Finance Ch. 12

Fama's Llamas has a WACC of 9.7 percent. The company's cost of equity is 12 percent, and its pretax cost of debt is 7.4 percent. The tax rate is 25 percent. What is the company's target debt-equity ratio?

= 0.5542 Here we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC equation, we find: WACC = .0970 = .12 (E/V) + .074 (D/V) (1 − .25) Rearranging the equation, we find: .0970 (V/E) = .12 + .074 (.75) (D/E) Now we must realize that the V/E is just the equity multiplier, which is equal to: V/E = 1 + D/E .0970 (D/E + 1) = .12 + .05550 (D/E) Now we can solve for D/E as: .04150 (D/E) = .023 D/E = .5542

Stock in Eduardo Industries has a beta of 1.13. The market risk premium is 7.3 percent, and T-bills are currently yielding 4.3 percent. The most recent dividend was $3.70 per share, and dividends are expected to grow at an annual rate of 5.3 percent, indefinitely. If the stock sells for $59 per share, what is your best estimate of the company's cost of equity?

= 12.23% We have the information available to calculate the cost of equity using the CAPM and the dividend growth model. Using the CAPM, we find: RE = .043 + 1.13 (.073) RE = .1255 , or 12.55% And using the dividend growth model, the cost of equity is: RE = [$3.70 (1.053) / $59] + .053 RE = .1190, or 11.90% Both estimates of the cost of equity seem reasonable based on the historical return on large capitalization stocks. Given this, we will use the average of the two, so: RE = (.1255 + .1190) / 2 RE = .1223, or 12.23%

The Tribiani Company just issued a dividend of $2.70 per share on its common stock. The company is expected to maintain a constant 6 percent growth rate in its dividends indefinitely. If the stock sells for $43.50 a share, what is the company's cost of equity?

= 12.58% With the information given, we can find the cost of equity using the dividend growth model. Using this model, the cost of equity is: RE = ($2.70 (1.06) / $43.50) + .06 RE = .1258, or 12.58%

The Swanson Corporation's common stock has a beta of 1.28. Assume the risk-free rate is 5.3 percent and the expected return on the market is 12.8 percent. What is the company's cost of equity capital?

= 14.90% Here we have information to calculate the cost of equity using the CAPM. The cost of equity is: RE = .053 + 1.28 (.128 − .053) RE = .1490, or 14.90%

Ying Import has several bond issues outstanding, each making semiannual interest payments. The bonds are listed in the table below. Bond 1 | CR 8.70% | PQ 106.7 | Maturity 7yrs | FaceValue $25m Bond 2 | CR 6.90% | PQ 93.7 | Maturity 10yrs | FaceValue $32m Bond 3 | CR 8.40% | PQ 105.5 | Maturity 17.5yrs | FaceValue $37m Bond 4 | CR 8.90% | PQ 95.3 | Maturity 27yrs | FaceValue $52m If the corporate tax rate is 22 percent, what is the aftertax cost of the company's debt?

= 6.46% To find the aftertax cost of equity for the company, we need to find the weighted average of the four debt issues. We will begin by calculating the market value of each debt issue, which is: MV1 = 1.067($26,000,000) MV1 = $27,742,000 MV2 = .937($32,000,000) MV2 = $29,984,000 MV3 = 1.055($37,000,000) MV3 = $39,035,000 MV4 = .953($52,000,000) MV4 = $49,556,000 So, the total market value of the company's debt is: MVD = $27,742,000 + 29,984,000 + 39,035,000 + 49,556,000 MVD = $146,317,000 The weight of each debt issue is: x1 = $27,742,000/$146,317,000 x1 = .1896, or 18.96% x2 = $29,984,000/$146,317,000 x2 = .2049, or 20.49% x3 = $39,035,000/$146,317,000 x3 = .2668, or 26.68% x4 = $49,556,000/$146,317,000 x4 = .3387, or 33.87% Next, we need to find the YTM for each bond issue. The YTM for each issue is: P1 = $1,067 = $43.50(PVIFAR%,14) + $1,000(PVIFR%,14) R1 = .03727, or 3.727% YTM1 = 3.727% × 2 YTM1 = 7.45% P2 = $937 = $34.50(PVIFAR%,20) + $1,000(PVIFR%,20) R2 = .03910, or 3.910% YTM2 = 3.910% × 2 YTM2 = 7.82% P3 = $1,055 = $42.00(PVIFAR%,35) + $1,000(PVIFR%,35) R3 = .03909, or 3.909% YTM3 = 3.909% × 2 YTM3 = 7.82% P4 = $953 = $44.50(PVIFAR%,54) + $1,000(PVIFR%,54) R4 = .04691, or 4.691% YTM4 = 4.691% × 2 YTM4 = 9.38% The weighted average YTM of the company's debt is thus: YTM = .1896 (.0745) + .2049 (.0782) + .2668 (.0782) + .3387(.0938) YTM = .0828, or 8.28% And the aftertax cost of debt is: RD = .0828(1 − .22) RD = .0646, or 6.46%

