Bond P is a premium bond with a 12 percent coupon. Bond D is a 6 percent coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 9 percent, and have five years to maturity. maturity. The current yield for Bonds P and D is
10.75 ± 1.0%
percent and
6.79 ± 1.0%
percent, respectively. respectively.
If interest rates remain unchanged, the expected capital gains yield over the next year for Bonds P and D is -1.75 ± 1.0%
percent and
2.21 ± 1.0%
percent, respectively. respectively.
Explanation:
To find the capital gains yield and the current yield, we need to find the price of the bond. The current price of Bond P and the price of Bond P in one year is: P: P0 = $120(PVIFA9%,5) + $1,000(PVIF 9%,5) = $1,116.69 P1 = $120(PVIFA9%,4) + $1,000(PVIF 9%,4) = $1,097.19 Current yield = $120 / $1,116.69 = .1075 or 10.75% The capital gains yield is: Capital gains yield = (New price – Original Original price) / Original price Capital gains yield = ($1,097.19 – 1,111.69) 1,111.69) / $1,116.69 = – .0175 .0175 or – 1.75% 1.75% The current price of Bond D and the price of Bond D in one year is: D: P0 = $60(PVIFA9%,5) + $1,000(PVIF 9%,5) = $883.31 P1 = $60(PVIFA9%,4) + $1,000(PVIF 9%,4) = $902.81 Current yield = $60 / $883.81 = .0679 or 6.79% Capital gains yield = ($902.81 – 883.31) 883.31) / $883.31 = +.0221 or +2.21% All else held constant, premium bonds pay high current income while having price depreciation as maturity nears; discount bonds do not pay high current income but have price appreciation as maturity nears. For either bond, the total return is still 9%, but this return is distributed differently between between current income and capital gains One More Time Software has 9.2 percent coupon bonds on the market with nine years to maturity. The bonds make semiannual payments and currently sell for 106.8 percent of par. The T he current yield on the bonds is percent, the YTM YTM is
8.12 ± 1%
percent, and the the effective annual yield is
Explanation:
The bond price equation for this bond is: P0 = $1,068 = $46(PVIFA R%,18) + $1,000(PVIF R%,18)
8.29 ± 1%
percent.
8.61 ± 1%
Using a spreadsheet, financial calculator, or trial and error we find: R = 4.06%
This is the semiannual interest rate, so the YTM is: YTM = 2 × 4.06% = 8.12% The current yield is: Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61% The effective annual yield is the same as the EAR, so using the EAR equation: Effective annual yield = (1 + 0.0406) 2 – 1 1 = .0829 or 8.29%
Grohl Co. issued 11-year bonds a year ago at a coupon rate of 6.9 percent. The bonds make semiannual payments. If the YTM on these bonds is 7.4 percent, the current bond price is $
965.1 ± 1%
.
Explanation:
To find the price of this bond, we need to realize that the maturity of the bond is 10 years. The bond was issued one year ago, with 11 years to maturity, so there are 10 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The T he price of the bond is: P = $34.50(PVIFA 3.7%,20) + $1,000(PVIF 3.7%,20) = $965.10
Kiss the Sky Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for $1,045. At this price, the bonds yield 7.5 percent. The coupon rate on the bonds is
8.05 ± 1%
percent.
Explanation:
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 = $1,045 = C(PVIFA 7.5%,13) + $1,000(PVIF 7.5%,13) Solving for the coupon payment, we get:
C = $80.54 The coupon payment is the coupon rate times par value. Using this relationship, we get: Coupon rate = $80.54 / $1,000 = .0805 or 8.05%
Ackerman Co. has 9 percent coupon bonds bo nds on the market with nine years left to maturity. The bonds make annual payments. If the bond currently sells for $934, the the YTM is
10.15 ± 1%
percent.
Explanation:
Here we need to find the YTM of a bond. The equation for the bond price is: P = $934 = $90(PVIFA R%,9) + $1,000(PVIF R%,9) Notice the equation equation cannot be solved solved directly for for R. Using a spreadsheet, a financial calculator, or trial and error, we find: R = YTM = 10.15%
Suppose you buy a 7 percent coupon, 20-year bond today when it's first issued. If interest rates suddenly rise to 15 percent, the value value of your bond will will decrease . Explanation:
Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. This is because the fixed coupon payments determined by the fixed coupon rate are not as valuable when interest rates rise — hence, hence, the price of the bond bond decreases.
Metroplex Corporation will pay a $3.04 per share dividend next year. The company pledges to increase its dividend by 3.8 percent per year indefinitely. indefinitely. If you you require an 11 percent return on your investment, investment, you will pay $ 42.22 ± 1.0%
for the company's stock today.
Explanation:
Using the constant growth model, we find the price of the stock today is:
P0 = D1 / ( R – g ) = $3.04 / (.11 – .038) = $42.22
Suppose you know a company's stock currently sells for $47 per share and the required return on the stock is 11 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, the current dividend is $
2.45 ± 1.0%
per share.
Explanation:
We know the stock has a required return of 11 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.11) = .055 = Capital gains yield Now we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so: D1 = .055($47) = $2.59 This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year: D1 = D0(1 + g ) We can solve for the dividend that was just paid: $2.59 = D0(1 + .055) D0 = $2.59 / 1.055 = $2.45
Resnor, Inc., has an issue of preferred stock outstanding that pays a $5.50 dividend every year in perpetuity. If this issue currently sells for $108 per share, the required return is
5.09 ± 1.0%
percent.
Explanation:
The price a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. Using this equation, we find the price per share of the preferred stock is: R = D/P 0 = $5.50/$108 = .0509 or 5.09%
Great Pumpkin Farms (GPF) just paid a dividend of $3.50 on its stock. The growth rate in dividends is expected to be a constant 5 percent per year indefinitely. Investors require a 14 percent return on the stock for the first three years, a 12 percent return for the next three years, and a 10 percent return thereafter. The current share price for GPF stock is $
63.47 ± 1.0%
.
Explanation:
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 required return are stable forever. The price of the stock in Year 6 will be the dividend in Year 7, divided by the required return minus the growth rate in dividends. So: P6 = D6 (1 + g ) / ( R - g ) = D0 (1 + g ) / ( R - g ) = $3.50 (1.05) / (.10 - .05) = $98.50 Now we can find the price of the stock in Year 3. We need to find the price here since the required return changes at that time. The price of the stock in Year 3 is the PV of the dividends in Years 4, 5, and 6, plus the PV of the stock price in Year 6. The price of the stock in Year 3 is: P3 = $3.50(1.05) 4 / 1.12 + $3.50(1.05) 5 / 1.12 2 + $3.50(1.05) 6 / 1.12 3 + $98.50 / 1.12 3 P3 = $80.81 Finally, we can find the price of the stock today. The price today will be the PV of the dividends in Years 1, 2, and 3, plus the PV of the stock in Year 3. The price of the stock today is: P0 = $3.50(1.05) / 1.14 + $3.50(1.05) 2 / (1.14)2 + $3.50(1.05) 3 / (1.14) 3 + $80.81 / (1.14) 3 P0 = $63.47
Far Side Corporation is expected to pay the following dividends over the next four years: $11, $8, $5, and $2. Afterward, the company pledges to maintain a constant 5 percent growth rate in dividends forever. If the required return on the stock is 12 percent, the current share price is $
40.09 ± 1.0%
.
