BU 381 Final Exam: The Cost of Capital

Capital Structure

the choice of the borrowing sources chosen by the firm

cost of capital

the cost of each financing component multiplied by that component's percent of the total borrowed

The cost of capital is ________ .

the cost of each financing component multiplied by that component's percent of the total borrowed.

Cost of Equity

the rate of return required by shareholders of the company with the rate of return determined by using either the security market line (SML) or the dividend growth model

Cost of Debt

the return that the bank or bondholder demands on new borrowing or, put another way, it is the rate that a company pays on its current debt

The appropriate capital budgeting decision rule is ________ .

to accept projects with an NPV greater than $0.

retained earnings

cash generated from the ongoing business and reinvested in the company

The ________ of an asset or liability is its cost carried on the balance sheet.

Book Value

Pure Play

refers to matching the project to a company with a single business focus in order to find the beta of that firm and assign that beta to your project

Assigning a beta to individual projects is more of a science than an art.

False

For estimating NPV, the IRR is the appropriate discount rate to use for an average-risk project.

False

On a practical basis, a manager should always accept all positive NPV projects even if this means exceeding a limited budget.

False

The formula for the WACC adjusted = (D/V)*(Rd) + (PS/V)*Rps + (E/V)*Re*(1-Tc).

False

Using the WACC to evaluate all projects has the effect of making low-risk projects look MORE attractive and high-risk projects look LESS attractive.

False

Richard works for a firm that is expanding into a completely new line of business. He has been assigned to determine an appropriate WACC for the average-risk project in the expansion division. Richard finds two publicly traded stand alone firms that produce the same products as his new division. The average of the two firms' betas is 1.25. Further, he determines that the expected return on the market portfolio is 13.00% and the risk-free rate of return is 4.00%. Richard's firm finances 50% of projects with equity and 50% with debt, has a before-tax cost of debt of 9% and a corporate tax rate of 30%. What is the WACC for the new line of business?

First, we solve for the cost of equity: Re = Rf + β * (Rm — Rf) = 4% + 1.25 * (13% - 4%) = 15.25%. We can now solve for WACC. We have: WACC = (D/V)*Rd*(1-Tc) + (E/V)*Re = 0.50*(9.00%)*(1-0.30) + 0.50*(15.25%) = 10.775%.

Ricky's Restaurant has an adjusted WACC of 8.96%. The company has a capital structure consisting of 70% equity and 30% debt, a cost of equity of 12.00%, a before-tax cost of debt of 8.00%, and a tax rate of 30%. Ricky is considering expanding by building a new restaurant in a distant city and considers the project to be riskier than his current operation. He estimates his existing beta is 1.0, the required return on the market portfolio to be 12.00%, the risk-free rate to be 3.00%, and the beta for the new project to be 1.40. Given this information, and assuming the cost of debt will not change if Ricky undertakes the new project, what adjusted WACC should be use in his decision-making?

First, we solve for the cost of equity: Re = Rf + β*(Rm - Rf) = 3.00% + 1.4*(12.00% - 3.00%) = 15.60%. We can now solve for WACC. We have: WACC = (D/V)*Rd*(1-Tc) + (E/V)*Re = 0.30*(8.00%)*(1-0.30) + 0.70*(15.60%) = 12.60%.

Define flotation costs and explain how they are used when estimating a firm's yield-to-maturity.

Flotation costs are the costs incurred to sell a security. They are the fees charged by the investment banker to facilitate the issuance and sale of the bond. To determine the yield-to-maturity of a new issue of bonds it is proper to use the bond selling price less the flotation cost as the net proceeds to the firm. The net proceeds become the price used in the equation to determine the yield-to-maturity.

Calculating NPV and IRR. A project that provides annual cash flows of $400 for seven years costs $1,500 today. Is this a good project if the required return is 6 percent? What if it is 22 percent?

For an annuity, we have: NPV = CF0 + CF*[1 - 1/(1+r)n] / r . For 6%, we have: NPV = CF0 + CF*[1 - 1/(1+r)n] / r = -$1,500 + $400*[1 - 1/(1.06)7] / 0.06 = -$1,500 + $400*5.5823814 = -$1,500 + $2,232.95 = $732.95. Thus, it would be a good project for r = 6%. For 22%, we have: NPV = CF0 + CF*[1 - 1/(1+r)n] / r = -$1,500 + $400*[1 - 1/(1.22)7] / 0.22 = -$1,500 + $400*{3.4155064} = -$1,500 + $1,366.20 = -$133.80. Thus, it would be a bad project for r = 22%