Savers has an issue of preferred stock with a $6.70 stated dividend that just sold for $87 per share. What is the bank's cost of preferred stock?

= 7.70% The cost of preferred stock is the dividend payment divided by the price, so: RP = $6.70 / $87 RP = .0770, or 7.70%

Branson Manufacturing has a target debt-equity ratio of .45. Its cost of equity is 11 percent, and its pretax cost of debt is 6 percent. If the tax rate is 25 percent, what is the company's WACC?

= 8.98% Here we need to use the debt-equity ratio to calculate the WACC. A debt-equity ratio of .45 implies a weight of debt of .45/1.45 and an equity of 1/1.45. Using this relationship, we find: WACC = 0.11 (1 / 1.45) + 0.06 (0.45 / 1.45) (1 − 0.25) WACC = .0898, or 8.98%

Occam Industrial Machines issued 130,000 zero coupon bonds 4 years ago. The bonds originally had 30 years to maturity with a yield to maturity of 6.1 percent. Interest rates have recently decreased, and the bonds now have a yield to maturity of 5.2 percent. The bonds have a par value of $2,000 and semiannual compounding. If the company has a $78.6 million market value of equity, what weight should it use for debt when calculating the cost of capital?

D/V = 0.4655 The bonds have 26 years to maturity so the price today is: P0 = $2,000 / (1 + .052 / 2) 52 P0 = $526.46 The market value of the debt is: MVD = 130,000 ($526.46) MVD = $68,440,092.47 So, the total value of the firm is: V = $68,440,092.47 + 78,600,000 V = $147,040,092.47 This means the weight of debt in the capital structure is: D/V = $68,440,092.47 / $147,040,092.47 D/V = 0.4655

You are given the following information on Parrothead Enterprises: -Debt: 9,200 7.3 percent coupon bonds outstanding, with 22 years to maturity and a quoted price of 108.5. These bonds pay interest semiannually and have a par value of $2,000. -Common stock: 315,000 shares of common stock selling for $66.30 per share. The stock has a beta of 1.08 and will pay a dividend of $4.50 next year. The dividend is expected to grow by 5.3 percent per year indefinitely. -Preferred stock: 9,800 shares of 4.65 percent preferred stock selling at $95.80 per share. The par value is $100 per share. -Market: 10.2 percent expected return, risk-free rate of 4.5 percent, and a 23 percent tax rate. Calculate the company's WACC.

WACC = .0821, or 8.21% We will begin by finding the market value of each type of financing. We find: MVD = 9,200 ($2,000) (1.0850) = $19,964,000 MVE = 315,000 ($66.30) = $20,884,500 MVP = 9,800 ($95.80) = $938,840 And the total market value of the firm is: V = $19,964,000 + 20,884,500 + 938,840 V = $41,787,340 Now, we can find the cost of equity using the CAPM. The cost of equity is: RE1 = .0450 + 1.08 (.102 − .0450) RE1 = .1066, or 10.66% We can also find the cost of equity using the dividend discount model. The cost of equity with the dividend discount model is: RE2 = $4.50/$66.30 + .053 RE2 = .1209, or 12.09% Both estimates for the cost of equity seem reasonable, so we will use the average of the two. The cost of equity estimate is: RE = (.1066 + .1209) / 2 RE = .1137, or 11.37% The cost of debt is the YTM of the bonds, so: P0 = $2,170.00 = $73.00 (PVIFAR%,44) + $2,000 (PVIFR%,44) R = 3.282% YTM = 3.282% × 2 YTM = 6.56% And the aftertax cost of debt is: RD = (1 − .23) (.0656) RD = .0505, or 5.05% The cost of preferred stock is: RP = $4.65 / $95.80 RP = .0485, or 4.85% Now, we have all of the components to calculate the WACC. The WACC is: WACC = 0.0505 ($19,964,000 / $41,787,340) + 0.0485 ($938,840 / $41,787,340) + 0.1137 ($20,884,500 / $41,787,340) WACC = .0821, or 8.21%