Explanation:
With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4, at the beginning of the constant dividend growth, as: P4 = D4(1 + g ) / ( R - g ) = $2.00(1.05) / (.12 - .05) = $30.00 The price of the stock today is the PV of the first four dividends, plus the PV of the Year 4 stock price. So, the price of the stock today will be: P0 = $11.00 / 1.12 + $8.00 / 1.12 + $5.00 / 1.12 + $2.00 / 1.12 + $30.00 / 1.12 = $40.09
Consider four different stocks, all of which have a required return of 19 percent and a most recent dividend of $4.50 per share. Stocks W, X, and Y are expected to maintain constant growth rates in dividends for the foreseeable future of 10 percent, 0 percent, and -5 percent per year, respectively. Stock Z is a growth stock that will increase its dividend by 20 percent for the next two years and then maintain a constant 12 percent growth rate thereafter. The dividend yield for Stocks W, X, Y, and Z is 6.6 ± 1.0%
percent,
0
9 ± 1.0%
percent,
19 ± 1.0%
percent,
24 ± 1.0%
percent, respectively. The expected capital gains yield for the respective stocks are percent,
-5
percent, and
12.4 ± 1.0%
percent, and 10 ± 1.0%
percent.
Explanation:
We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have a 19 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield. W:
P0 = D0(1 + g ) / ( R - g ) = $4.50(1.10)/(.19 - .10) = $55.00 Dividend yield = D 1/P0 = $4.50(1.10)/$55.00 = .09 or 9% Capital gains yield = .19 - .09 = .10 or 10%
X:
P0 = D0(1 + g ) / ( R - g ) = $4.50/(.19 - 0) = $23.68 Dividend yield = D 1/P0 = $4.50/$23.68 = .19 or 19% Capital gains yield = .19 - .19 = 0%
Y:
P0 = D0(1 + g ) / ( R - g ) = $4.50(1 - .05)/(.19 + .05) = $17.81 Dividend yield = D 1/P0 = $4.50(0.95)/$17.81 = .24 or 24% Capital gains yield = .19 - .24 = -.05 or -5%
Z:
P2 = D2(1 + g 2) / ( R - g 2) = D0(1 + g 1)2(1 + g 2)/( R - g 2) = $4.50(1.20) 2(1.12)/(.19 - .12) = $103.68 P0 = $4.50 (1.20) / (1.19) + $4.50 (1.20) 2 / (1.19)2 + $103.68 / (1.19) 2 = $82.33 Dividend yield = D 1/P0 = $4.50(1.20)/$82.33 = .066 or 6.6% Capital gains yield = .19 - .066 = .124 or 12.4%
In all cases, the required return is 19%, but the return is distributed differently between current income and capital gains. High growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time.
Most corporations pay quarterly dividends on their common stock rather than annual dividends. Barring any unusual circumstances during the year, the board raises, lowers, or maintains the current dividend once a year and then pays this dividend out in equal quarterly installments to its shareholders.
Suppose a company currently pays a $3.20 annual dividend on its common stock in a single annual installment, and management plans on raising this dividend by 6 percent per year indefinitely. If the required return on this
a.
stock is 12 percent, the current share price is $
b.
56.53 ± 1.0%
.
Now suppose the company in (a) actually pays its annual dividend in equal quarterly installments; thus, this company has just paid a $.80 dividend per share, as it has for the previous three quarters. The value for the current share price is now $ year.)
59.02 ± 1.0%
. ( Hint: Find the equivalent annual end-of-year dividend for each
Explanation:
a. Using the constant growth model, the price of the stock paying annual dividends will be: P0 = D0(1 + g ) / ( R - g ) = $3.20(1.06)/(.12 - .06) = $56.53 b.If the company pays quarterly dividends instead of annual dividends, the quarterly dividend will be one-fourth of annual dividend, or: Quarterly dividend: $3.20(1.06)/4 = $0.848 To find the equivalent annual dividend, we must assume that the quarterly dividends are reinvested at the required return. We can then use this interest rate to find the equivalent annual dividend. In other words, when we receive the quarterly dividend, we reinvest it at the required return on the stock. So, the effective quarterly rate is: Effective quarterly rate: 1.12 .25 - 1 = .0287 The effective annual dividend will be the FVA of the quarterly dividend payments at the effective quarterly required return. In this case, the effective annual dividend will be: Effective D1 = $0.848(FVIFA2.87%,4) = $3.54 Now, we can use the constant growth model to find the current stock price as: P0 = $3.54/(.12 - .06) = $59.02 Note that we can not simply find the quarterly effective required return and growth rate to find the value of the stock. This would assume the dividends increased each quarter, not each year.
Storico Co. just paid a dividend of $2.45 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on Storico stock is 11 percent, a share of stock will sell for $
55.7 ± 1.0%
today.
Explanation:
Here we have a stock with supernormal growth, but the dividend growth changes every year for the first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be: P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 - .05) = $65.08
The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, so: P0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.11 2 + $2.45(1.20)(1.15)(1.10)/1.113 + $65.08/1.11 3 P0 = $55.70
Storico Co. just paid a dividend of $2.45 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate, forever. If a share of Storico stock sells for $63.82 today, the required return on Storico stock is
10.24 ± 1.0%
percent. (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16)) ( Hint: Set up the valuation formula with all the relevant cash flows, and use trial and error to find the unknown rate of return.) Explanation:
Here we want to find the required return that makes the PV of the dividends equal to the current stock price. The equation for the stock price is: P = $2.45(1.20)/(1 + R) + $2.45(1.20)(1.15)/(1 + R)2 + $2.45(1.20)(1.15)(1.10)/(1 + R)3 + [$2.45(1.20)(1.15)(1.10)(1.05)/( R Â – .05)]/(1 + R)3 = $63.82 We need to find the roots of this equation. Using spreadsheet, trial and error, or a calculator with a root solving function, we find that: R = 10.24%
Suppose you bought a 7 percent coupon bond one year ago for $1,040. The bond sells for $1,070 today. Required: (a) Assuming a $1,000 face value, what was your total include the dollar sign ($).)
