5-9a.01
||$500(1.06) = $530.00.
-500FV = ?
Using a financial calculator, enter N = 1, I/YR = 6, PV = -500, PMT = 0, and FV = ? Solve for FV = $530.00.
b.012
|||$500(1.06)2 = $561.80.
-500FV = ?
Using a financial calculator, enter N = 2, I/YR = 6, PV = -500, PMT = 0, and FV = ? Solve for FV = $561.80.
c.01
||$500(1/1.06) = $471.70.
PV = ?500
Using a financial calculator, enter N = 1, I/YR = 6, PMT = 0, and FV = 500, and PV = ? Solve for PV = $471.70.
d.012
|||$500(1/1.06)2 = $445.00.
PV = ?500
Using a financial calculator, enter N = 2, I/YR = 6, PMT = 0, FV = 500, and PV = ? Solve for PV = $445.00.
5-10a.012345678910
|||||||||||$500(1.06)10 = $895.42.
-500FV = ?
Using a financial calculator, enter N = 10, I/YR = 6, PV = -500, PMT = 0, and FV = ? Solve for FV = $895.42.
b.012345678910
|||||||||||$500(1.12)10 = $1,552.92.
-500FV = ?
Using a financial calculator, enter N = 10, I/YR = 12, PV = -500, PMT = 0, and FV = ? Solve for FV = $1,552.92.
c.012345678910
|||||||||||$500/(1.06)10 = $279.20.
PV = ?500
Using a financial calculator, enter N = 10, I/YR = 6, PMT = 0, FV = 500, and PV = ? Solve for PV = $279.20.
d.012345678910
|||||||||||
PV = ?1,552.90
$1,552.90/(1.12)10 = $499.99.
Using a financial calculator, enter N = 10, I/YR = 12, PMT = 0, FV = 1552.90, and PV = ? Solve for PV = $499.99.
$1,552.90/(1.06)10 = $867.13.
Using a financial calculator, enter N = 10, I/YR = 6, PMT = 0, FV = 1552.90, and PV = ? Solve for PV = $867.13.
e.The present value is the value today of a sum of money to be received in the future. For example, the value today of $1,552.90 to be received 10 years in the future is about $500 at an interest rate of 12%, but it is approximately $867 if the interest rate is 6%. Therefore, if you had $500 today and invested it at 12%, you would end up with $1,552.90 in 10 years. The present value depends on the interest rate because the interest rate determines the amount of interest you forgo by not having the money today.
5-11a.200320042005200620072008
||||||
-612 (in millions)
With a calculator, enter N = 5, PV = -6, PMT = 0, FV = 12, and then solve for I/YR = 14.87%.
b.The calculation described in the quotation fails to consider the compounding effect. It can be demonstrated to be incorrect as follows:
$6,000,000(1.20)5 = $6,000,000(2.48832) = $14,929,920,
which is greater than $12 million. Thus, the annual growth rate is less than 20%; in fact, it is about 15%, as shown in Part a.
5-12These problems can all be solved using a financial calculator by entering the known values shown on the time lines and then pressing the I/YR button.
a.01
||
+700-749
With a financial calculator, enter: N = 1, PV = 700, PMT = 0, and FV = -749. I/YR = 7%.
b.01
||
-700+749
With a financial calculator, enter: N = 1, PV = -700, PMT = 0, and FV = 749. I/YR = 7%.
c.010
||
+85,000-201,229
With a financial calculator, enter: N = 10, PV = 85000, PMT = 0, and FV = -201229. I/YR = 9%.
d.012345
||||||
+9,000-2,684.80-2,684.80-2,684.80-2,684.80-2,684.80
With a financial calculator, enter: N = 5, PV = 9000, PMT = -2684.80, and FV = 0. I/YR = 15%.
5-13a.?
||
-200400
With a financial calculator, enter I/YR = 7, PV = -200, PMT = 0, and FV = 400. Then press the N key to find N = 10.24. Override I/YR with the other values to find N = 7.27, 4.19, and 1.00.
b.?
||Enter: I/YR = 10, PV = -200, PMT = 0, and FV = 400.
