CHAPTER 19

Financing and Valuation

 

 

Answers to Practice Questions

 

1.         If the bank debt is treated as permanent financing, the capital structure proportions are:

 

Bank debt (rD = 10 percent)

$280

 

9.4%

 

Long-term debt (rD = 9 percent)

1800

 

60.4

 

Equity (rE = 18 percent, 90 x 10 million shares)

900

 

30.2

 

 

$2980

 

100.0%

 

WACC* = [0.10´(1 - 0.35)´0.094] + [0.09´(1 - 0.35)´0.604] + [0.18´0.302]

= 0.096 = 9.6%

 

 

 

 

2.         Forecast after-tax incremental cash flows as explained in Section 6.1.  Interest is not included; the forecasts assume an all-equity financed firm.

 

 

3.         Calculate APV by subtracting $4 million from base-case NPV.

 

 

4.                  We make three adjustments to the balance sheet:

·        Ignore deferred taxes; this is an accounting entry and represents neither a liability nor a source of funds

·        ‘Net out’ accounts payable against current assets

·        Use the market value of equity (7.46 million x $46)

 

Now the right-hand side of the balance sheet (in thousands) looks like:

Short-term debt                                   $75,600

Long-term debt                                    208,600

Share holder equity                             343,160

                        Total                                       $627,360

 

The after-tax weighted-average cost of capital formula, with one element for each source of funding, is:

 

            WACC = [rD-ST´(1 – Tc)´(D-ST/V)]+[rD-LT´(1 – Tc)´(D-LT/V)]+[rE ´(E/V)]

            WACC = [0.06´(1 - 0.35)´(75,600/627,360)] + [0.08´(1 - 0.35)´(208,600/627,360)]

                        + [0.15´(343,160/627,360)]

                        = 0.004700 + 0.017290 + 0.082049 = 0.1040 = 10.40%

 

5.                  Assume that short-term debt is temporary.  From Practice Question 4:

Long-term debt                                 $208,600

Share holder equity                             343,160

                        Total                                       $551,760

            Therefore:

(D/V) = ($208,600/$551,760) = 0.378

(E/V) = ($343,160/$551,760) = 0.622

            Step 1:

                        r = rD (D/V) + rE (E/V) = (0.08 ´ 0.378) + (0.15 ´ 0.622) = 0.1235

            Step 2:

                        rE = r + (r – rD) (D/E) = 0.1235 + (0.1235 - .08) ´ (0.4) = 0.1409

            Step 3:           

                        WACC = [rD ´ (1 – TC) ´ (D/V)] + [rE ´ (E/V)]

                                     = (0.08 ´ 0.65 ´ 0.286) + (0.1409 ´ 0.714) = 0.1155 = 11.55%

 

6.        

Pre-tax operating income

 

$100.5

 

Short-term interest

 

4.5

 

Long-term interest

 

16.7

 

Earnings before tax

 

$79.3

 

Tax

 

27.8

 

Net income

 

$51.5

 

Value of equity = $51.5/0.15 = $343.3

Value of firm = $343.3 + $75.6 + $208.6 = $627.5

 

 

7.                  The problem here is that issue costs are a one-time expenditure, while adjusting the WACC implies a correction every year.  The only way to account for issue costs in project evaluation is to use the APV formulation and adjust directly by subtracting the issue costs from the base case NPV.

 

 

8.         a.         Base case NPV = -1,000 + (600/1.12) + (700/1.122) = $93.75 or $93,750

 

 

Year

Debt Outstanding at Start Of  Year

 

 

Interest

 

Interest

Tax Shield

 

PV

(Tax Shield)

1

300

24

7.20

6.67

2

150

12

3.60

3.09

                        APV = 93.75 + 6.67 + 3.09 = 103.5 or $103,500

9.                  [$100,000 ´ (1 - 0.35)] + [$100,000 ´ (1 - 0.35) ´ (Annuity Factor5/9 (1 – 0.35)%)]

            = $65,000 + $274,925 = $339,925

 

 

10.       a.         Base-case NPV = -$1,000,000 + ($85,000/0.10) = -$150,000

                        PV(tax shields) = 0.35 ´ $400,000 = $140,000

                        APV = -$150,000 + $140,000 = -$10,000

b.                  PV(tax shields, approximate) = (0.35 ´ 0.07 ´ $400,000)/0.10 = $98,000

                        APV = -$150,000 + $98,000 = -$52,000

                        PV(tax shields, exact) = $98,000 ´ (1.10/1.07) = $100,748

                        APV = -$150,000 + $100,748 = -$49,252

            The present value of the tax shield is higher when the debt is fixed and therefore the tax shield is certain.  When borrowing a constant proportion of the market value of the project, the interest tax shields are as uncertain as the value of the project, and therefore must be discounted at the project’s opportunity cost of capital.