Total dollar return
$
dollar return on this investment over the past year? (Do not
100 ± 1%
(b) What was your total nominal rate of return on this investment over the past year? (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16))
Nominal rate of return (c)
9.62 ± 1%
percent
If the inflation rate last year was 4 percent, what was your total real rate of return on this investment? (Do not
include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16))
Real rate of return
5.4 ± 1%
percent
Explanation: (a)
The total dollar return is the increase in price plus the coupon payment, so: Total dollar return = $1,070 – 1,040 + 70 = $100 (b)
The total percentage return of the bond is: R = [($1,070 – 1,040) + 70] / $1,040 = .0962 or 9.62% Notice here that we could have simply used the total dollar return of $100 in the numerator of this equation (c)
Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.0962 / 1.04) – 1 = .0540 or 5.40%
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. (Do not include the percent signs (%). For average return and standard deviation round your answers to 2 decimal places, (e.g., 32.16) and for variance round your answers to 6 decimal places. (e.g., 32.161616))
Returns Year 1 2 3 4 5
X
Y 16% 38 14 – 21 26
8% 21 17 – 16 9
X Average Return Variance Standard Deviation
7.8 ± 1%
Y %
.020670 ± 1% 14.38 ± 1%
%
14.6 ± 1%
%
.048680 ± 1% 22.06 ± 1%
%
Explanation:
The average return is the sum of the returns, divided by the number of returns. The average return for each stock was:
[.08 + .21 + .17 – .16 + .09] / N =
= .0780 or 7.80%
5
[.16 + .38 + .14 – .21 + .26] / N =
5
= .1460 or 14.60%
Remembering back to statistics, we calculate the variance of each stock as:
/ ( N – 1)
σx2
=
σy2
=
1 5 – 1
=.020670
1 5 – 1
=.048680
The standard deviation is the square root of the variance, so the standard deviation of each stock is: = .1438 or 14.38% σ X = (.020670) = .2206 or 22.06% σ Y = (.048680)
Consider the following table for the period from 1970 through 1975. Returns Years 1970 1971 1972 1973 1974 1975
LargeCompany Stocks 3.94% 14.30 18.99 -14.69 -26.47 37.23
U.S. Treasury Bills 6.50% 4.36 4.23 7.29 7.99 5.87
Required:
a.
The arithmetic average returns for large-company stocks and T-bills over this time period was percent and
6.04 ± 1%
5.55 ± 1%
percent, respectively. (Do not include the percent signs (%). Round your answers to
2 decimal places. (e.g., 32.16))
b.
The standard deviation of the returns for large-company stocks and T-bills over this time period was
23.23 ± 1%
percent and
1.53 ± 1%
percent, respectively. (Do not include the percent signs (%). Round
your answers to 2 decimal places. (e.g., 32.16))
c.
The average risk premium over this period was
-0.49 ± 1%
percent and the standard deviation was
24.4 ± 1%
percent. (Negative amount should be indicated by a minus sign. Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16)) Explanation: a.
We will calculate the sum of the returns for each asset and the observed risk premium first. Doing so, we get:
Year 1970 1971 1972 1973 1974 1975
Large co. stock return 3.94% 14.30 18.99 -14.69 -26.47 37.23 33.30
T-bill return 6.50% 4.36 4.23 7.29 7.99 5.87 36.24
Risk premium -2.56% 9.94 14.76 -21.98 -34.46 31.36 -2.94
The average return for large company stocks over this period was: Large company stocks average return = 33.30% / 6 = 5.55% And the average return for T-bills over this period was: T-bills average return = 36.24% / 6 = 6.04% b.
Using the equation for variance, we find the variance for large company stocks over this period was: Variance = 1/5[(.0394 – .0555)2 + (.1430 – .0555)2 + (.1899 – .0555)2 + ( – .1469 – .0555)2 + ( – .2647 – .0555)2 + (.3723 – .0555)2] Variance = 0.053967 And the standard deviation for large company stocks over this period was: Standard deviation = (0.053967) 1/2 = 0.2323 or 23.23% Using the equation for variance, we find the variance for T-bills over this period was: Variance = 1/5[(.0650 – .0604)2 + (.0436 – .0604)2 + (.0423 – .0604)2 + (.0729 – .0604)2 + (.0799 – .0604)2 + (.0587 – .0604)2] Variance = 0.000234 And the standard deviation for T-bills over this period was: Standard deviation = (0.000234) = 0.0153 or 1.53% c.
The average observed risk premium over this period was: Average observed risk premium = – 2.94% / 6 = – 0.49% The variance of the observed risk premium was: Variance = 1/5[( – .0256 – ( – .0049)) + (.0994 – ( – .0049)) + (.1476 – ( – . 0049)) + ( – .2198 – ( – . 0049)) + ( – .3446 – ( – .0049))2 + (.3136 – ( – .0049))2] Variance = 0.059517
And the standard deviation of the observed risk premium was: Standard deviation = (0.059517) = 0.2440 or 24.40% A stock has had the following year-end prices and dividends: Year 1 2 3 4 5 6
Price $60.18 73.66 94.18 89.35 78.49 95.05
Dividend —
$.60 .64 .72 .80 1.20
Required:
The arithmetic and geometric returns for the stock are
11.83 ± 1%
percent and
10.58 ± 1%
percent, respectively.
(Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16)) Explanation:
To calculate the arithmetic and geometric average returns, we must first calculate the return for each year. The return for each year is: R 1 = ($73.66 – 60.18 + 0.60) / $60.18 = .2340 or 23.40% R 2 = ($94.18 – 73.66 + 0.64) / $73.66 = .2873 or 28.73% R 3 = ($89.35 – 94.18 + 0.72) / $94.18 = – .0436 or – 4.36% R 4 = ($78.49 – 89.35 + 0.80)/ $89.35 = – .1126 or 11.26% R 5 = ($95.05 – 78.49 + 1.20) / $78.49 = .2263 or 22.63% The arithmetic average return was: R A = (0.2340 + 0.2873 – 0.0436 + 0.1126 + 0.2263)/5 = 0.1183 or 11.83% And the geometric average return was: R G = [(1 + .2340)(1 + .2873)(1 – .0436)(1 + .1126)(1 + .2263)] 1/5 – 1 = 0.1058 or 10.58% You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14 percent and Stock Y with an expected return of 10.5 percent. If your goal is to create a portfolio with an expected return of 12.4 percent, you will invest $
5,428.57 ± 0.1%
in Stock X and $
4,574.43 ± 0.1%
in Stock Y. (Do not include
the dollar signs ($). Round your answer to 2 decimal places. (e.g., 32.16)) Explanation:
Here we are given the expected return of the portfolio and the expected return of each asset in the portfolio, and are asked to find the weight of each asset. We can use the equation for the expected return of a portfolio to solve this problem. Since the total weight of a portfolio must equal 1 (100%), the weight of Stock Y must be one minus the weight of Stock X. Mathematically speaking, this means: E(R p) = .124 = .14w X + .105(1 – wX) We can now solve this equation for the weight of Stock X as:
.124 = .14wX + .105 – .105wX .019 = .035wX So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or: Investment in X = 0.542857($10,000) = $5,428.57 And the dollar amount invested in Stock Y is: Investment in Y = (1 – 0.542857)($10,000) = $4,574.43
You own a stock portfolio invested 25 percent in Stock Q, 20 percent in Stock R, 15 percent in Stock S, and 40 percent in Stock T. The betas for these four stocks are .84, 1.17, 1.11, and 1.36, respectively. The portfolio beta is 1.15 ± 1.0%
. (Round your answer to 2 decimal places. (e.g., 32.16.))