Dani Corporation has 6 million shares of common stock outstanding. The current share price is $72, and the book value per share is $9. The company also has two bond issues outstanding. The first bond issue has a face value of $85 million, has a coupon rate of 5 percent, and sells for 97 percent of par. The second issue has a face value of $70 million, has a coupon rate of 4 percent, and sells for 109 percent of par. The first issue matures in 21 years, the second in 8 years. Suppose the most recent dividend was $4.40 and the dividend growth rate is 4.7 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 23 percent. What is the company's WACC?

WACC = .0895, or 8.95% The market value of equity is the share price times the number of shares, so: MVE = 6,000,000 ($72) MVE = $432,000,000 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 = 0.97($85,000,000) + 1.09 ($70,000,000) MVD = $158,750,000 This makes the total market value of the company: V = $432,000,000 + 158,750,000 V = $590,750,000 And the market value weights of equity and debt are: E/V = $432,000,000 / $590,750,000 E/V = 0.7313 D/V = 1 − E/V D/V = 0.2687 Next, 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: RE = [$4.40 (1.047) / $72] + .047 RE = 0.1110, or 11.10% Next, we need to find the YTM on both bond issues. Doing so, we find: P1 = $970 = $25 (PVIFA R%, 42) + $1,000 (PVIF R%, 42) R = 2.619% YTM = 2.619% × 2 = 5.24% P2 = $1,090 = $20 (PVIFA R%, 16) + $1,000 (PVIF R%, 16) R = 1.370% YTM = 1.370% × 2 = 2.74% 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: xD1 = 0.97 ($85,000,000) / $158,750,000 xD1 = 0.5194 xD2 = 1.09 ($70,000,000) / $158,750,000 xD2 = 0.4806 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: RD = (1 − .23) [(.5194) (.0524) + (.4806) (.0274)] RD = 0.0311, or 3.11% Using these costs and the weight of debt we calculated earlier, the WACC is: WACC = .7313 (0.1110) + 0.2687 (0.0311) WACC = .0895, or 8.95%

You are given the following information for Lightning Power Company. Assume the company's tax rate is 21 percent. -Debt: 16,000 6.5 percent coupon bonds outstanding, $1,000 par value, 27 years to maturity, selling for 105 percent of par; the bonds make semiannual payments. -Common stock: 490,000 shares outstanding, selling for $67 per share; beta is 1.18.Preferred stock:21,500 shares of 4.3 percent preferred stock outstanding, a $100 par value, selling for $88 per share. -Market: 6 percent market risk premium and 5.4 percent risk-free rate. What is the company's WACC?

WACC = .0971, or 9.71% We will begin by finding the market value of each type of financing. We find: MVD = 16,000 ($1,000) (1.05) = $16,800,000 MVE = 490,000 ($67) = $32,830,000 MVP = 21,500 ($88) = $1,892,000 And the total market value of the firm is: V = $16,800,000 + 32,830,000 + 1,892,000 V = $51,522,000 Now, we can find the cost of equity using the CAPM. The cost of equity is: RE = .054 + 1.18 (0.06) RE = .1248, or 12.48% The cost of debt is the YTM of the bonds, so: P0 = $1,050 = $32.50 (PVIFAR%,54) + $1,000 (PVIFR%,54) R = 3.060% YTM = 3.060% × 2 = 6.12% And the aftertax cost of debt is: RD = (1 − 0.21) (.0612) RD = .0483, or 4.83% The cost of preferred stock is: RP = $4.30 / $88 RP = .0489, or 4.89% Now we have all of the components to calculate the WACC. The WACC is: WACC = .0483 ($16.800 / $51.522) + 0.1248 ($32.830 / $51.522) + 0.0489 ($1.892 / $51.522) WACC = 0.0971, or 9.71% 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.