 

 

11.             The immediate source of funds (i.e., both the proportion borrowed and the expected return on the stocks sold) is irrelevant.  The project would not be any more valuable if the university sold stocks offering a lower return.  If borrowing is a zero-NPV activity for a tax-exempt university, then base-case NPV equals APV, and the adjusted cost of capital r* equals the opportunity cost of capital with all-equity financing.  Here, base-case NPV is negative; the university should not invest.

 

 

12.       r* is the after-tax adjusted weighted average cost of capital.  An adjusted discount rate does not equal the WACC when it takes into account major changes in expected capital structure or costs.

 

 

13.       Note the following:

·        The costs of debt and equity are not 8.5% and 19%, respectively.  These figures assume the issue costs are paid every year, not just at issue.

·        The fact that Bunsen can finance the entire cost of the project with debt is irrelevant.  The cost of capital does not depend on the immediate source of funds; what matters is the project’s contribution to the firm’s overall borrowing power.

·        The project is expected to support debt in perpetuity.  The fact that the first debt issue is for only 20 years is irrelevant.

 

            Assume the project has the same business risk as the firm’s other assets.  Because it is a perpetuity, we can use the firm’s weighted-average cost of capital.  If we ignore issue costs:

 

 

                        WACC = [rD ´ (1 - TC) ´ (D/V)] + [rE ´ (E/V)]

 

                        WACC = [0.07 ´ (1 - .35) ´ (0.4)] + [0.14 ´ 0.6] = 0.1022 = 10.22%

 

            Using this discount rate:

                       

            The issue costs are:

Stock issue:

(0.050 ´ $1,000,000) = $50,000

Bond issue:

(0.015 ´ $1,000,000) = $15,000

 

            Debt is clearly less expensive.  Project NPV net of issue costs is reduced to:

            ($272,016 - $15,000) = $257,016.  However, if debt is used, the firm’s debt ratio will be above the target ratio, and more equity will have to be raised later.  If debt financing can be obtained using retaining earnings, then there are no other issue costs to consider.  If stock will be issued to regain the target debt ratio, an additional issue cost is incurred.

 

            A careful estimate of the issue costs attributable to this project would require a comparison of Bunsen’s financial plan ‘with’ as compared to ‘without’ this project.

 

14.             From the text, Section 19.6, footnote 29, solving for bA, we find that:

 

                       

 

                       

 

                       

 

Using the Security Market Line, we calculate the opportunity cost of capital for Sphagnum’s assets:

 

 

rA = rf + bA (rm – rf) = 0.09 + (0.6738 ´ 0.085) = 0.147 = 14.7%

 

Following MM’s original analysis and considering only corporate taxes, we have:

 

r* = r (1 – TC L)

 

r* = 0.147 ´ [1 – (0.35 ´ 0.55)] = 0.1187 or approximately 12%

 

            This matches the consultant’s estimate for the weighted-average cost of capital.

15.             Disagree.  The Banker’s Tryst calculations are based on the assumption that the cost of debt will remain constant, and that the cost of equity capital will not change even though the firm’s financial structure has changed.  The former assumption is appropriate while the latter is not.

 

 

16.             Tax or financing side effects in international projects:

§         Project financing issues, such as early cash flows going to debt service resulting in a non-constant debt ratio.

§         Subsidized financing rates.

§         Guaranteed contracts for output.

§         Government restrictions on the flow of funds.

 

 

17.             a.

 

 

Year

 

Principal at

Start of Year

 

Principal

Repayment

 

 

Interest

 

Interest

Less Tax

Net Cash

Flow

On Loan

1

5000.0

397.5

250.0

162.5

560.0

2

4602.5

417.4

230.1

149.6

567.0

3

4185.1

438.2

209.3

136.0

574.2

4

3746.9

460.2

187.3

121.7

581.9

5

3286.7

483.2

164.3

106.8

590.0

6

2803.5

507.3

140.2

91.1

598.4

7

2296.2

532.7

114.8

74.6

607.3

8

1763.5

559.3

88.2

57.3

616.6

9

1204.2

587.3

60.2

39.1

626.4

10

616.9

616.9

30.8

20.0

636.9

 

                        Therefore:

 

                       

 

                        Value of subsidy = $5,000,000 - $4,530,000 = $470,000

 

b.                  Yes.  The value of the subsidy measures the additional value to the firm from a government loan at 5 percent, compared to an unsubsidized loan at 10 percent.  Therefore, the company should calculate APV, including

PV (tax shields) on the unsubsidized loan, and then add in the value of subsidy.