Explanation:
The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is: β p = .25(.84) + .20(1.17) + .15(1.11) + .40(1.36) = 1.15
A stock has a beta of 1.35 and an expected return of 16 percent. A risk-free asset currently earns 4.8 percent. Required:
(a)
The expected return on a portfolio that is equally invested in the two assets is
10.4 ± 1.0%
percent. (Do not
include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16.))
(b)
If a portfolio of the two assets has a beta of .95, the weight of the stock is of the risk-free is
29.63 ± 1.0%
70.37 ± 1.0%
percent and the weight
percent. (Do not include the percent signs (%). Round your answers to 2
decimal places. (e.g., 32.16.))
(c)
If a portfolio of the two assets has an expected return of 8 percent, its beta is
0.386 ± 1.0%
. (Round your
answer to 3 decimal places. (e.g., 32.161))
(d)
If a portfolio of the two assets has a beta of 2.70, the weight of the stock is
200 ± 1.0%
percent and the weight
of the risk-free is
-100 ± 1.0%
percent (Negative amount should be indicated by a minus sign. Do not
include the percent signs (%)) .
Explanation: (a)
Again we have a special case where the portfolio is equally weighted, so we can sum the returns of each asset and divide by the number of assets. The expected return of the portfolio is: E(R p) = (.16 + .048)/2 = .1040 or 10.40% (b)
We need to find the portfolio weights that result in a portfolio with a b of 0.95. We know the b of the risk-free asset is zero. We also know the weight of the risk-free asset is one minus the weight of the stock since the portfolio weights must sum to one, or 100 percent. So: b p = 0.95 = wS(1.35) + (1 – wS)(0) 0.95 = 1.35wS + 0 – 0wS wS = 0.95/1.35 wS = .7037 And, the weight of the risk-free asset is: wRf = 1 – .7037 = .2963 (c)
We need to find the portfolio weights that result in a portfolio with an expected return of 8 percent. We also know the weight of the risk-free asset is one minus the weight of the stock since the portfolio weights must sum to one, or 100 percent. So: E(R p) = .08 = .16w S + .048(1 – wS) .08 = .16wS + .048 – .048wS wS = .2857 So, the b of the portfolio will be: b p = .2857(1.35) + (1 – .2857)(0) = 0.386 (d)
Solving for the β of the portfolio as we did in part b, we find: β p = 2.70 = w S(1.35) + (1 – wS)(0)
wS = 2.70/1.35 = 2 wRf = 1 – 2 = – 1 The portfolio is invested 200% in the stock and – 100% in the risk-free asset. This represents borrowing at the riskfree rate to buy more of the stock.
Consider the following information on three stocks:
State of Economy Boom Normal Bust
Required:
Probability of State of Economy .35 .50 .15
Rate of Return if State Occurs Stock A Stock B Stock C .24 .36 .55 .17 .13 .09 – .28 – .45 .00
(a) If your portfolio is invested 40 percent each 16.12 ± 1%
percent. (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 0.03253 ± 1%
32.16.) The variance is
deviation is
in A and B and 20 percent in C, the portfolio expected return is
18.04 ± 1%
(Round your answer to 5 decimal places. (e.g., 32.16125.) and standard
percent. (Do not include the percent sign (%). Round your answer to 2 decimal
places. (e.g., 32.16.))
(b)
If the expected T-bill rate is 3.80 percent, the expected risk premium on the portfolio is
12.32 ± 1%
percent.
(Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16.))
(c)
If the expected inflation rate is 3.50 percent, the approximate and exact expected real returns on the portfolio are 12.62 ± 1%
percent and
12.19 ± 1%
premiums on the portfolio are
percent, respectively. The approximate and exact expected real risk
12.32 ± 1%
percent and
11.9 ± 1%
percent, respectively. (Do not include the
percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16.))
Explanation: (a)
We need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get: Boom: E(R p) = .4(.24) + .4(.36) + .2(.55) = .3500 or 35.00% Normal: E(R p) = .4(.17) + .4(.13) + .2(.09) = .1380 or 13.80% Bust: E(R p) = .4(.00) + .4( – .28) + .2( – .45) = – .2020 or – 20.20% And the expected return of the portfolio is: E(R p) = .35(.35) + .50(.138) + .15( – .202) = .1612 or 16.12% To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, than add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio is: σ p = .35(.35 – .1612) + .50(.138 – .1612) + .15( – .202 – .1612) σ p = .03253 σ p = (.03253) = .1804 or 18.04% (b)
The risk premium is the return of a risky asset, minus the risk-free rate. T -bills are often used as the risk-free rate, so: RPi = E(R p) – R f = .1612 – .0380 = .1232 or 12.32% (c)
The approximate expected real return is the expected nominal return minus the inflation rate, so: Approximate expected real return = .1612 – .035 = .1262 or 12.62% To find the exact real return, we will use the Fisher equation. Doing so, we get: 1 + E(R i) = (1 + h)[1 + e(r i)] 1.1612 = (1.0350)[1 + e(r i)] e(r i) = (1.1612/1.035) – 1 = .1219 or 12.19% The approximate real risk premium is the expected return minus the risk-free rate, so: Approximate expected real risk premium = .1612 – .038 = .1232 or 12.32%
The exact expected real risk premium is the approximate expected real risk premium, divided by one plus the inflation rate, so: Exact expected real risk premium = .1232/1.035 = .1190 or 11.90%
You want to create a portfolio equally as risky as the market, and you have $1,000,000 to invest. Given this information, fill in the rest of the following table. (Do not include the dollar signs ($). Leave no cells blank - be certain to enter "0" wherever required. Round your answers to the nearest whole dollar amount. (e.g., 32))
Asset Stock A Stock B Stock C
Investment $210,000 $320,000 $
Risk-free asset
$
Beta
324,074 ± 1%
.85 1.20 1.35
145,926 ± 1%
0 ± 1%
Explanation:
Since the portfolio is as risky as the market, the β of the portfolio must be equal to one. We also know the β of the risk-free asset is zero. We can use the equation for the β of a portfolio to find the weight of the third stock. Doing so, we find: β p = 1.0 = w A(.85) + wB(1.20) + wC(1.35) + wRf (0) Solving for the weight of Stock C, we find: wC = .324074 So, the dollar investment in Stock C must be: Invest in Stock C = .324074($1,000,000) = $324,074 We know the total portfolio value and the investment of two stocks in the portfolio, so we can find the weight of these two stocks. The weights of Stock A and Stock B are: wA = $210,000 / $1,000,000 = .210 wB = $320,000/$1,000,000 = .320 We also know the total portfolio weight must be one, so the weight of the risk-free asset must be one minus the asset weight we know, or: 1 = wA + wB + wC + wRf = 1 – .210 – .320 – .324074 = wRf wRf = .145926 So, the dollar investment in the risk-free asset must be: Invest in risk-free asset = .145926($1,000,000) = $145,926
Suppose you observe the following situation: Security Pete Corp. Repete Co.