-200400N = 7.27.
c.?
||Enter: I/YR = 18, PV = -200, PMT = 0, and FV = 400.
-200400N = 4.19.
d.?
||Enter: I/YR = 100, PV = -200, PMT = 0, and FV = 400.
-200 400N = 1.00.
5-14a.012345678910
|||||||||||
400400400400400400400400400400
FV = ?
With a financial calculator, enter N = 10, I/YR = 10, PV = 0, and PMT = -400. Then press the FV key to find FV = $6,374.97.
b.012345
||||||
200200200200200
FV = ?
With a financial calculator, enter N = 5, I/YR = 5, PV = 0, and PMT = -200. Then press the FV key to find FV = $1,105.13.
c.012345
||||||
400400400400400
FV = ?
With a financial calculator, enter N = 5, I/YR = 0, PV = 0, and PMT = -400. Then press the FV key to find FV = $2,000.
d.To solve Part d using a financial calculator, repeat the procedures discussed in Parts a, b, and c, but first switch the calculator to “BEG” mode. Make sure you switch the calculator back to “END” mode after working the problem.
1.012345678910
|||||||||||
400400400400400400400400400400FV = ?
With a financial calculator on BEG, enter: N = 10, I/YR = 10, PV = 0, and PMT = -400. FV = $7,012.47.
2.012345
||||||
200200200200200FV = ?
With a financial calculator on BEG, enter: N = 5, I/YR = 5, PV = 0, and PMT = -200. FV = $1,160.38.
3.012345
||||||
400400400400400FV = ?
With a financial calculator on BEG, enter: N = 5, I/YR = 0, PV = 0, and PMT = -400. FV = $2,000.
5-15a.012345678910
|||||||||||
PV = ?400400400400400400400400400400
With a financial calculator, simply enter the known values and then press the key for the unknown. Enter: N = 10, I/YR = 10, PMT = -400, and FV = 0. PV = $2,457.83.
b.012345
||||||
PV = ?200200200200200
With a financial calculator, enter: N = 5, I/YR = 5, PMT = -200, and FV = 0. PV = $865.90.
c.012345
||||||
PV = ?400400400400400
With a financial calculator, enter: N = 5, I/YR = 0, PMT = -400, and FV = 0. PV = $2,000.00.
d.1.012345678910
|||||||||||
400400400400400400400400400400
PV = ?
With a financial calculator on BEG, enter: N = 10, I/YR = 10, PMT = -400, and FV = 0. PV = $2,703.61.
2.012345
||||||
200200200200200
PV = ?
With a financial calculator on BEG, enter: N = 5, I/YR = 5, PMT = -200, and FV = 0. PV = $909.19.
3.012345
||||||
400400400400400
PV = ?
With a financial calculator on BEG, enter: N = 5, I/YR = 0, PMT = -400, and FV = 0. PV = $2,000.00.
5-20Contract 1: PV=
= $2,727,272.73+$2,479,338.84+$2,253,944.40 + $2,049,040.37
= $9,509,596.34.
Using your financial calculator, enter the following data: CF0 = 0; CF1-4 = 3000000; I/YR = 10; NPV = ? Solve for NPV = $9,509,596.34.
Contract 2: PV=
= $1,818,181.82 + $2,479,338.84 + $3,005,259.20 + $3,415,067.28
= $10,717,847.14.
Alternatively, using your financial calculator, enter the following data: CF0 = 0; CF1 = 2000000; CF2 = 3000000; CF3 = 4000000; CF4 = 5000000; I/YR = 10; NPV = ? Solve for NPV = $10,717,847.14.
Contract 3: PV=
= $6,363,636.36 + $826,446.28 + $751,314.80 + $683,013.46
= $8,624,410.90.
Alternatively, using your financial calculator, enter the following data: CF0 = 0; CF1 = 7000000; CF2 = 1000000; CF3 = 1000000; CF4 = 1000000; I/YR = 10; NPV = ? Solve for NPV = $8,624,410.90.