 


 

18.       a.         Assume that the expected future Treasury-bill rate is equal to the 20-year Treasury bond rate (5.8%) less the average historical premium of Treasury bonds over Treasury bills (1.8%), so that the risk-free rate (rf) is 4%.  Also assume that the market risk premium (rm – rf) is 8%.  Then, using the CAPM, we find rE as follows:

 

                                    rE = rf + bA ´ [rm - rf] = 4% + (0.66 ´ 8%) = 9.28%

                        Market value of equity (E) is equal to: 256.2 ´ $59 = $15,115.8 so that:

                        V = $6,268 + $15,115.8 = $21,383.8

                        D/V = $6,268/$21,383.8 = 0.293

                        E/V = $15,115.8/$21,383.8 = 0.707

                        WACC = (0.707 ´ 9.28%) + (0.293 ´ 0.65 ´ 7.4%) = 7.97%

b.                  Step 1. Calculate the opportunity cost of capital.

Opportunity cost of capital = r = rD ´ (D/V) + rE ´ (E/V)

                                                = 7.4% ´ 0.293 + 9.28% ´ 0.707 = 8.73%

Step 2. Estimate the cost of debt and calculate the new cost of equity.

Assume that the interest rate on the debt falls to 7.2% so that:

rE = r + (r - rD) ´ (D/E) = 8.73% + (8.73% - 7.2%) ´ (0.25/0.75) = 9.25%

Step 3. Recalculate WACC.

WACC = (0.75 ´ 9.25%) + (0.25 ´ 0.65 ´ 7.2%) = 8.11%

 

19.             The company weighted-average cost of capital is appropriate for evaluating capital budgeting projects that are exact replicas of the firm as it currently exists.  If the project in question is more like the industry as a whole than it is like the company, then the industry weighted-average cost of capital would be a better choice.


 

Challenge Questions

 

1.                  a.         For a one-period project to have zero APV:

 

 

 

 


                        Rearranging gives:

 

 

 


                        For a one-period project, the left-hand side of this equation is the project IRR.  Also, (D/ -C0) is the project’s debt capacity.  Therefore, the minimum acceptable return is:

 

 

 

 


b.                  For a company that follows Financing Rule 2, all of the variables in the Miles-Ezzell formula are constant.  For example, we know that debt is assumed to be a constant proportion of market value, so that the adjusted cost of capital (r*) is also constant over time.  In other words, when we are at period 1, the Miles-Ezzell formula gives the same value for r* as at period 0.  We know from part (a) that the formula is correct for a one-period cash flow.  So the value, in period 1, of the period 2 cash flow is:

 

            PV1 = C2/(1 + r * )

The value today is:

            PV0 = PV1/(1 + r * ) = C2/(1 + r * )2

By analogy, we would discount the period 3 cash flow, at r*, in period 2 to give:

 

            PV2 = C3/(1 + r * )

Therefore, the value today is:

            PV0 = C3/(1 + r * )3

 

 


2.        

D/V

E/V

D/E

r

rd

rE

WACC

ME

0.20

0.80

0.250

12.00%

8.00%

13.00%

11.44%

11.42%

0.40

0.60

0.667

12.00%

8.00%

14.67%

10.88%

10.84%

0.60

0.40

1.500

12.00%

10.00%

15.00%

9.90%

9.86%

T* = TC = 0.35

 

 

 

 

 

 

 

 

            Different values result because the Miles-Ezzell formula assumes debt is rebalanced at the end of every period (Financing Rule 2).

 

 

3.         The expected cash flow from the firm is: (Vu r + Tc rD D) where r is the return on assets and rD is the rate on debt (the interest tax shield has the same level of risk).  The cash flow to the stockholders and bondholders is:

 

                        Er* + DrD

            Because the firm generates a perpetual cash flow stream:

                        Er* + DrD = Vur + Tc rD D

            Divide by E and subtract DrD:

 

 

 


            Substitute L = D/E

 

 

 


            We know that: Vu = E + (1 - Tc)D:

 

 

 

 

 


a.                  Whenever r > rD, r* increases with leverage.

b.         The formulas for levering and relevering the cost of equity implicitly assume on-going corporate profitability so that the interest tax shields can be exploited.

 

 

4.                  This is not necessarily true.  Note that, when the debt is rebalanced, next year’s interest tax shields are fixed and, thus, discounted at a lower rate.  The following year’s interest is not known with certainty for one year and, hence, is discounted for one year at the higher risky rate and for one year at the lower rate.  This is much more realistic since it recognizes the uncertainty of future events.