Beta 1.35 .80
Expected Return .132 .101
Assume these securities are correctly priced. Based on the CAPM, the expected return on the market is 11.23 ± 1%
percent. The risk-free rate is
5.59 ± 1%
your answers to 2 decimal places. (e.g., 32.16.))
percent. (Do not include the percent signs (%). Round
Explanation:
Here we have the expected return and beta for two assets. We can express the returns of the two assets using CAPM. If the CAPM is true, then the security market line holds as well, which means all assets have the same risk premium. Setting the risk premiums of the assets equal to each other and solving for the risk-free rate, we find: (.132 – R f)/1.35 = (.101 – R f)/.80 .80(.132 – R f) = 1.35(.101 – R f) .1056 – .8R f = .13635 – 1.35R f .55R f = .03075 R f = .0559 or 5.59% Now using CAPM to find the expected return on the market with both stocks, we find: .132 = .0559 + 1.35(R M – .0559) .101 = .0559 + .80(R M – .0559) R M = .1123 or 11.23% R M = .1123 or 11.23%
Suppose you observe the following situation:
State of Economy Bust Normal Boom
Probability of State .15 .70 .15
Return if State Occurs Stock A Stock B – .08 – .05 .13 .14 .48 .29
Required: (a) Calculate the expected return on each stock. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16.))
Expected return Stock A Stock B
15.1 ± 1% 13.4 ± 1%
percent percent
(b) Assuming the capital asset pricing model holds and stock A's beta is greater than stock B's beta by .25, what is the expected market risk premium? (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16))
Expected market risk premium
6.8 ± 1%
percent
Explanation: (a)
The expected return of an asset is the sum of the probability of each return occurring times the probability of that
return occurring. So, the expected return of each stock is: E(R A) = .15( – .08) + .70(.13) + .15(.48) = .1510 or 15.10% E(R B) = .15( – .05) + .70(.14) + .15(.29) = .1340 or 13.40% (b)
We can use the expected returns we calculated to find the slope of the Security Market Line. We know that the beta of Stock A is .25 greater than the beta of Stock B. Therefore, as beta increases by .25, the expected return on a security increases by .017 (= .1510 – .1340). The slope of the security market line (SML) equals: SlopeSML = Rise / Run SlopeSML = Increase in expected return / Increase in beta SlopeSML = (.1510 – .1340) / .25 SlopeSML = .0680 or 6.80% Since the market's beta is 1 and the risk-free rate has a beta of zero, the slope of the Security Market Line equals the expected market risk premium. So, the expected market risk premium must be 6.8 percent.
Stock in Country Road Industries has a beta of .85. The market risk premium is 8 percent, and T-bills are currently yielding 5 percent. The company's most recent dividend was $1.60 per share, and dividends are expected to grow at a 6 percent annual rate indefinitely. If the stock sells for $37 per share, your best estimate of Country Road's cost of equity is
11.19 ± 1.0%
percent. (Do not include the percent sign (%). Round your answer to 2 decimal places.
(e.g., 32.16))
Explanation:
We have the information available to calculate the cost of equity using the CAPM and the dividend growth model. Using the CAPM, we find: R E = .05 + 0.85(.08) = .1180 or 11.80% And using the dividend growth model, the cost of equity is R E = [$1.60(1.06)/$37] + .06 = .1058 or 10.58% Both estimates of the cost of equity seem reasonable. If we remember the historical return on large capitalization stocks, the estimate from the CAPM model is about two percent higher than average, and the estimate from the dividend growth model is about one percent higher than the historical average, so we cannot definitively say one of the estimates is incorrect. Given this, we will use the average of the two, so: R E = (.1180 + .1058)/2 = .1119 or 11.19%
Suppose In a Found Ltd. just issued a dividend of $1.43 per share on its common stock. The company paid dividends of $1.05, $1.12, $1.19, and $1.30 per share in the last four years. If the stock currently sells for $45, your best estimate of the company's cost of equity capital using the arithmetic average growth rate in dividends is 11.47 ± 1.0%
percent. If you use the geometric average growth rate, your best estimate is
11.46 ± 1.0%
(Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16))
rev: 10_18_2011
percent.
Explanation:
To use the dividend growth model, we first need to find the growth rate in dividends. So, the increase in dividends each year was: g1 = ($1.12 – 1.05)/$1.05 = .0667 or 6.67% g2 = ($1.19 – 1.12)/$1.12 = .0625 or 6.25% g3 = ($1.30 – 1.19)/$1.19 = .0924 or 9.24% g4 = ($1.43 – 1.30)/$1.30 = .1000 or 10.00% So, the average arithmetic growth rate in dividends was: g = (.0677 + .0625 + .0924 + .1000)/4 = .0804 or 8.04% Using this growth rate in the dividend growth model, we find the cost of equity is: R E = [$1.43(1.0804)/$45.00] + .0804 = .1147 or 11.47% Calculating the geometric growth rate in dividends, we find: $1.43 = $1.05(1 + g) 4 g = 0.0803 or 8.03% The cost of equity using the geometric dividend growth rate is: R E = [$1.43(1.0803)/$45.00] + .0803 = .1146 or 11.46%
Mullineaux Corporation has a target capital structure of 60 percent common stock, 5 percent preferred stock, and 35 percent debt. Its cost of equity is 14 percent, the cost of preferred stock is 6 percent, and the cost of debt is 8 percent. The relevant tax rate is 35 percent. (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16))
10.52 ± 1.0%
(a)
Mullineaux's WACC is
(b)
Which of the following statement is true?
percent.