Contract 2 gives the quarterback the highest present value; therefore, he should accept Contract 2.
3-5 Ending R/E= Beg. R/E Net income Dividends
$278,900,000= $212,300,000 Net income $22,500,000
$278,900,000= $189,800,000 Net income
Net income= $89,100,000.
3-7a.NWC2007= Total CA – (A/P + Accruals)
= $59,000 – ($9,000 + $6,000)
= $44,000.
NWC2008= $72,125 – ($10,800 + $7,600)
= $53,725.
b.FCF= EBIT (1 – T) + Deprec. – Capital expenditures – ΔNWC
= $39,000 (1 – 0.4) + $5,000 – $8,000 –$9,725
= $10,675.
Note: To arrive at capital expenditures you add depreciation to the change in net FA, so
Capital expenditures = $5,000 + $3,000 = $8,000.
c.Statement of Stockholders’ Equity, 2008
Common StockRetainedTotal Stockholders’
SharesAmountEarningsEquity
Balances, 12/31/075,000$50,000 $20,850$70,850
2008 Net Income 22,350
Cash Dividends (11,175)
Addition (Subtraction)
to retained earnings 11,175 11,175
Balances, 12/31/085,000$50,000 $32,025$82,025
3-10a.= Current assets – (A/P + Accruals)
= $360,000,000 – ($90,000,000 + $60,000,000)
= $210,000,000.
= $372,000,000 – $180,000,000 = $192,000,000.
b.FCF08= EBIT (1 – T) + Deprec. – Cap. expend. - ΔNWC
= $150,000,000 (0.6) + $30,000,000 – $80,000,000 – (-$18,000,000)
= $90,000,000 + $30,000,000 - $80,000,000 + $18,000,000
= $58,000,000.
Note that depreciation must be added to ΔNet P&E to arrive at capital expenditures.
c.The large increase in dividends for 2008 can most likely be attributed to a large increase in free cash flow from 2007 to 2008, since FCF represents the amount of cash available to be paid out to stockholders after the company has made all investments in fixed assets, new products, and working capital necessary to sustain the business.
Comprehensive/Spreadsheet Problem
Note to Instructors:
The solution to this problem is not provided to students at the back of their text. Instructors can access the Excel file on the textbook’s web site or the Instructor’s Resource CD.
3-11a.
KEY INPUT DATA: Laiho IndustriesSales / $455,150
EBITDA as a percentage of sales / 15%
Depr. as a % of fixed assets / 11%
Tax rate / 40%
Interest expense / $8,575
Dividend payout ratio / 40%
Laiho Industries Income Statement
(in thousands of dollars)
2008
Sales / $455,150
Expenses excluding depreciation and amortization / 386,878 / Found after finding EBITDA
EBITDA / $68,273 / Found this first
Depreciation and amortization / 7,388
EBIT / $60,884
Interest expense / 8,575
EBT / $52,309
Taxes (40%) / 20,924
Net Income / $31,386
Common dividends / $12,554
Addition to retained earnings / $18,831
b.
Statement of Stockholders' Equity(in thousands of dollars)
Balance of Retained Earnings, December 31, 2007 / $38,774
Add: Net Income, 2008 / $31,386
Less: Common dividends paid, 2008 / (12,554)
Balance of Retained Earnings, December 31, 2008 / $57,605
Statement of Cash Flows /
/
(in thousands of dollars)
Operating Activities
Net Income / $31,386
Depreciation and amortization / 7,388
Increase in accounts payable / 7,652
Increase in accruals / 7,821
Increase in accounts receivable / (17,838)
Increase in inventories / (3,462)
Net cash provided by operating activities / $32,947
Investing Activities
Additions to property, plant, and equipment / ($32,117)
Net cash used in investing activities / ($32,117)
Financing Activities
Increase in notes payable / $2,500
Increase in long-term debt / 12,350
Increase in common stock / 10,000
Payment of common dividends / (12,554)
Net cash provided by financing activities / $12,295
Summary
Net increase/decrease in cash / $13,125
Cash balance at the beginning of the year / 89,725
Cash balance at the end of the year / $102,850
c.
