FIN322 Week 6
27/08/18
Chapter 18. CQ: 4. Capital Budgeting You are determining whether your company should undertake a new project and have calculated the NPV of the project using the WACC method when the CFO, a former accountant, notices that you did not use the interest payments in calculating the cash flows of the project. What should you tell him? If he insists that you include the interest payments in calculating the cash flows, what method can you use?
Ans: The WACC method does not explicitly include the interest cash flows, but it does implicitly include the interest cost in the WACC. If he insists that the interest payments are explicitly shown, you should use the FTE method.
QP: 10. APV Triad Corporation has established a joint venture with Tobacco Road Construction, Inc., to build a toll road in North Carolina. The initial investment in paving equipment is $93 million. The equipment will be fully depreciated using the straight-line method over its economic life of five years. Earnings before interest, taxes, and depreciation collected from the toll road are projected to be $12.9 million per annum for 20 years starting from the end of the first year. The corporate tax rate is 35 percent. The required rate of return for the project under all-equity financing is 13 percent. The pretax cost of debt for the joint partnership is 8.5 percent. To encourage investment in the country’s infrastructure, infrastructure, the U.S. government will subsidize the project with a $30 million, 15-year loan at an interest rate of 5 percent per year. All principal will be repaid in one balloon payment at the end of Year 15. What is the adjusted present value of this project?
Ans: The adjusted present value of a project equals the net present value of the project under allequity financing plus the net present value of any financing side effects. In the joint venture’s case, the NPV of financing side effects equals the aftertax present value of cash flows resulting from the firms’ debt. So, the APV is: APV = NPV(All-Equity) + NPV (Financing Side Effects) The NPV for an all-equity firm is: NPV(All-Equity) NPV = – Initial Initial Investment + PV [(1 – t C) (EBITD)] + PV(Depreciation Tax Shield) Since the initial investment will be fully depreciated over five years using the straight-line method, annual depreciation expense is: Annual depreciation = $93,000,000 / 5 Annual depreciation = $18,600,000 1|Page
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NPV = – $93,000,000 + (1 – .35) ($12,900,000) PVIFA13%, 20 + (.35)($18,600,000)PVIFA8.5%,5 NPV = – $8,443,878.08 (Think about why using 8.5% instead of 13% in calculating the PV of depreciation tax shield) NPV (Financing Side Effects) The NPV of financing side effects equals the after-tax present value of cash flows resulting from the firm’s debt. The coupon rate on the debt is relevant to determine the interest payments, but the resulting cash flows should still be discounted at the pretax cost of debt. So, the NPV of the financing effects is: NPV = Proceeds – Aftertax PV (Interest Payments) – PV (Principal Repayments) NPV = $30,000,000 – (1 – .35) (.05) ($30,000,000) PVIFA8.5%, 15 – $30,000,000 / 1.08515 NPV = $13,079,172.61 So, the APV of the project is: (Please note that the way the aftertax PV (interest payments) is calculated has essentially incorporated two effects that are discussed in the lecture: the benefit of lower interest rate and the benefit of lower value of debt) APV = NPV(All-Equity) + NPV (Financing Side Effects) APV = – $8,443,878.08 + $13,079,172.61 APV = $4,635,294.52 11. APV For the company in the previous problem, what is the value of being able to issue subsidized debt instead of having to issue debt at the terms it would normally receive? Assume the face amount and maturity of the debt issue are the same.
Ans: If the company had to issue debt under the terms it would normally receive, the interest rate on the debt would increase to the company’s normal cost of debt. The NPV of an all -equity project would remain unchanged, but the NPV of the financing side effects would change. The NPV of the financing side effects would be: NPV = Proceeds – Aftertax PV (Interest Payments) – PV (Principal Repayments) NPV = $30,000,000 – (1 – .35) (.085) ($30,000,000) PVIFA8.5%, 15 – $30,000,000 / 1.08515 NPV = $7,411,531.14 Using the NPV of an all-equity project from the previous problem, the new APV of the project would be: APV = NPV(All-Equity) + NPV (Financing Side Effects) APV = – $8,443,878.08 + $7,411,531.14 APV = – $1,032,346.94 The gain to the company from issuing subsidized debt is the difference between the two APVs, so: Gain from subsidized debt = $4,635,294.52 – ( – 1,032,346.94) Gain from subsidized debt = $5,667,641.46 Most of the value of the project is in the form of the subsidized interest rate on the debt issue.