On an aftertax basis, debt is cheaper than the preferred stock. Explanation: a:
Using the equation to calculate the WACC, we find: WACC = .60(.14) + .05(.06) + .35(.08)(1 – .35) = .1052 or 10.52% b:
Since interest is tax deductible and dividends are not, we must look at the aftertax cost of debt, which is: .08(1 – .35) = .0520 or 5.20% Hence, on an aftertax basis, debt is cheaper than the preferred stock.
Sixx AM Manufacturing has a target debt – equity ratio of 0.65. Its cost of equity is 15 percent, and its cost of debt is 9 percent. If the tax rate is 35 percent, the company's WACC is
11.40 ± 1.0%
percent. (Do not include the
percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16))
Explanation:
Here we need to use the debt – equity ratio to calculate the WACC. Doing so, we find: WACC = .15(1/1.65) + .09(.65/1.65)(1 – .35) = .1140 or 11.40%
Filer Manufacturing has 11 million shares of common stock outstanding. The current share price is $68, and the book value per share is $6. Filer Manufacturing also has two bond issues outstanding. The first bond issue has a face value of $70 million, has a 7 percent coupon, and sells for 93 percent of par. The second issue has a face value of $55 million, has an 8 percent coupon, and sells for 104 percent of par. The first issue matures in 21 years, the second in 6 years. The most recent dividend was $4.10 and the dividend growth rate is 6 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 35 percent. The company's WACC is
11.33 ± 1.0%
percent.(Do not include the percent sign (%).
Round your answer to 2 decimal places. (e.g., 32.16))
Explanation:
First, we will find the cost of equity for the company. The information provided allows us to solve for the cost of equity using the dividend growth model, so: R E = [$4.10(1.06)/$68] + .06 = .1239 or 12.39% Next, we need to find the YTM on both bond issues. Doing so, we find: P1 = $930 = $35(PVIFA R%,42) + $1,000(PVIF R%,42) R = 3.838% YTM = 3.838% × 2 = 7.68% P2 = $1,040 = $40(PVIFAR%,12) + $1,000(PVIF R%,12) R = 3.584% YTM = 3.584% × 2 = 7.17%
Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: MVD = .93($70,000,000) + 1.04($55,000,000) = $122,300,000 To find the weighted average aftertax cost of debt, we need the weight of each bond as a percentage of the total debt. We find: wD1 = .93($70,000,000)/$122,300,000 = .5323 wD2 = 1.04($55,000,000)/$122,300,000 = .4677 Now we can multiply the weighted average cost of debt times one minus the tax rate to find the weighted average aftertax cost of debt. This gives us: R D = (1 – .35)[(.5323)(.0768) + (.4677)(.0717)] = .0484 or 4.84% The market value of equity is the share price times the number of shares, so: MVE = 11,000,000($68) = $748,000,000 This makes the total market value of the company: V = $748,000,000 + 122,300,000 = $870,300,000 And the market value weights of equity and debt are: E/V = $748,000,000/$870,300,000 = .8595 D/V = 1 – E/V = .1405 Using these costs we have found and the weight of debt we calculated earlier, the WACC is: WACC = .8595(.1239) + .1405(.0484) = .1133 or 11.33%
Jungle, Inc., has a target debt – equity ratio of 1.05. Its WACC is 9.4 percent, and the tax rate is 35 percent. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16))
Required: 7.72 ± 1.0%
(a)
If Jungle's cost of equity is 14 percent, its pretax cost of debt is
(b)
If instead you know the aftertax cost of debt is 6.8 percent, the cost of equity is
Explanation:
percent. 12.13 ± 1.0%
percent.
Req a:
Using the equation to calculate WACC, we find: WACC = .094 = (1/2.05)(.14) + (1.05/2.05)(1 – .35)R D R D = .0772 or 7.72% Req b:
Using the equation to calculate WACC, we find: WACC = .094 = (1/2.05)R E + (1.05/2.05)(.068) R E = .1213 or 12.13%
9.83 ± 1.0%
Given the following information for Evenflow Power Co., the WACC is percent. Assume the company's tax rate is 35 percent. (Do not include the percent sign (%). Round your answer to 2 decimal places. (e.g., 32.16))
Debt: Common stock: Preferred stock: Market:
8,000 6.5 percent coupon bonds outstanding, $1,000 par value, 20 years to maturity, selling for 92 percent of par; the bonds make semiannual payments. 250,000 shares outstanding, selling for $57 per share; the beta is 1.05. 15,000 shares of 5 percent preferred stock outstanding, currently selling for $93 per share. 8 percent market risk premium and 4.5 percent risk-free rate.
Explanation:
We will begin by finding the market value of each type of financing. We find: MVD = 8,000($1,000)(0.92) = $7,360,000 MVE = 250,000($57) = $14,250,000 MVP = 15,000($93) = $1,395,000 And the total market value of the firm is: V = $7,360,000 + 14,250,000 + 1,395,000 = $23,005,000 Now, we can find the cost of equity using the CAPM. The cost of equity is: R E = .045 + 1.05(.08) = .1290 or 12.90% The cost of debt is the YTM of the bonds, so: P0 = $920 = $32.50(PVIFAR%,40) + $1,000(PVIFR%,40) R = 3.632% YTM = 3.632% × 2 = 7.26%
And the aftertax cost of debt is: R D = (1 – .35)(.0726) = .0472 or 4.72% The cost of preferred stock is: R P = $5/$93 = .0538 or 5.38% Now we have all of the components to calculate the WACC. The WACC is: WACC = .0472(7.36/23.005) + .1290(14.25/23.005) + .0538(1.395/23.005) = .0983 or 9.83% Notice that we didn't include the (1 – tC) term in the WACC equation. We used the aftertax cost of debt in the equation, so the term is not needed here
Suppose your company needs $20 million to build a new assembly line. Your target debt-equity ratio is .75. The flotation cost for new equity is 8 percent, but the flotation cost for debt is only 5 percent. Your boss has decided to fund the project by borrowing money because the flotation costs are lower and the needed funds are relatively small.
Required: (a)
Your company's weighted average flotation cost is
6.71 ± 1.0%
percent. (Do not include the percent sign
(%). Round your answer to 2 decimal places. (e.g., 32.16))
(b)
The true cost of building the new assembly line after taking flotation costs into account is $
21,439,510 ± 0.01%
(Do not include the dollar sign ($). Round your answer to the nearest whole dollar amount. (e.g., 32))
Explanation:
Req a:
The weighted average floatation cost is the weighted average of the floatation costs for debt and equity, so: f T = .05(.75/1.75) + .08(1/1.75) = .0671 or 6.71% Req b:
The total cost of the equipment including floatation costs is: Amount raised(1 – .0671) = $20,000,000 Amount raised = $20,000,000/(1 – .0671) = $21,439,510 Even if the specific funds are actually being raised completely from debt, the flotation costs, and hence
.
true investment cost, should be valued as if the firm’s target capital structure is used.