Net Working Capital (must be financed by external sources)NWC07 = / current assets / - / (A/P and accruals)
NWC07 = / $210,234 / - / $45,765
NWC07 = / $164,469
NWC08 = / current assets / - / (A/P and accruals)
NWC08 = / $244,659 / - / $61,238
NWC08 = / $183,421
d.An increase in the firm's dividend payout ratio would have no effect on its corporate taxes paid becausedividends are paid with after-tax dollars. However, the company's shareholders would pay additionaltaxes on the additional dividends they would receive. As of 10/08, dividends are generally taxed at amaximum rate of 15%.
Chapter 4
4-7Step 1:Calculate total assets from information given.
Sales = $6 million.
3.2= Sales/TA
3.2=
Assets= $1,875,000.
Step 2:Calculate net income.
There is 50% debt and 50% equity, so Equity = $1,875,000 0.5 = $937,500.
ROE= NI/S S/TA TA/E
0.12= NI/$6,000,000 3.2 $1,875,000/$937,500
0.12=
$720,000= 6.4NI
$112,500= NI.
4-10We are given ROA = 3% and Sales/Total assets = 1.5.
From the DuPont equation:ROA= Profit margin Total assets turnover
3%= Profit margin(1.5)
Profit margin= 3%/1.5 = 2%.
We can also calculate the company’s debt ratio in a similar manner, given the facts of the problem. We are given ROA(NI/A) and ROE(NI/E); if we use the reciprocal of ROE we have the following equation:
Alternatively, using the DuPont equation:
ROE= ROA EM
5%= 3% EM
EM= 5%/3% = 5/3 = TA/E.
Take reciprocal: E/TA = 3/5 = 60%; therefore, D/A = 1 – 0.60 = 0.40 = 40%.
Thus, the firm’s profit margin = 2% and its debt ratio = 40%.
4-17TA = $5,000,000,000; T = 40%; EBIT/TA = 10%; ROA = 5%; TIE ?
Now use the income statement format to determine interest so you can calculate the firm’s TIE ratio.
EBIT$500,000,000See above.
INT 83,333,333
EBT$416,666,667EBT = $250,000,000/0.6
Taxes (40%) 166,666,667
NI$250,000,000See above.
TIE= EBIT/INT
= $500,000,000/$83,333,333
= 6.0.
4-18Present current ratio = = 2.5.
Minimum current ratio = = 2.0.
$1,312,500 + NP= $1,050,000 + 2NP
NP= $262,500.
Short-term debt can increase by a maximum of $262,500 without violating a 2 to 1 current ratio, assuming that the entire increase in notes payable is used to increase current assets. Since we assumed that the additional funds would be used to increase inventory, the inventory account will increase to $637,500 and current assets will total $1,575,000, and current liabilities will total $787,500.
4-211.Total debt = (0.50)(Total assets) = (0.50)($300,000) = $150,000.
2.Accounts payable = Total debt – Long-term debt= $150,000 – $60,000
= $90,000.
3.Common stock= – Debt – Retained earnings
= $300,000 – $150,000 – $97,500 = $52,500.
4.Sales = (1.5)(Total assets) = (1.5)($300,000) = $450,000.
5.Inventories = Sales/5 = $450,000/5 = $90,000.
6.Accounts receivable= (Sales/365)(DSO) = ($450,000/365)(36.5) = $45,000.
7.Cash + Accounts receivable + Inventories= (1.8)(Accounts payable)
Cash + $45,000 + $90,000= (1.8)($90,000)
Cash + $135,000= $162,000
Cash= $27,000.
8.Fixed assets= Total assets – (Cash + Accts rec. + Inventories)
= $300,000 – ($27,000 + $45,000 + $90,000)
= $138,000.
9.Cost of goods sold = (Sales)(1 – 0.25) = ($450,000)(0.75) = $337,500.
