63
12. To find the FV of a lump sum, we use:
FV = PV(1 + r)t
FV = $50(1.041)108 = $3,833.97
13. To answer this question, we can use either the FV or the PV fo
7.
To find the length of time for money to double, triple, etc., the present value and future value are
irrelevant as long as the future value is twice the present value for doubling, three times as large for
tripling, etc. To answer this question, we can
6.
To answer this question, we can use either the FV or the PV formula. Both will give the same
answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 + r)t
Solving for r, we get:
r = (FV / PV)1 / t 1
r = ($300,000
Quick ratio
Quick ratio 2011
Quick ratio 2012
= (Current assets Inventory) / Current liabilities
= ($61,886 25,392) / $46,755 = 0.78 times
= ($66,645 27,155) / $53,773 = 0.73 times
Cash ratio
Cash ratio 2011
Cash ratio 2012
= Cash / Current liabilities
=
23. This problem requires you to work backward through the income statement. First, recognize that
Net income = (1 t)EBT. Plugging in the numbers given and solving for EBT, we get:
EBT = $15,185 / (1 0.34) = $23,007.58
Now, we can add interest to EBT to g
Substituting the total equity into the equation and solving for long-term debt gives the following:
2.857 = 1 + (3,301.89 / LTD)
LTD = $3,301.89 / 1.857 = $1,777.94
Now, we can find the total debt of the company:
TD = CL + LTD = $910 + 1,777.94 = $2,687.9
PM = [(0.13)($2,805)] / [(1 + 1.4)( $6,189)] = .0245
Now that we have the profit margin, we can use this number and the given sales figure to solve for
net income:
PM = .0245 = NI / S
NI = .0245($6,189) = $151.94
19. This is a multistep problem involving
$347,645
Total liabilities and owners' equity
$34,170
S
$381,815
The firm used $34,170 in cash to acquire new assets. It raised this amount of cash by increasing
liabilities and owners equity by $34,170. In particular, the needed funds were raised by inte
Total liabilities and owners' equity
$347,645
100%
$381,815
100%
1.0983
1.0000
The common-size balance sheet answers are found by dividing each category by total assets. For
example, the cash percentage for 2011 is:
$9,279 / $347,645 = .0267, or 2.67%
Thi
12. The equity multiplier is:
EM = 1 + D/E
EM = 1 + 0.80 = 1.80
One formula to calculate return on equity is:
ROE = (ROA)(EM)
ROE = .079(1.80) = .1422, or 14.22%
ROE can also be calculated as:
ROE = NI / TE
So, net income is:
NI = ROE(TE)
NI = (.1422)($48
7.
8.
ROE = (PM)(TAT)(EM)
ROE = (.055)(1.80)(1.45) = .1436, or 14.36%
This question gives all of the necessary ratios for the DuPont Identity except the equity multiplier,
so, using the DuPont Identity:
ROE = (PM)(TAT)(EM)
ROE = .1914 = (.046)(2.30)(EM)
E
To find ROE, we need to find total equity. Since TL & OE equals TA:
TA = TD + TE
TE = TA TD
TE = $15,600,000 6,300,000 = $9,300,000
ROE = Net income / TE = 1,440,000 / $9,300,000 = .1548, or 15.48%
3.
Receivables turnover = Sales / Receivables
Receivables
c.
We can calculate net capital spending as:
Net capital spending = Net fixed assets 2011 Net fixed assets 2010 + Depreciation
Net capital spending = $4,536 3,767 + 1,033 = $1,802
So, the company had a net capital spending cash flow of $1,802. We also kno