James Corporation is comparing two different capital structures: an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, the company would have 160,000 shares of stock outstanding. Under Plan II, there would be 80,000 shares of stock outstanding and $2.8 million in debt outstanding. The interest rate on the debt is 8 percent, and there are no taxes. Required:
(a)
If EBIT is $350,000, Plan I's EPS is $
2.19 ± 1%
while Plan II's EPS is $
1.58 ± 1%
. (Do not include the
dollar signs ($). Round your answers to 2 decimal places. (e.g., 32.16))
(b)
If EBIT is $500,000, Plan I's EPS is $
3.13 ± 1%
and Plan II's EPS is $
3.45 ± 1%
. (Do not include the
dollar signs ($). Round your answers to 2 decimal places. (e.g., 32.16))
(c)
The break-even EBIT is $
448,000 ± 0.1%
. (Do not include the dollar sign ($). Round your answer to the
nearest whole dollar amount. (e.g., 32.))
Explanation: (a)
Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax. The EPS under this capitalization will be: EPS = $350,000/160,000 shares EPS = $2.19 Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so: NI = $350,000 – .08($2,800,000) NI = $126,000 And the EPS will be: EPS = $126,000/80,000 shares EPS = $1.58 Plan I has the higher EPS when EBIT is $350,000. (b)
Under Plan I, the net income is $500,000 and the EPS is: EPS = $500,000/160,000 shares EPS = $3.13 Under Plan II, the net income is: NI = $500,000 – .08($2,800,000) NI = $276,000 And the EPS is: EPS = $276,000/80,000 shares EPS = $3.45 Plan II has the higher EPS when EBIT is $500,000. (c)
To find the breakeven EBIT for two different capital structures, we simply set the equations for EPS equal to each other and solve for EBIT. The breakeven EBIT is: EBIT/160,000 = [EBIT – .08($2,800,000)]/80,000 EBIT = $448,000
Keenan Corp. is comparing two different capital structures. Plan I would result in 7,000 shares of stock and $160,000 in debt. Plan II would result in 5,000 shares of stock and $240,000 in debt. The interest rate on the debt is 10 percent. (a) Ignoring taxes, compare both of these plans to an
all-equity plan assuming that EBIT will be $39,000. The all3.29 ± 1%
equity plan would result in 11,000 shares of stock outstanding. Plan I has an EPS of $ an EPS of $
3 ± 1%
, and the All-Equity Plan has an EPS of $
3.55 ± 1%
, Plan II has
. (Do not include the dollar signs
($). Round your answers to 2 decimal places. (e.g., 32.16))
(b)
44,000 ± 0.1%
44,000 ± 0.1%
In part (a), the break-even levels of EBIT for Plans I and II are $ and $ , (Do not include the dollar signs ($). Round your respectively, as compared to that for an all-equity plan. answers to the nearest whole dollar amount. (e.g., 32))
(c)
Ignoring taxes, EPS will be identical for Plans I and II when their EBITs are each $
44,000 ± 0.1%
. (Do not
include the dollar sign ($). Round your answer to the nearest whole dollar amount. (e.g., 32)) (d) Repeat parts (a), (b), and (c)
(I)
assuming that the corporate tax rate is 40 percent.
EPSs for Plans I, II and all-equity are $
1.97 ± 1%
,$
1.8 ± 1%
, and $
2.13 ± 1%
, respectively. (Do not
include the dollar signs ($). Round your answers to 2 decimal places. (e.g., 32.16))
(ii)
44,000 ± 0.1%
44,000 ± 0.1%
Break-even EBITs for Plans I and II compared to an all-equity plan are $ and $ , respectively. (Do not include the dollar signs ($). Round your answers to the nearest whole dollar amount. (e.g., 32))
(iii)
Break-even EBIT for Plan I versus Plan II: $
44,000 ± 0.1%
. (Do not include the dollar sign ($). Round your
answer to the nearest whole dollar amount. (e.g., 32))
Explanation: (a)
The income statement for each capitalization plan is: I
II
All-equity
EBIT Interest NI EPS
$39,000 16,000 $23,000 $3.29
$39,000 24,000 $15,000 $3.00
$39,000 0 $39,000 $3.55
The all-equity plan has the highest EPS; Plan II has the lowest EPS. (b)
The breakeven level of EBIT occurs when the capitalization plans result in the same EPS. The EPS is calculated as: EPS = (EBIT – R DD)/Shares outstanding This equation calculates the interest payment (R DD) and subtracts it from the EBIT, which results in the net income. Dividing by the shares outstanding gives us the EPS. For the all-equity capital structure, the interest term is zero. To find the breakeven EBIT for two different capital structures, we simply set the equations equal to each other and solve for EBIT. The breakeven EBIT between the all-equity capital structure and Plan I is: EBIT/11,000 = [EBIT – .10($160,000)]/7,000 EBIT = $44,000 And the breakeven EBIT between the all-equity capital structure and Plan II is: EBIT/11,000 = [EBIT – .10($240,000)]/5,000 EBIT = $44,000 The break-even levels of EBIT are the same because of M&M Proposition I. (c)
Setting the equations for EPS from Plan I and Plan II equal to each other and solving for EBIT, we get: [EBIT – .10($160,000)]/7,000 = [EBIT – .10($240,000)]/5,000 EBIT = $44,000 This break-even level of EBIT is the same as in part b again because of M&M Proposition I. (d)
The income statement for each capitalization plan with corporate income taxes is:
EBIT Interest Taxes NI EPS
I $39,000 16,000 9,200 $13,800 $1.97
II $39,000 24,000 $6,000 $9,000 $1.80
All-equity $39,000 0 $15,600 $23,400 $2.13
The all-equity plan still has the highest EPS; Plan II still has the lowest EPS. We can calculate the EPS as: EPS = [(EBIT – R DD)(1 – tC)]/Shares outstanding This is similar to the equation we used before, except now we need to account for taxes. Again, the interest expense term is zero in the all-equity capital structure. So, the breakeven EBIT between the all-equity plan a nd Plan I is: EBIT(1 – .40)/11,000 = [EBIT – .10($160,000)](1 – .40)/7,000 EBIT = $44,000 The breakeven EBIT between the all-equity plan and Plan II is: EBIT(1 – .40)/11,000 = [EBIT – .10($240,000)](1 – .40)/5,000 EBIT = $44,000 And the breakeven between Plan I and Plan II is: [EBIT – .10($160,000)](1 – .40)/7,000 = [EBIT – .10($240,000)](1 – .40)/5,000 EBIT = $44,000 The break-even levels of EBIT do not change because the addition of taxes reduces the income of all three plans by the same percentage; therefore, they do not change relative to one another.