Solutions to End-of-Chapter Problems
7-1With your financial calculator, enter the following:
N = 10; I/YR = YTM = 9%; PMT = 0.08 1,000 = 80; FV = 1000; PV = VB = ?
PV = $935.82.
7-2VB = $985; M = $1,000; Int = 0.07 $1,000 = $70.
a.N = 10; PV = -985; PMT = 70; FV = 1000; YTM = ?
Solve for I/YR = YTM = 7.2157% 7.22%.
b.N = 7; I/YR = 7.2157; PMT = 70; FV = 1000; PV = ?
Solve for VB = PV = $988.46.
7-3The problem asks you to find the price of a bond, given the following facts: N = 2 8 = 16; I/YR = 8.5/2 = 4.25; PMT = 45; FV = 1000.
With a financial calculator, solve for PV = $1,028.60.
7-4With your financial calculator, enter the following to find YTM:
N = 10 2 = 20; PV = -1100; PMT = 0.08/2 1,000 = 40; FV = 1000; I/YR = YTM = ?
YTM = 3.31% 2 = 6.62%.
With your financial calculator, enter the following to find YTC:
N = 5 2 = 10; PV = -1100; PMT = 0.08/2 1,000 = 40; FV = 1050; I/YR = YTC = ?
YTC = 3.24% 2 = 6.49%.
Since the YTC is less than the YTM, investors would expect the bonds to be called and to earn the YTC.
7-5a.1.5%:Bond L:Input N = 15, I/YR = 5, PMT = 100, FV = 1000, PV = ?, PV = $1,518.98.
Bond S:Change N = 1, PV = ? PV = $1,047.62.
2.8%:Bond L:From Bond S inputs, change N = 15 and I/YR = 8, PV = ?, PV = $1,171.19.
Bond S:Change N = 1, PV = ? PV = $1,018.52.
3.12%:Bond L:From Bond S inputs, change N = 15 and I/YR = 12, PV = ?, PV = $863.78.
Bond S:Change N = 1, PV = ? PV = $982.14.
b.Think about a bond that matures in one month. Its present value is influenced primarily by the maturity value, which will be received in only one month. Even if interest rates double, the price of the bond will still be close to $1,000. A 1-year bond’s value would fluctuate more than the one-month bond’s value because of the difference in the timing of receipts. However, its value would still be fairly close to $1,000 even if interest rates doubled. A long-term bond paying semiannual coupons, on the other hand, will be dominated by distant receipts, receipts that are multiplied by 1/(1 + rd/2)t, and if rd increases, these multipliers will decrease significantly. Another way to view this problem is from an opportunity point of view. A 1month bond can be reinvested at the new rate very quickly, and hence the opportunity to invest at this new rate is not lost; however, the long-term bond locks in subnormal returns for a long period of time.
7-6a.TimeYears to MaturityPrice of Bond CPrice of Bond Z
t = 0 4 $1,012.79 $ 693.04
t = 1 3 1,010.02 759.57
t = 2 2 1,006.98 832.49
t = 3 1 1,003.65 912.41
t = 4 0 1,000.00 1,000.00
b.
7-7Percentage
Price at 8%Price at 7% Change
10-year, 10% annual coupon $1,134.20 $1,210.71 6.75%
10-year zero 463.19 508.35 9.75
5-year zero 680.58 712.99 4.76
30-year zero 99.38 131.37 32.19
$100 perpetuity 1,250.00 1,428.57 14.29
7-20a.Bond A is selling at a discount because its coupon rate (7%) is less than the going interest rate (YTM = 9%). Bond B is selling at par because its coupon rate (9%) is equal to the going interest rate (YTM = 9%). Bond C is selling at a premium because its coupon rate (11%) is greater than the going interest rate (YTM = 9%).
b.
c.
d.
e.
1.5.83%
2.5.26%
3.The bond is selling at a premium, which means that interest rates have declined. If interest rates remain at current levels, then Mr. Clark should expect the bond to be called. Consequently, he would earn the YTC not the YTM.
f.