Phillip Enterprises Inc. needs to determine their cost of equity capital. Use the following information to estimate the firm's cost of equity using both the security market line and the dividend growth model. The current market price of stock is $22.89, the risk-free rate is 4.00%, the required return on the market portfolio is 13.50%, the firm has a constant growth rate in dividends of 3.00% per year, current dividends are $2.00, and the firm's beta is 0.90

For the Dividend Growth Model, we have: return on equity (Re) = [(D0*(1+g) / P0] + g [($2.00*(1.03) / $22.89] + 0.03 = 12.00%. For the Security Market Line, we have: return on equity (Re) = Rf + β * (Rm - Rf) = 4.00 + 0.9*(13.50% - 4.00%) = 12.55%. Both methods give similar answers. If we are indifferent as to which method to use and believe they both are equal, then we might use 12.275% as our cost of capital as this percentage would be the average of 12.00% and 12.55%.

Boulder Corp. has a new project that will require the company to borrow $4,000,000. Boulder has made an agreement with three lenders for the needed financing. Citizens Bank will give $1,500,000 and wants 10% interest on the loan. Visitors Bank will give $1,000,000 and wants 12% interest on the loan. Peoples Bank will give $1,500,000 and wants 16% interest on the loan. What is the weighted average cost of capital for this $4,000,000 loan?

Letting M = millions and assigning weights, we have: weighted average cost = [($1.5M/$4M)*10%] + [($1M/$4M*12%] + [($1.5M/$4M)*16%] = (3/8)*10% + (1/4)*12% + (3/8)*16% = 3.75% + 3.00% + 6.00% = 12.75%.

Downtown Corp. has a new project that will require the company to borrow $6,000,000. Downtown has made an agreement with three lenders for the needed financing. First National will give $3,000,000 and wants 10% interest on the loan. Commerce Bank will give $2,000,000 and wants 9% interest on the loan. Peoples Bank will give $1,000,000 and wants 8% interest on the loan. What is the weighted average cost of capital for this $6,000,000 loan?

Letting M = millions and assigning weights, we have: weighted average cost = [($3M/$6M)*10%] + [($2M/$6M*9%] + [($1M/$6M)*8%] = (1/2)*10% + (1/3)*9% + (1/6)*8% = 5.00% + 3.00% + 1.3333% = 9.3333% or about 9.33%.

With an unlimited amount of funds a firm could accept all positive NPV projects. However, with limited budgets managers are forced to accept some positive NPV projects while rejecting others. What overall financial rule should managers follow when choosing the portfolio of projects to accept? Why?

Managers should maximize the NPV of the portfolio of accepted projects. NPV measures the total financial benefit to existing shareholders. Other techniques are flawed in some fashion. For instance, IRR measures the return per dollar spent but does not necessarily maximize the total return to shareholders.

Your firm has an average-risk project under consideration. You choose to fund this project in the same manner as the firm's existing capital structure. Its cost of debt is 9.00%, the cost of preferred stock is 12.00%, the cost of common stock is 16.00%, and the WACC adjusted for taxes is 14.00%. The expected cash flows for this project (which lasts three years) are $2 million investment, $0.25 million in net working capital, operating cash flows of $0.85 million at the end of years 1, 2, and 3, and a selling value of assets of $0.05 million at the end of year 3. What is the NPV of this project?

NPV = PV of cash inflows - the initial investment. Using business calculator with PMT = $850,000, FV = $300,000, N = 3, and I% = 14.00%, we have: NPV = $2,175,879 - $2,250,000 = -$74,121. (NOTE: Salvage Value or FV = $250,000 + $50,000 = $300,000.) NPV = PMT*[1 - 1/(1+r)n] / r + FV/(1+r)n - the initial investment = $850,000*[1 - 1/(1.14)3] / 0.14 + $300,000/(1.14)3 - $2,250,000 = $850,000*2.32163203 + $300,000/1.481544 - $2,250,000 =$1,973,387.22 + $202,491.45 - $2,250,000 = -$74,121.

The simplest application of assigning a beta to an individual project is called a "pure play" where a manager finds the beta of a firm whose sole business is similar to that of the project in question and then assigns that firm's beta to its project

True

The author labels preferred stock as "hybrid equity financing." Define preferred stock, identify and explain the features of preferred stock that give it characteristics similar to bonds and those similar to common stock.

Preferred stock is identified as a hybrid equity security because even though it is equity it has features of debt as well as equity. Like debt, preferred stock typically has a fixed regular cash flow (dividend). It is treated like stock because it has no specific maturity and the principal is usually not repaid. Like debt, preferred stock does not ordinarily have voting rights but under certain conditions it may be converted to common stock. Preferred stock dividends are not tax deductible but have a greater seniority than common stock dividends under financial distress.