Wood Corp. uses no debt. The weighted average cost of capital is 9 percent. If the current market value of the equity is $23 million and there are no taxes, EBIT is $
2,070,000 ± 0.01%
. (Do not include the dollar sign ($).
Input your answer in dollars, not in millions. (e.g., 1,234,567)) Explanation:
With no taxes, the value of an unlevered firm is equal to EBIT divided by the unlevered cost of equity, so: V = EBIT/WACC $23,000,000 = EBIT/.09 EBIT = .09($23,000,000) EBIT = $2,070,000
Wood Corp. uses no debt. The weighted average cost of capital is 9 percent. If the current market value of the equity is $23 million and the corporate tax rate is 35 percent, EBIT is $ 9 ± 1%
3,184,615 ± 0.01%
and the WACC is
percent. (Do not include the dollar ("$") and percent sign (%). Round your answers to the nearest
whole number. (e.g., 32))
Explanation:
If there are corporate taxes, the value of an unlevered firm is: VU = EBIT(1 – tC)/R U Using this relationship, we can find EBIT as: $23,000,000 = EBIT(1 – .35)/.09 EBIT = $3,184,615 Due to taxes, EBIT for an all-equity firm would have to be higher than it would if there were no taxes for the firm to still be worth $23 million
Maxwell Industries has a debt-equity ratio of 1.5. Its WACC is 10 percent, and its cost of debt is 7 percent. The corporate tax rate is 35 percent. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16))
Required: 18.18 ± 1%
a.
Maxwell's cost of equity capital is
b.
Maxwell's unlevered cost of equity capital is
c.
The cost of equity would be debt-equity ratio were 1.0, and
20.01 ± 1%
percent. 12.66 ± 1%
percent.
percent if the debt-equity ratio were 2,
12.66 ± 1%
16.34 ± 1%
percent if the
percent if the debt-equity ratio were zero.
Explanation: a.
With the information provided, we can use the equation for calculating WACC to find the cost of equity. The equation for WACC is: WACC = (E/V)R E + (D/V)R D(1 – tC) The company has a debt-equity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the weight of equity is 1/2.5, so WACC = .10 = (1/2.5)R E + (1.5/2.5)(.07)(1 – .35) R E = .1818 or 18.18% b.
To find the unlevered cost of equity we need to use M&M Proposition II with taxes, so: R E = R U + (R U – R D)(D/E)(1 – tC) .1818 = R U + (R U – .07)(1.5)(1 – .35) R U = .1266 or 12.66% c.
To find the cost of equity under different capital structures, we can again use M&M Proposition II with taxes. With
a debt-equity ratio of 2, the cost of equity is: R E = R U + (R U – R D)(D/E)(1 – tC) R E = .1266 + (.1266 – .07)(2)(1 – .35) R E = .2001 or 20.01% With a debt-equity ratio of 1.0, the cost of equity is: R E = .1266 + (.1266 – .07)(1)(1 – .35) R E = .1634 or 16.34% And with a debt-equity ratio of 0, the cost of equity is: R E = .1266 + (.1266 – .07)(0)(1 – .35) R E = R U = .1266 or 12.66%
Empress Corp. has no debt but can borrow at 8.2 percent. The firm's WACC is currently 11 percent, and the tax rate is 35 percent. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16)) 11 ± 1%
a.
Empress' cost of equity is
b.
If the firm converts to 25 percent debt, its cost of equity will be
c.
If the firm converts to 50 percent debt, its cost of equity will be
d.
Empress' WACC in parts (b) and (c) is
percent.
10.04 ± 1%
11.61 ± 1% 12.82 ± 1%
percent and
9.08 ± 1%
percent. percent. percent, respectively.
Explanation:
a.
For an all-equity financed company: WACC = R U = R E = .11 or 11%
b.
To find the cost of equity for the company with leverage we need to use M&M Proposition II with taxes, so: R E = R U + (R U – R D)(D/E)(1 – tC) R E = .11 + (.11 – .082)(.25/.75)(.65) R E = .1161 or 11.61%
c.
Using M&M Proposition II with taxes again, we get: R E = R U + (R U – R D)(D/E)(1 – tC) R E = .11 + (.11 – .082)(.50/.50)(1 – .35) R E = .1282 or 12.82%
d.
The WACC with 25 percent debt is: WACC = (E/V)R E + (D/V)R D(1 – tC) WACC = .75(.1161) + .25(.082)(1 – .35) WACC = .1004 or 10.04% And the WACC with 50 percent debt is: WACC = (E/V)R E + (D/V)R D(1 – tC) WACC = .50(.1282) + .50(.082)(1 – .35) WACC = .0908 or 9.08%
Frederick & Co. expects its EBIT to be $92,000 every year forever. The firm can borrow at 9 percent. Frederick currently has no debt, and its cost of equity is 15 percent. If the tax rate is 35 percent, the value of the firm is $ 398,666.67 ± 0.1%
. The value will be $
419,666.67 ± 0.1%
if Frederick borrows $60,000 and uses the proceeds to repurchase shares. (Do not include the dollar signs ($). Round your answers to 2 decimal places. (e.g., 32.16)) Explanation:
If the tax rate is 35%, the value of the unlevered firm is: VU = EBIT(1 – tC)/R U VU = $92,000(1 – .35)/.15 VU = $398,666.67 If Frederick borrows $60,000, the value of the levered firm is: VU = VU + tCD VU = $398,666.67 + .35($60,000) VU = $419,666.67
Assume a firm's debt is risk-free, so that the cost of debt equals the risk-free rate, . Define as the firm's asset beta — that is, the systematic risk of the firm's assets. Define to be the beta of the firm's equity. Assuming the tax rate is zero, it can be shown from the capital asset pricing model, (CAPM), along with M&M P roposition II that , where D/E is the debt−equity ratio. Suppose a firm's business operations are such that they mirror movements in the economy as a whole very closely; that is, the firm's asset beta is 1.0. By using the above result find the equity beta for this firm for debt−equity ratios of 0, 1, 5, and 20.
Debt-equity ratio 0
Equity beta 1 ± 1%
1
2 ± 1%
5
6 ± 1%
20
21 ± 1%
Explanation:
Using the equation βE = βA(1 + D/E).
The equity beta for the respective asset betas is: Debt-equity ratio 0 1 5 20
Equity beta 1(1 + 0) = 1 1(1 + 1) = 2 1(1 + 5) = 6 1(1 + 20) = 21