Interest rate (price) risk is the risk of a decline in a bond's price due to an increase in interest rates.Reinvestment rate risk is the risk that a decline in interest rates will lead to a decline in incomefrom a bond portfolio.
Ranking the bonds above in order from the most interest rate risk to the least interest rate risk: 10-year bond with a zero coupon, 10-year bond with a 9% annual coupon, 5-year bond with azero coupon, and 5-year bond with a 9% annual coupon.
You can double check this ranking by calculating the prices of each bond at 2 different interest rates, and thendetermining the percentage change in value. (See calculations above.)
g.
1.
2.
3.
8-1= (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)
= 11.40%.
2 = (-50% – 11.40%)2(0.1) + (-5% – 11.40%)2(0.2) + (16% – 11.40%)2(0.4)
+ (25% – 11.40%)2(0.2) + (60% – 11.40%)2(0.1)
2 = 712.44; = 26.69%.
CV = = 2.34.
8-2InvestmentBeta
$35,000 0.8
40,000 1.4
Total$75,000
bp = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.
8-3rRF = 6%; rM = 13%; b = 0.7; r = ?
r= rRF + (rM – rRF)b
= 6% + (13% – 6%)0.7
= 10.9%.
8-4rRF = 5%; RPM = 6%; rM = ?
rM = 5% + (6%)1 = 11%.
r when b = 1.2 = ?
r = 5% + 6%(1.2) = 12.2%.
8-5a.r = 11%; rRF = 7%; RPM = 4%.
r= rRF + (rM – rRF)b
11%= 7% + 4%b
4%= 4%b
b= 1.
b.rRF = 7%; RPM = 6%; b = 1.
r= rRF + (rM – rRF)b
= 7% + (6%)1
= 13%.
8-6a..
= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)
= 14% versus 12% for X.
b. = .
= (-10% – 12%)2(0.1) + (2% – 12%)2(0.2) + (12% – 12%)2(0.4)
+ (20% – 12%)2(0.2) + (38% – 12%)2(0.1) = 148.8%.
X = 12.20% versus 20.35% for Y.
CVX = X/X = 12.20%/12% = 1.02, while
CVY = 20.35%/14% = 1.45.
If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.
8-12a.ri = rRF + (rM – rRF)bi = 9% + (14% – 9%)1.3 = 15.5%.
b.1.rRF increases to 10%:
rM increases by 1 percentage point, from 14% to 15%.
ri = rRF + (rM – rRF)bi = 10% + (15% – 10%)1.3 = 16.5%.
2.rRF decreases to 8%:
rM decreases by 1%, from 14% to 13%.
ri = rRF + (rM – rRF)bi = 8% + (13% – 8%)1.3 = 14.5%.
c.1.rM increases to 16%:
ri = rRF + (rM – rRF)bi = 9% + (16% – 9%)1.3 = 18.1%.
2.rM decreases to 13%:
ri = rRF + (rM – rRF)bi = 9% + (13% – 9%)1.3 = 14.2%.
8-17After additional investments are made, for the entire fund to have an expected return of 13%, the portfolio must have a beta of 1.5455 as shown below:
13%= 4.5% + (5.5%)b
b= 1.5455.
Since the fund’s beta is a weighted average of the betas of all the individual investments, we can calculate the required beta on the additional investment as follows:
1.5455= +
1.5455= 1.2 + 0.2X
0.3455= 0.2X
X= 1.7275.
8-21a. = 0.1(-28%) + 0.2(0%) + 0.4(12%) + 0.2(30%) + 0.1(50%) = 13%.
rRF = 6%. (given)
Therefore, the SML equation is:
ri = rRF + (rM – rRF)bi = 6% + (13% – 6%)bi = 6% + (7%)bi.
b.First, determine the fund’s beta, bF. The weights are the percentage of funds invested in each stock:
A = $160/$500 = 0.32.
B = $120/$500 = 0.24.
C = $80/$500 = 0.16.
D = $80/$500 = 0.16.