Ursala, Incorporated, has a target debt-equity ratio of .90. Its WACC is 8.2 percent, and the tax rate is 22 percent. a. If the company's cost of equity is 11 percent, what is its pretax cost of debt? b. If instead you know that the aftertax cost of debt is 6.3 percent, what is the cost of equity?

a. b. a. Using the equation to calculate WACC, we find: WACC = .082 = (1/1.90)(.11) + (.90/1.90)(1 − .22)RD RD = .0652, or 6.52% b. Using the equation to calculate WACC, we find: WACC = .082 = (1 / 1.90) RE + (0.90 / 1.90) (.063) RE = .0991, or 9.91%

Jiminy's Cricket Farm issued a 20-year, 6 percent semiannual coupon bond 3 years ago. The bond currently sells for 103 percent of its face value. The company's tax rate is 22 percent. The book value of the debt issue is $60 million. In addition, the company has a second debt issue, a zero coupon bond with 9 years left to maturity; the book value of this issue is $25 million, and the bonds sell for 64 percent of par. a. What is the company's total book value of debt? b. What is the company's total market value of debt? c. What is the aftertax cost of debt?

a. $85,000,000 b. $77,800,000 c. 4.35% The book value of debt is the total par value of all outstanding debt, so: BVD = $60,000,000 + 25,000,000 BVD = $85,000,000 ------- To find the market value of debt, we find the price of the bonds and multiply by the number of bonds. Alternatively, we can multiply the price quote of the bond times the par value of the bonds. Doing so, we find: MVD = 1.03 ($60,000,000) + 0.64 ($25,000,000) MVD = $61,800,000 + 16,000,000 MVD = $77,800,000 --------- The YTM of the company's coupon bonds is: P0 = $1,030 = $30(PVIFA R%, 34) + $1,000(PVIF R%, 34) R = 2.861% YTM = 2 × 2.861% = 5.72% The aftertax cost of the coupon bonds is: RD = .0572 (1 − .22) RD = .0446, or 4.46% The YTM of the zero coupon bonds is: PZ = $640 = $1,000 (PVIF R%, 18) R = 2.510% YTM = 2 × 2.510% = 5.02% So, the aftertax cost of the zero coupon bonds is: RZ = .0502 (1 − .22) RZ = .0392, or 3.92% The aftertax cost of debt for the company is the weighted average of the aftertax cost of debt for all outstanding bond issues. We need to use the market value weights of the bonds. The total aftertax cost of debt for the company is: RD = .0446 ($61.80 / $77.80) + .0392 ($16.00 / $77.80) RD = .0435, or 4.35%

Ninecent Corporation has a target capital structure of 65 percent common stock, 5 percent preferred stock, and 30 percent debt. Its cost of equity is 13 percent, the cost of preferred stock is 5 percent, and the pretax cost of debt is 6 percent. The relevant tax rate is 25 percent. a. What is the company's WACC? b. What is the aftertax cost of debt?

a. 10.05% b. 4.50% Using the equation to calculate the WACC, we find: WACC = .65(.13) + .05(.05) + .30(0.06)(1 − .25) WACC = .1005, or 10.05% The aftertax cost of debt is: RD = .06(1 − .25) RD = .0450, or 4.50% Hence, on an aftertax basis, debt is cheaper than the preferred stock.

Ginger Industries stock has a beta of 1.37. The company just paid a dividend of $.87, and the dividends are expected to grow at 5.2 percent. The expected return on the market is 11.7 percent, and Treasury bills are yielding 5.2 percent. The most recent stock price is $84.00. a. Calculate the cost of equity using the dividend growth model method. b. Calculate the cost of equity using the SML method.

a. 6.29% b. 14.11% Using the dividend discount model, the cost of equity is: RE = [(.87) (1.052) / $84.00] + .052 RE = .0629, or 6.29% Using the CAPM, the cost of equity is: RE = .052 + 1.37 (.1170 − .052) RE = .1411, or 14.11%

Jiminy's Cricket Farm issued a 15-year, 6 percent semiannual coupon bond 4 years ago. The bond currently sells for 93 percent of its face value. The company's tax rate is 23 percent. a. What is the company's pretax cost of debt? b. What is the company's aftertax cost of debt?

a. 6.92% b. 5.33% The pretax cost of debt is the YTM of the company's coupon bonds, so: P0 = $930 = $30 (PVIFA R%, 22) + $1,000 (PVIF R%, 22) R = 3.460% YTM = 2 × 3.460% = 6.92% The aftertax cost of debt is: RD = .0692 (1 − .23) RD = .0533, or 5.33% The aftertax rate is more relevant because that is the actual cost to the company.