Define "pure play" as it applies to assigning a beta to a project. Under what circumstances do you think the pure play approach to assigning project betas would be particularly useful?

Pure play is the art of determining the beta of an individual project by matching it to a publicly traded company whose sole business is similar to the project. This technique is particularly useful when a company is looking to expand its business into an area where it has no internal projects that it can use for estimating the new project's beta.

Richard works for a firm that is expanding into a completely new line of business. He has been assigned to determine an appropriate WACC for the average-risk project in the expansion division. Richard finds two publicly traded stand alone firms that produce the same products as his new division. The average of the two firms' betas is 1.25. Further, he determines that the expected return on the market portfolio is 13.00% and the risk-free rate of return is 4.00%. Richard's firm finances 50% of projects with equity and 50% with debt, has a before-tax cost of debt of 9% and a corporate tax rate of 30%. What is the WACC for the new line of business?

Re = Rf + Beta*(Rm - Rf) = 4% + 1.25*(13% - 4%) = 15.25%. WACC = (D/V)*Rd*(1 - Tc) + (PS/V)*Rp + (E/V)*Re = 0.50*(9.00%)*( 1 - 0.30) + 0.50*(15.25%) = 10.775%

Bob's Discount Shoe Source is adding a new line of shoes to the company portfolio and has the following information: the expected market return is 13%, the risk-free rate is 3%, and the expected return on the new project is 11%. What is the beta of the project?

Rearranging Re = Rf + Beta*(Rm - Rf), we get: Beta = (Re - Rf) / (Rm - Rf). Inserting in our given values, we have: Beta = (11% - 3%) / (13% - 3%) = 0.80.

Unused capital budget funds are assumed to earn the same rate of return as the firm's "going rate".

True

Your firm has just issued a 10-year $1,000.00 par value, 10% annual coupon bond for a net price of $964.00. What is the yield to maturity?

Solving for the YTM is an iterative (trial and error) process using the bond pricing formula. Bond Price = PMT * { 1 - [1/(1+r)^n] } / r + FV / (1+r)^n = $100 * { 1 - [1/(1+r)^10] } / r + $1,000 / (1+r)^10 = $964.00 implies that r = YTM = 10.60%.

It is necessary to assign the appropriate cost of capital for each individual project that reflects that project's ________ when doing capital budgeting.

riskiness

Your firm has an average-risk project under consideration. You choose to fund this project in the same manner as the firm's existing capital structure. Its cost of debt is 9.00%, the cost of preferred stock is 12.00%, the cost of common stock is 16.00%, and the WACC adjusted for taxes is 14.00%. The expected cash flows for this project (which lasts three years) are $2 million equipment investment, $0.25 million in net working capital (NWC), operating cash flows of $0.85 million at the end of years 1, 2, and 3, and a salvage value of $50,000 at the end of year 3. What is the NPV of this project?

The future terminal value at t = 3 consists of the releast of $0.25M in net working capital (NWC) and sale of the assets (or salvage value) of $0.50M for a total of $0.75M or $750,000. Proceeding, we have: Initial investment = Investment + NWC = $2,000,000 + $250,000 = $2,250,000. NPV = PV of cash inflows - initial investment = $850,000/(1.14^1) + $850,000/(1.14^2) + ($850,000+$75,000)/(1.14^3) - $2,250,000 = $2,175,879 - $2,250,000 = -$74,121.32.

In capital budgeting, the ________ is the appropriate discount rate to use when calculating the NPV of an average risk project.

WACC

Louisville Sports Gear, Inc. has debt with a market value of $0.25B (where B = billions), preferred stock with a market value of $0.25B, and common stock with a market value of $0.5B. If debt has a cost of 8%, preferred stock a cost of 12%, common stock a cost of 14%, and the firm has a tax rate of 30%, what is the WACC?

We add up all forms of financing to get: $0.25B + $0.25B + $0.50B = $1B. We now have weighted average cost of capital (WACC) = (D/V)*Rd*(1-Tc) + (PS/V)*Rp + (E/V)*Re = ($0.25B/$1B)*(8%)*(1 - 0.30) + ($0.25B/$1B)*12% + ($0.5B/$1B)*14% = 1.40% + 3.00% + 7.00% = 11.40%.

The following information comes from the balance sheet of Roamer Enterprises. The value of common stock is $60,000, retained earnings equal $40,000, preferred stock has a value of $10,000 and long-term debt totals $120,000. For purposes of estimating the firm's WACC, what are the weights of long-term debt, preferred stock, and equity?

We have V = D + P + E = $120,000 + $10,000 + $60,000 = $230,000. Thus, D/V = $120,000/$230,000 = 52.17%, P/V = $10,000/$230,000 = 4.35%, E/V = $100,000/$230,000 = 43.48%. One can note that the weights add up to 100%.