E = $60/$500 = 0.12.
bF= 0.32(0.5) + 0.24(1.2) + 0.16(1.8) + 0.16(1.0) + 0.12(1.6)
= 0.16 + 0.288 + 0.288 + 0.16 + 0.192 = 1.088.
Next, use bF = 1.088 in the SML determined in Part a:
= 6% + (13% – 6%)1.088 = 6% + 7.616% = 13.616%.
c.rN = Required rate of return on new stock = 6% + (7%)1.5 = 16.5%.
An expected return of 15% on the new stock is below the 16.5% required rate of return on an investment with a risk of b = 1.5. Since rN = 16.5% > = 15%, the new stock should not be purchased. The expected rate of return that would make the fund indifferent to purchasing the stock is 16.5%.
9-1D0 = $1.50; g1-3 = 7%; gn = 5%; D1 through D5 = ?
D1 = D0(1 + g1) = $1.50(1.07) = $1.6050.
D2 = D0(1 + g1)(1 + g2) = $1.50(1.07)2 = $1.7174.
D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.07)3 = $1.8376.
D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.07)3(1.05) = $1.9294.
D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.07)3(1.05)2 = $2.0259.
9-2D1 = $0.50; g = 7%; rs = 15%;= ?
9-3P0 = $20; D0 = $1.00; g = 6%; = ?; rs = ?
= P0(1 + g) = $20(1.06) = $21.20.
= + g = + 0.06
= + 0.06 = 11.30%. rs = 11.30%.
9-5The firm’s free cash flow is expected to grow at a constant rate, hence we can apply a constant growth formula to determine the total value of the firm.
Firm value= FCF1/(WACC – g)
= $150,000,000/(0.10 – 0.05)
= $3,000,000,000.
To find the value of an equity claim upon the company (share of stock), we must subtract out the market value of debt and preferred stock. This firm happens to be entirely equity funded, and this step is unnecessary. Hence, to find the value of a share of stock, we divide equity value (or in this case, firm value) by the number of shares outstanding.
Equity value per share= Equity value/Shares outstanding
= $3,000,000,000/50,000,000
= $60.
Each share of common stock is worth $60, according to the corporate valuation model.
9-8a.
b.
9-11First, solve for the current price.
= D1/(rs – g)
= $0.50/(0.12 – 0.07)
= $10.00.
If the stock is in a constant growth state, the constant dividend growth rate is also the capital gains yield for the stock and the stock price growth rate. Hence, to find the price of the stock four years from today:
= P0(1 + g)4
= $10.00(1.07)4
= $13.10796 ≈ $13.11.
10-1rd(1 – T) = 0.12(0.65) = 7.80%.
10-2Pp = $47.50; Dp = $3.80; rp = ?
rp= = = 8%.
10-340% Debt; 60% Common equity; rd = 9%; T = 40%; WACC = 9.96%; rs = ?
WACC= (wd)(rd)(1 – T) + (wc)(rs)
0.0996= (0.4)(0.09)(1 – 0.4) + (0.6)rs
0.0996= 0.0216 + 0.6rs
0.078= 0.6rs
rs= 13%.
10-8Debt = 40%, Common equity = 60%.
P0 = $22.50, D0 = $2.00, D1 = $2.00(1.07) = $2.14, g = 7%.
rs = + g = + 7% = 16.51%.
WACC= (0.4)(0.12)(1 – 0.4) + (0.6)(0.1651)
= 0.0288 + 0.0991 = 12.79%.
10-17a.rs= + g
0.09= + g
0.09= 0.06 + g
g= 3%.
b.Current EPS $5.400 Alternatively:
Less: Dividends per share 3.600EPS1 = EPS0(1 + g) = $5.40(1.03) = $5.562.
Retained earnings per share $1.800
Rate of return 0.090
Increase in EPS $0.162
Plus: Current EPS 5.400
Next year’s EPS $5.562
11-1Financial calculator solution: Input CF0 = -52125, CF1-8 = 12000, I/YR = 12, and then solve for NPV = $7,486.68.
11-2Financial calculator solution: Input CF0 = -52125, CF1-8 = 12000, and then solve for IRR = 16%.