Lingenburger Cheese Corporation has 7.5 million shares of common stock outstanding, 275,000 shares of 4.7 percent preferred stock outstanding, par value of $100; and 160,000 bonds with a semiannual coupon rate of 5.6 percent outstanding, par value $2,000 each. The common stock currently sells for $62 per share and has a beta of 1.10, the preferred stock has a par value of $100 and currently sells for $94 per share, and the bonds have 18 years to maturity and sell for 108 percent of par. The market risk premium is 7.2 percent, T-bills are yielding 3.4 percent, and the company's tax rate is 24 percent. a. What is the firm's market value capital structure? b. If the company is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows?

a. Debt: 0.4132 Preferred Stock: 0.0309 Equity: 0.5559 b. Discount rate: 7.99% a. We will begin by finding the market value of each type of financing. We find: MVD = 160,000 ($2,000) (1.08) = $345,600,000 MVP = 275,000 ($94) = $25,850,000 MVE = 7,500,000 ($62) = $465,000,000 And the total market value of the firm is: V = $345,600,000 + 465,000,000 + 25,850,000 = $836,450,000 So, the market value weights of the company's financing are: D/V = $345,600,000 / $836,450,000 = 0.4132 P/V = $25,850,000 / $836,450,000 = 0.0309 E/V = $465,000,000 / $836,450,000 = 0.5559 b. For projects equally as risky as the firm itself, the WACC should be used as the discount rate. First we can find the cost of equity using the CAPM. The cost of equity is: RE = 0.034 + 1.10 (.072) RE = 0.1132, or 11.32% The cost of debt is the YTM of the bonds, so: P0 = $2,160 = $56.00(PVIFAR%,36) + $2,000(PVIFR%,36) R = 2.462% YTM = 2.462% × 2 = 4.92% And the aftertax cost of debt is: RD = (1 − 0.24) (0.0492) RD = .0374, or 3.74% The cost of preferred stock is: RP = $4.70/$94 RP = 0.0500, or 5.00% Now we can calculate the WACC as: WACC = 0.4132 (0.0374) + 0.0309 (0.0500) + 0.5559 (0.1132) WACC = 0.0799, or 7.99%

Dani Corporation has 8 million shares of common stock outstanding. The current share price is $74, and the book value per share is $7. The company also has two bond issues outstanding. The first bond issue has a face value of $95 million, has a coupon rate of 7 percent, and sells for 97 percent of par. The second issue has a face value of $80 million, has a coupon rate of 6 percent, and sells for 109 percent of par. The first issue matures in 23 years, the second in 6 years. Both bonds make semiannual coupon payments. a. What are the company's capital structure weights on a book value basis? b. What are the company's capital structure weights on a market value basis? c. Which are more relevant, the book or market value weights?

a. EV = 0.2424 DV = 0.7576 b. EV = 0.7675 DV = 0.2325 c. More relevant: market value a. The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company's debt, so: BVE = 8,000,000 ($7) BVE = $56,000,000 BVD = $95,000,000 + 80,000,000 BVD = $175,000,000 So, the total value of the company is: V = $56,000,000 + 175,000,000 V = $231,000,000 And the book value weights of equity and debt are: E/V = $56,000,000 / $231,000,000 E/V = 0.2424 D/V = 1 − E/V D/V = 0.7576 b. The market value of equity is the share price times the number of shares, so: MVE = 8,000,000($74) MVE = $592,000,000 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 = 0.97 ($95,000,000) + 1.09 ($80,000,000) MVD = $179,350,000 This makes the total market value of the company: V = $592,000,000 + 179,350,000 V = $771,350,000 And the market value weights of equity and debt are: E/V = $592,000,000/$771,350,000 E/V = .7675 D/V = 1 − E/V D/V= 0.2325 c. The market value weights are more relevant because they represent a more current valuation of the debt and equity.