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13. WACC Neon Corporation’s stock returns have a covariance with the market portfolio of .0415. The standard deviation of the returns on the market portfolio is 20 percent, and the expected market risk premium is 7.5 percent. The company has bonds outstanding with a total market value of $45 million and a yield to maturity of 6.5 percent. The company also has 4.2 million shares of common stock outstanding, each selling for $30. The company’s CEO considers the firm’s current debt – equity ratio optimal. The corporate tax rate is 35 percent, and Treasury bills currently yield 3.4 percent. The company is considering the purchase of additional equipment that would cost $47 million. The expected unlevered cash flows from the equipment are $13.5 million per year for five years. Purchasing the equipment will not change the risk level of the firm. (a) Use the weighted average cost of capital approach to determine whether Neon should purchase the equipment. (b) Suppose the company decides to fund the purchase of the equipment entirely with debt. What is the cost of capital for the project now? Explain.
a.
To calculate the NPV of the project, we first need to find the company’s WACC. In a world with corporate taxes, a firm’s weighted average cost of capital equals: RWACC = [ B / ( B + S )]
(1 – t C) RB + [S / ( B + S )] RS
The market value of the company’s equity is:
Market value of equity = 4,200,000($30) Market value of equity = $126,000,000 So, the debt – value ratio and equity – value ratio is: Debt/value = $45,000,000 / ($45,000,000 + 126,000,000) Debt/value = .2632 Equity/value = $126,000,000 / ($45,000,000 + 126,000,000) Equity/value = .7368 Since the CEO believes its current capital structure is optimal, these values can be used as the target weights in the firm’s weighted average cost of capital calculation. The yield to maturity of the company’s debt is its pretax cost of debt. To find the company’s cost of equity, we need to calculate the stock beta. The stock beta can be calculated as: = S, M / 2M = .0415 / .202 = 1.04
Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is: RS = RF +
β ( RM – RF) RS = 3.4% + 1.04(7.50%) RS = 11.18%
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Now, we can calculate the company’s WACC, which is: RWACC = [ B / ( B + S )]
(1 – t C) RB + [S / ( B + S )] RS RWACC = .2632(1 – .35) (.065) + .7368(.1118) RWACC = .0935, or 9.35% Finally, we can use the WACC to discount the unlevered cash flows, which gives us an NPV of: NPV = – $47,000,000 + $13,500,000(PVIFA9.35%,5) NPV = $5,035,988.82 b.
The weighted average cost of capital used in part a will not change if the firm chooses to fund the project entirely with debt. The weighted average cost of capital i s based on optimal capital structure weights. Since the current capital structure is optimal, all-debt funding for the project implies that the firm will have to use more equity in the future to bring the capital structure back towards the target.
14. Beta and Leverage Dorman Industries has a new project available that requires an initial investment of $4.3 million. The project will provide unlevered cash flows of $710,000 per year for the next 20 years. The company will finance the project with a debt-to-value ratio of .40. The company’s bonds have a YTM of 6.8 percent. The companies with operations comparable to this project have unlevered betas of 1.15, 1.08, 1.30, and 1.25. The risk-free rate is 3.8 percent, and the market risk premium is 7 percent. The company has a tax rate of 34 percent. What is the NPV of this project?