11-4Since the cash flows are a constant $12,000, calculate the payback period as: $52,125/$12,000 = 4.3438, so the payback is about 4 years.
11-5Project K’s discounted payback period is calculated as follows:
AnnualDiscounted @12%
PeriodCash Flows Cash Flows Cumulative
0 ($52,125) ($52,125.00) ($52,125.00)
1 12,000 10,714.29 (41,410.71)
2 12,000 9,566.33 (31,844.38)
3 12,000 8,541.36 (23,303.02)
4 12,000 7,626.22 (15,676.80)
5 12,000 6,809.12 (8,867.68)
6 12,000 6,079.57 (2,788.11)
7 12,000 5,428.19 2,640.08
8 12,000 4,846.60 7,486.68
The discounted payback period is 6 + years, or 6.51 years.
11-6a.Project A: Using a financial calculator, enter the following:
CF0 = -25, CF1 = 5, CF2 = 10, CF3 = 17, I/YR = 5; NPV = $3.52.
Change I/YR = 5 to I/YR = 10; NPV = $0.58.
Change I/YR = 10 to I/YR = 15; NPV = -$1.91.
Project B: Using a financial calculator, enter the following:
CF0 = -20, CF1 = 10, CF2 = 9, CF3 = 6, I/YR = 5; NPV = $2.87.
Change I/YR = 5 to I/YR = 10; NPV = $1.04.
Change I/YR = 10 to I/YR = 15; NPV = -$0.55.
b.Using the data for Project A, enter the cash flows into a financial calculator and solve for IRRA = 11.10%. The IRR is independent of the WACC, so it doesn’t change when the WACC changes.
Using the data for Project B, enter the cash flows into a financial calculator and solve for IRRB = 13.18%. Again, the IRR is independent of the WACC, so it doesn’t change when the WACC changes.
c.At a WACC = 5%, NPVA > NPVB so choose Project A.
At a WACC = 10%, NPVB > NPVA so choose Project B.
At a WACC = 15%, both NPVs are less than zero, so neither project would be chosen.
12-8a.The $5,000 spent last year on exploring the feasibility of the project is a sunk cost and should not be included in the analysis.
b.The net cost is $126,000:
Price($108,000)
Modification(12,500)
Increase in NWC (5,500)
Cash outlay for new machine($126,000)
c.The annual cash flows follow:
Year 1 Year 2 Year 3
After-tax savings$28,600$28,600 $28,600
Depreciation tax savings13,91818,979 6,326
Salvage value $65,000
Tax on SV (19,798)
Return of NWC 5,500
Project cash flows$42,518$47,579 $85,628
Notes:
1.The after-tax cost savings is $44,000(1 – T) = $44,000(0.65) = $28,600.
2.The depreciation expense in each year is the depreciable basis, $120,500, times the MACRS allowance percentages of 0.33, 0.45, and 0.15 for Years 1, 2, and 3, respectively. Depreciation expense in Years 1, 2, and 3 is $39,765, $54,225, and $18,075. The depreciation tax savings is calculated as the tax rate (35%) times the depreciation expense in each year.
3.Tax on SV = ($65,000 – $8,435)(0.35) = $19,798.
BV in Year 4 = $120,500(0.07) = $8,435.
d.The project has an NPV of $10,841; thus, it should be accepted.
YearCash FlowPV @ 12%
0 ($126,000) ($126,000)
1 42,518 37,963
2 47,579 37,930
3 85,628 60,948
NPV = $ 10,841
Alternatively, place the cash flows on a time line:
0123
||||
-126,00042,51847,57934,926
50,702
85,628
With a financial calculator, input the appropriate cash flows into the cash flow register, input I/YR = 12, and then solve for NPV = $10,840.51 $10,841.
13-2The optimal capital structure is that capital structure where WACC is minimized and stock price is maximized. Because Jackson’s stock price is maximized at a 30% debt ratio, the firm’s optimal capital structure is 30% debt and 70% equity. This is also the debt level where the firm’s WACC is minimized.