Use the security market line to determine the required rate of return for the following firm's stock. The firm has a beta of 1.5, the required return in the market place is 12.00%, the standard deviation of returns for the market portfolio is 25.00%, the standard deviation of returns for your firm is also 25.00%, and the risk-free rate is 8.00%

We have return on equity (Re) = Rf + β * (Rm - Rf) = 8.00% + 1.5*(12.00% - 8.00%) = 8.00% + 1.5*(4.00%) = 14.00%

Use the dividend growth model to determine the required rate of return for equity. Your firm has just paid a dividend of $1.50 per share, has a recent price of $31.82 per share, and anticipates a growth rate in dividends of 4.00% per year for the foreseeable future.

We have return on equity (Re) = [(D0*(1+g) / P0] + g = [($1.50*(1.04) / $31.82] + 0.04 = 8.90%.

Ladies & Gentlemen Ltd. has debt with a market value of $350,000, preferred stock with a market value of $150,000, and common stock with a market value of $450,000. If debt has a cost of 6.25%, preferred stock a cost of 9.17%, common stock a cost of 12.33%, and the firm has a tax rate of 25%, what is its WACC?

We have weighted average cost of capital (WACC) = (D/V)*Rd*(1-Tc) + (PS/V)*Rp + (E/V)*Re = ($350,000/$950,000)*(6.25%)*(1 - 0.25) + ($150,000/$950,000)*9.17% + ($450,000/$950,000)*12.33% = 1.73% + 1.45% + 5.84% = 9.02%.

United Mobile Homes has debt with a market value of $350,000, preferred stock with a market value of $150,000, and common stock with a market value of $450,000. If debt has a cost of 8%, preferred stock a cost of 11%, common stock a cost of 12%, and the firm has a tax rate of 30%, what is its WACC?

We have weighted average cost of capital (WACC) = (D/V)*Rd*(1-Tc) + (PS/V)*Rp + (E/V)*Re = ($350,000/$950,000)*(8%)*(1 - 0.30) + ($150,000/$950,000)*11% + ($450,000/$950,000)*12% = 2.06% + 1.74% + 5.68% = 9.48%.

The following information comes from the Galaxy Construction balance sheet. The value of common stock is $10,000, retained earning equals $7,000, preferred stock has a value of $3,000 and long-term debt totals $15,000. If the cost of debt is 8.00%, preferred stock has a cost of 10.00% and common stock a cost of 12.00%, and the firm has a corporate tax rate of 30%, calculate the firm's WACC adjusted for taxes.

We have: V = D + P + E = $15,000 + $3,000 + $10,000 = $35,000. Thus, given that WACC = (D/V)*Rd*(1-Tc) + (PS/V)*Rp + (E/V)*Re, we have WACC = ($15,000/$35,000)*8%*(1-0.3) + ($3,000/$35,000)*10% + ($17,000/$35,000)*12% = 9.09%.

The Otto Group, Inc., has identified the following two mutually exclusive projects. The cash flows for project L for years 0 through 4 are respectively: -$12,500, $4,000, $5,000, $6,000 and $1,000. For project S, the cash flows for years 0 through 4 are respectively: -$12,500, $1,000, $6,000, $5,000 and $4,000. Which project do we accept if the discount rate is 11%?

We use the following equation: NPV = CF0 + CF1/(1+r)1 + CF1/(1+r)2 + ... + CFn/(1+r)n where CF0 < zero, r is the discount rate, and n is the number of years for the project. For project L, we have NPV = -$12,500 + $4,000/(1.11)1 + $5,000/(1.11)2 + $6,000/(1.11)3 + $1,000/(1.11)4 = $207.60. For project S, we have NPV = -$12,500 + $1,000/(1.11)1 + $6,000/(1.11)2 + $5,000/(1.11)3 + $4,000/(1.11)4 = -$438.48. Since NPVL > NPVS, the NPV decision rule implies that we accept project L not only because it adds value but it is the only project of the two that has a positive NPV

You have learned how to use NPV and IRR to evaluate projects as part of a capital budgeting decision-making process. How is WACC used in each of these capital-budgeting processes?

When calculating the NPV of a project the WACC is the appropriate required rate of return if the project is of average risk. It is also the starting point for making subjective adjustments to the required rate of return for projects of greater or lesser risk than average. When calculating the IRR the WACC is the appropriate hurdle rate for determining if a project meets the investment criteria.

subjective modification

involves managers intuitively adjusting the company's beta for individual projects because these projects result from the company operating in a variety of business areas

preferred stock

provides a constant cash dividend based on its original par value and stated dividend rate