Ans: We have four companies with comparable operations, so the industry average beta can be used as the beta for this project. So, the average unlevered beta is: Unlevered = (1.15 + 1.08 + 1.30 + 1.25) / 4 Unlevered = 1.20
A debt-to-value ratio of .40 means that the equity-to-value ratio is .60. This implies a debt – equity ratio of .67{=.40/.60}. Since the project will be levered, we need to calculate the levered beta, which is: Levered = [1 + (1 – t C) (Debt/Equity)]Unlevered Levered = [1 + (1 – .34) (.67)]1.20 Levered = 1.72
Now we can use the Capital Asset Pricing Model to determine the cost of equity. The Capital Asset Pricing Model is: RS = RF
+ β ( RM – RF) RS = 3.8% + 1.72(7.00%) RS = 15.85% Now, we can calculate the company’s WACC, which is: RWACC = [ B / ( B + S )]
(1 – t C) RB + [S / ( B + S )] RS RWACC = .40(1 – .34) (.068) + .60(.1585) RWACC = .1130, or 11.30% 4|Page
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Finally, we can use the WACC to discount the unlevered cash flows, which gives us an NPV of: NPV = – $4,300,000 + $710,000(PVIFA11.30%,20) NPV = $1,243,895.08 18. Projects That Are Not Scale Enhancing Blue Angel, Inc., a private firm in the holiday gift industry, is considering a new project. The company currently has a target debt –equity ratio of .40, but the industry target debt –equity ratio is .35. The industry average beta is 1.2. The market risk premium is 7 percent, and the risk-free rate is 5 percent. Assume all companies in this industry can issue debt at the risk-free rate. The corporate tax rate is 40 percent. The project requires an initial outlay of $785,000 and is expected to result in a $93,000 cash inflow at the end of the first year. The project will be financed at the company’s target debt–equity ratio. Annual cash flows from the project will grow at a constant rate of 5 percent until the end of the fifth year and remain constant forever thereafter. Should Blue Angel invest in the project?
Since the company is not publicly traded, we need to use the industry numbers to calculate the industry levered return on equity. We can then find the industry unlevered return on equity, and re-lever the industry returns on equity to account for the different use of leverage. So, using the CAPM to calculate the industry levered return on equity, we find: RS = RF
+ β(MRP) RS = 5% + 1.2(7%) RS = 13.40%
Next, to find the average cost of unlevered equity in the holiday gift industry we can use Modigliani-Miller Proposition II with corporate taxes, so: RS = R0 + ( B/S ) ( R0 – RB) (1 – t C) .1340 = R0 + (.35) ( R0 – .05) (1 – .40) R0 =
.1194, or 11.94%
Now, we can use the Modigliani-Miller Proposition II with corporate taxes to re-lever the return on equity to account for this company’s debt– equity ratio. Doing so, we find: RS = R0 + ( B/S ) ( R0 – RB) (1 – t C) RS = .1194 + (.40) (.1194 – .05) (1 – .40) RS =
.1361, or 13.61% (Note that we can’t directly calculate Blue Angel’s Rs using t he CAPM model because the question only gives the industry beta, which is different from Blue Angel’s beta due to different capital structure. This also suggests that an alternative approach is first find out Blue Angel’s beta and then use the CAPM model to calculate Rs. You are encouraged to practice yourself.) Since the project is financed at the firm’s target debt– equity ratio, it must be discounted at the company’s weighted average cost of capital. In a world with corporate taxes, a firm’s weighted average cost of capital equals: RWACC = [ B / ( B + S )]
(1 – tC) RB + [S / ( B + S )] RS
So, we need the debt – value and equity – value ratios for the company. The debt – equity ratio for the company is: 5|Page
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B/S =
.40 B = .40S Substituting this in the debt – value ratio, we get: B/V =
.40S / (.40S + S ) B/V = .40 / 1.40 B/V = .29 And the equity – value ratio is one minus the debt – value ratio, or: S /V =
1 – .29 S /V = .71 So, using the capital structure weights, the company’s WACC is: RWACC = [ B / ( B + S )]
(1 – t C) RB + [S / ( B + S )] RS RWACC = .29(1 – .40) (.05) + .71(.1361) RWACC = .1058, or 10.58% Now we need the project’s cash flows. The cash flows increase for the first five years before leveling off into perpetuity. So, the cash flows from the project for the next six years are:
Year 1 cash flow Year 2 cash flow Year 3 cash flow Year 4 cash flow Year 5 cash flow Year 6 cash flow
$93,000.00 $97,650.00 $102,532.50 $107,659.13 $113,042.08 $113,042.08
So, the NPV of the project is: NPV = – $785,000 + $93,000 / 1.1058 + $97,650 / 1.10582 + $102,532.50 / 1.10583 + $107,659.13 / 1.10584 + $113,042.08 / 1.10585 + ($113,042.08 / .1058) / 1.10585 NPV = $241,633.59
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