13-50 SOLUTIONS
Notice that the length of time to quadruple your money is twice as long as the time needed to double
your money (the difference in these answers is due to rounding). This is an importa
B-62 SOLUTIONS
46.
47.
48.
To find the value of the perpetuity at r = 7, we first need to use the PV of a perpetuity equation.
Using this equation we find:
PV = $3,000! .065 = $46,153.85
Remember that
B-38 SOLUTIONS
The pro forma balance sheet will look like this:
25 9b Soles Growth:
Assets
Current assets
Cash
Accounts receivable
Inventory
Total
Fixed assets
Net plant and
equipment
Total assets
So,
B-36 SOLUTIONS
And the addition to retained earnings will be:
Addition to retained earnings = $123,988 - 49,595
Addition to retained earnings = $74,393
The new accumulated retained earnings on the pro
B-64 SOLUTIONS
Now we can set the present value of the lease payments equal to the cost of the equipment, or
$4,000. The lease payments are in the form of an annuity due, so:
PVAdu, = (1 + r)C(cfw_1-
B-58 SOLUTIONS
33. The company will accept the project if the present value of the increased cash ows is greater than
the cost. The cash ows are a growing perpetuity, so the present value is:
PV = C c
27.
28.
CHAPTER 3 1343
This implies the payout ratio is:
Payout ratio = 1 - b
Payout ratio = 1 - 2.36
Payout ratio = 1.36
This is a negative dividend payout ratio of 136 percent, which is impossible.
30.
CHAPTER 3 1345
Which is equivalent to:
Sustainable rate = (NI / TEE) x I?
Since ROBE = NI / TEE
The sustainable growth rate equation is:
Sustainable growth rate = ROEB x b
For the internal growth
CHAPTER 3 1341
So, the new long-term debt will be the new total debt minus the new short-term debt, or:
New long-term debt = $300,405 93,500
New long-term debt = $206,905
Soles growth rate = 30% and d
CHAPTER 4 1349
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 = P
The new accumulated retained earnings on the pro forma balance sheet will be:
New accumulated retained earnings = $257,000 + 77,961
New accumulated retained earnings = $334,961
The pro forma balance s
CHAPTER 4 1357
This is the value of the annuity in Year 5, one period before the rst payment. Finding the value of
this amount today, we find:
PV = FV/(l + r)if
PV 2 $2,923.69/(l + .12)5
PV 2 $1,658.9
13-54 SOLUTIONS
Now, we solve for 2:
110.0091: 1 - [($16,500)(.009) 1' ($500)]
1.0091: l/(0.703) = 1.422
2111 1.422111 1.009 = 39.33 months
20. Here, we are trying to find the interest rate when we kn
43.
45.
CHAPTER 4 1361
And the firms profit is:
Profit = $79,700.77 - 72,000.00 = $7,700.77
To find the interest rate at which the firm will break even, we need to find the interest rate using the
PV
49.
50.
51.
CHAPTER 4 1363
Note, that you can also calculate this present value (as well as the remaining present values) using
the number of years. To do this, you need the EAR. The EAR is:
EAR =(1+.
CHAPTER 3 1339
Under the sustainable growth rate assumption, the company maintains a constant debt-equity ratio.
The DIE ratio of the company is:
DIE = ($156,000 + 74,000) / $278,000
DIE = .82734
At a
B-48 SOLUTIONS
Solutions to Questions and Problems
NOTE: Ali-end-af chapter problems were solved rising a spreadsheet. Many problems reaaire maitipt'e
steps. Bee in spaee and readability constraints,
B-46 SOLUTIONS
So, the equity at the end of the year was:
Ending equity = $165,000 + 31,000
Ending equity = $196,000
The ROE based on the end of period equity is:
ROE = $30,000 1' $196,000
ROE = 40.32
B-52 SOLUTIONS
To find the interest rate that equates the perpetuity cash ows with the PV of the cash ows. Using
the PV of a perpetuity equation:
PV= C/r
$195,000 = $15,000 I r
We can now solve for th
B-44 SOLUTIONS
Since:
ROA = NI / A
ROA = PM(S) / A
We can substitute this into the internal growth rate equation and divide both the numerator and
denominator by A. This gives:
Internal growth rate =
CHAPTER 3 1335
23. The DIE ratio of the company is:
DIE = ($156,000 + 74,000) / $278,000
DIE = .82734
So the new total debt amount will be:
New total debt 2 .82734($355,961)
New total debt = $294,500.
36.
37.
38.
CHAPTER 4 1359
Here, we are given the FVA, the interest rate, and the amount of the annuity. We need to solve for
the number of payments. Using the FVA equation:
FVA = $20,000 = $125[cfw_[
B-34 SOLUTIONS
The pro forma balance sheet will look like this:
MOOSE TOURS INC.
Pro Forma Balance Sheet
Assets Liabilities and Owners Equity
Current assets Current liabilities
Cash $ 30,000 Account
23.
24.
25.
CHAPTER 4 1355
First Complex Bank pays compound interest, so the interest paid by this bank will be the FV factor
of $1, or:
(1 + 19
Setting the two equal, we get:
(.03)(10) = (1 + r) 1
r
CHAPTER 4
DISCOUNTED CASH FLOW VALUATION
Answers to Concepts Review and Critical Thinking Questions
1.
10.
Assuming positive cash ows and interest rates, the future value increases and the present val
B-60 SOLUTIONS
40.
41.
42.
So, the PV of the missing CF is:
$5,979 909.09 - 1,502.63 - 1,366.03 = $2,201.25
The question asks for the value of the cash flow in Year 2, so we must nd the future value o
B-40 SOLUTIONS
The pro forma balance sheet will look like this:
Sales growth rate = 20% and Debt/Eqaim ratio = .82734:
Assets
Current assets
MOOSE TOURS INC.
Pro Forma Balance Sheet
Liabilities and
B-56 SOLUTIONS
26.
27.
28.
29.
This is a growing perpetuity. The present value of a growing perpetuity is:
PV = C l (r g)
PV = $200,000 / (.10 - .05)
PV = $4,000,000
It is important to recognize that
CHAPTER 4 1353
17. For discrete compounding, to find the EAR. we use the equation:
EAR = [1 + (APR 1 m)] -1
So. for each bank. the EAR is:
First National: EAR = [1 +(.122/12)]12 1 = 12.91%
First Unite