Discount rates for project appraisal

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1 Discount rates for project appraisal We know that we have to discount cash flows in order to value projects We can identify the cash flows BUT What discount rate should we use? 1

2 The Discount Rate and Capital Budgeting Weighted Average Cost of Capital Method Adjusted Present Value (APV) Flow-to-equity (FTE) Example Summary and Conclusions 2

3 Method 1: Weighted Average Cost of Capital (WACC) We use a discount rate that reflects the average returns that the company should be making to satisfy (a) its bondholders (b) its shareholders (c ) the proportion of debt in its capital structure 3

4 Component costs Cost of bonds = interest rate expected by bond holders Bonds are cheaper for companies because the interest paid can offset tax Cost of shares = dividends + capital gain expected by shareholders 4

5 5 WACC calculation r E D = r+ r( T) e d C V V WACC 1 E = Value of shares (equity) = 500 D = Value of Debt (bonds) = 500 Note V = Value of firm = E+D = 1000 T c =Corporate tax=30% r e = return expected by shareholders r d = return expected by bondholders

6 Note on Miles and Ezzell formula M&M assumed perpetuities for their cash flows. M&E looked at the case of finite projects where the leverage was adjusted to be a constant of the remaining value. The complication is that V depends on the amount of debt which depends on the value of the project WACC(M& E) where r 0 r 0 D (1 V (1 the cost of capital of the firmif ithad no debt (theall - equity cost of capital)and r T c.r D r r 0 D ) ) D the cost of debt

7 Example: WACC calculation Cost of equity = 13.5%, If firm were all-equity, the WACC would be 10% (see later) Cost of Debt = 5% Corporate Tax rate = 30% D/V= 0.5 So WACC = 0.5 x x 5 x 0.7 = 8.5% WACC(M&E) = 9.21% The two WACCs differ because future tax shields are less valuable if uncertain. 7

8 8 Example: Project with cash flows of -1000, 400, 400, 600, 500-1, After tax cash flows (pre-tax cash flows x 0.7) -1,

9 9 Valuation using WACC To find the value of the project, discount the after-tax cash flows at the weighted average cost of capital. NOTE: we do not include the interest payments NPV, ()085 NPV % ()085.1()

10 How is WACC affected by changing level of debt? As debt rises, shareholders demand higher returns because their investment is riskier Debt is cheaper than equity But the average will either (a) stay constant (if no tax effect of debt) (b) become lower as the advantage of debt becomes more important (c ) rise as cost of bankruptcy rises Note: Shareholders will always get a higher return if debt increases... 10

11 11 WACC Very popular but not always relevant. Companies that finance their projects using very different debt packages should not use the WACC. Not the method used in property investment.

12 Method 2: Adjusted Present Value (APV) This method identifies the precise financing package for the project and adds in the tax advantages of the financing directly. The discount rate used is the rate that would apply if the company were entirely financed by equity. (r 0 ) 12

13 13 Adjusted Present Value Approach The value of a project to the firm can be thought of as the value of the project to an all-equity financed firm (NPV) plus the present value of the financing side effects (NPVF): There are four side effects of financing: The Tax Subsidy to Debt The Costs of Issuing New Securities The Costs of Financial Distress Subsidies to Debt Financing APV NPV NPVF

14 The cost of capital for an allequity firm (r o ) We can use the formula r 0 = WACC/(1-T c D/V) = 8.5%/(1-0.3x0.5) = 10% Again we use the after-tax cash flows without taking the interest into account. 14

15 APV cont. PV PV = , (1.10) (1.10) (1.10) (1.10) = But we also look at the benefits of having the tax shield for interest payments We assume that we issue a bond at 10% which matures at the end of the fourth year. 15

16 APV cont. Treat loan as a project ( 1.3 ) 500 NPV loan = 500 t 4 ( 1.05 ) ( 1.05 ) =t 1 NPV = loan or just calculate the tax saved.5% of 500 = 25 p.a. So saves 25x.3 = 7.5 p.a for 4 years. PV(loan) = 7.5/ / / / = (note discount rate is the before tax cost of debt) So APV = =

17 17 APV cont. Note that the PV is not quite the same as calculated by the WACC approach. Useful because we can calculate the benefits of specific loans attached to projects. See discussion paper on APV approach in property investment Much proposed by text books, not used much in practice partly because of the use of r 0 a difficult concept.

18 Method 3: Flow to Equity approach (FTE) We take the viewpoint of the shareholders and discount their cash flows at the cost of equity after taking the cash flows for the loan, interest and tax have been taken into account. To calculate the cost of equity, we use... 18

19 Another formula! r e = r 0 + (r 0 -r d )(1-T c )D/E Here r 0 is the cost of equity if there is no debt in the company (as before). r 0 = the all-equity cost of capital The discount rate (re) will be higher than either WACC or r0 but the cash flows are after financing charges so will be lower. 19

20 20 Calculation of r e r 0 = 10%,r d = 5%, T c =.3 and D/E=1 r e = 10% +(10%-5%)(0.7)1 = 10% + 3.5% = 13.5%

21 Example using FTE Debt = 500, r e = 13.5% CF Interest Tax Loan CFE NPV(13.5%) IRR 27.2% 21

22 Notes on FTE Investment = 500 because debt is used to finance half of the investment cost Cash flows include paying interest and paying back loan at end of period. NPV = highest of all methods but assumptions are not quite right because D/E too low, thus r e too low. To get a similar NPV as the other two methods, re 18% But this is nearest to the methods used in property development appraisal 22

23 23 Summary of WACC, APV, FTE WACC used commonly APV more flexible but little used FTE used in Property Development

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