An all-equity firm is considering the following projects: Project W | Beta 0.51 | IRR 10.4% Project X | Beta 0.94 | IRR 10.9% Project Y | Beta 1.06 | IRR 14.4% Project Z | Beta 1.78 | IRR 17.4% The T-bill rate is 5.4 percent, and the expected return on the market is 12.4 percent. a. Which projects have a higher/lower expected return than the firm's 12.4 percent cost of capital? b. Which projects should be accepted? c. Which projects will be incorrectly accepted/rejected or correctly accepted/rejected if the firm's overall cost of capital were used as a hurdle rate?

a. Project W has a LOWER expected return, Project X has a LOWER expected return, Project Y has a HIGHER expected return, and Project Z has a HIGHER expected return. b. Project W should be ACCEPTED, Project X should be REJECTED. Project Y should be ACCEPTED, Project Z should be REJECTED. c. Project W would be INCORRECTLY REJECTED, Project X would be CORRECTLY REJECTED, Project Y would be CORRECTLY ACCEPTED, and Project Z would be INCORRECTLY ACCEPTED. a. Projects Y and Z have a higher expected return than the firm's cost of capital. b. Using the CAPM to consider the projects, we need to calculate the expected return of the project, given its level of risk. This expected return should then be compared to the expected return of the project. If the return calculated using the CAPM is lower than the project expected return, we should accept the project; if not, we reject the project. After considering risk via the CAPM: E(W) = .054 + .51 (.124 - .054) = .0897 < .104, so accept W E(X) = .054 + .94(.124 - .054) = .1198 > .109, so reject X E(Y) = .054 + 1.06(.124 - .054) = .1282 < .144, so accept Y E(Z) = .054 + 1.78(.124 - .054) = .1786 > .174, so reject Z

Gnomes R Us is considering a new project. The company has a debt-equity ratio of .74. The company's cost of equity is 14.5 percent, and the aftertax cost of debt is 7.8 percent. The firm feels that the project is riskier than the company as a whole and that it should use an adjustment factor of +3 percent. a. What is the company's WACC? b. What discount rate should the firm use for the project?

a. WACC = 11.65% b. Project discount rate = 14.65% To find the required return for the project, we need to adjust the company's WACC for the level of risk in the project. A debt-equity ratio of .74 implies a weight of debt of .74/1.74 and a weight of equity of 1/1.74, so the company's WACC is: WACC = (.74 / 1.74) (.0780) + (1 / 1.74) (.1450) WACC = .1165, or 11.65% Adjusting for risk, the project discount rate is: Project discount rate = .1165 + .03 Project discount rate = .1465, or 14.65%

Suppose Wacken, Limited just issued a dividend of $2.65 per share on its common stock. The company paid dividends of $2.15, $2.22, $2.39, and $2.49 per share in the last four years. If the stock currently sells for $84, what is your best estimate of the company's cost of equity capital using arithmetic and geometric growth rates?

arithmetic growth rate = 8.71% geometric growth rate = 8.69% 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 = ($2.22 − 2.15) / $2.15 g1 = .0326, or 3.26% g2 = ($2.39 − 2.22) / $2.22 g2 = .0766, or 7.66% g3 = ($2.49 − 2.39) / $2.39 g3 = .0418, or 4.18% g4 = ($2.65 − 2.49) / $2.49 g4 = .0643, or 6.43% So, the average arithmetic growth rate in dividends was: g = (.0326 + .0766 + .0418 + .0643) / 4 g = .0538, or 5.38% Using this growth rate in the dividend growth model, we find the cost of equity is: RE = ($2.65 (1.0538) / $84) + .0538 RE = .0871, or 8.71% ------------------------ Calculating the geometric growth rate in dividends, we find: $2.65 = $2.15 (1 + g)^4 g = .0537, or 5.37% The cost of equity using the geometric dividend growth rate is: RE = ($2.65 (1.0537) / $84) + 0.0537 RE = 0.0869, or 8.69%