1. Valuation of
the Firm’s Cash Flows
(Revisited)
Chapter 15

2. Two new approaches to discounting cash flows
We introduce two additional approaches to discounting
(1) the adjusted present value (APV)
method,
(2) the capital cash flow (CCF)
method

3. Two new approaches to discounting cash flows
(1) the adjusted present value or APV method
is designed to isolate the implications of the project’s capital structure, so that the project can be considered independently of debt, which is then followed by an independent assessment of the corporate tax advantages of debt.
(2) the capital cash flow (CCF) method
allows an explicit assessment of the interest payments incurred by the project in the cash flows, while also allowing that the discount rate can be assumed independent of leverage.

4. Two new approaches to discounting cash flows
Both methods have the theoretical advantage of avoiding the circularity of requiring prior knowledge of the value of market equity in the project (which is the objective of the discounting exercise) as an input to the calculation for the required discount rate. This observation represents a considerable advantage for both methods. Again, the methods can be shown to be algebraically consistent with the discounting of dividends model and the WACC approaches to discounting of Chapter 9.

5. (1) the adjusted present value (APV) method
The adjusted present value (APV) method commences by side- stepping the complexity of debt by discounting the project’s operating free cash flow (FCF) available to shareholders – which as we observed in Eqn 9.3 is defined by assuming that the project has no debt:
FCF = EBIT(1–Tc) + DEP&A – NINV
by the unlevered cost of equity (kU).

6. (1) the adjusted present value (APV) method
The APV method then captures the implications of debt separately in the “adjusted present value” term.
The outcome is that the method requires input of the free cash flow (the unlevered cash flow that assumes no debt) and the firm’s (unlevered) cost of capital, which as we have observed, are likely to be much more stable quantities than their leveraged counterparts.
An additional advantage of the method is that it avoids the circularity of needing to know the market value of equity in the project as an input to the calculation of the levered discount rate to be applied to the project cash flows.

7. (1) the adjusted present value (APV) method (cont)
Thus, the APV method allows us to express the market value of a project, Vproject, as
𝑉 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 = 𝑉 𝑈 +𝑃𝑉𝑇𝑆 (15.1)
where VU represents the value of the project assuming no debt.
If, for simplicity, we imagine the operating free cash flow (FCF) in perpetuity, we have
VU = 𝐹𝐶𝐹 𝑘 𝑈 , (15.2)
And, thus, we have
𝑉 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 = 𝐹𝐶𝐹 𝑘 𝑈 +𝑃𝑉𝑇𝑆 (15.3)

8. (1) the adjusted present value (APV) method (cont)
The present value of the tax savings (PVTS) due to the tax deductibility (at the corporate tax rate, Tc) of the firm’s interest payments is calculated separately, as Eqn 14.2 (again, for simplicity, allowing a perpetuity):
𝑃𝑉𝑇𝑆= 𝐷𝐸𝐵𝑇 𝑖 𝐷 𝑇 𝑐 𝑘 𝑇𝑆
and added to VU = 𝐹𝐶𝐹 𝑘 𝑈 in Eqn 15.3 to determine the value of the project, Vproject as the present value of the levered cash flow to the project:
𝑉 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 = 𝐹𝐶𝐹 𝑘 𝑈 + 𝐷𝐸𝐵𝑇 𝑖 𝐷 𝑇 𝑐 𝑘 𝑇𝑆

9. (2) The capital cash flow (CCF) method
This method estimates the value of the project, Vproject, by discounting the levered capital cash flow (CCF) that combines the operating cash flows available to the holders of both equity and debt in the project:
capital cash flow (CCF) to debt plus equity =
CFD + CFE (15.4)

10. (2) The capital cash flow (CCF) method (cont)
We have the debt component , CFD = cash flow to debt,
which is the interest payment on the debt (= DEBT x iD,) plus any repayment of the borrowed principal:
CFD = DEBT x iD + repayment of the debt principal (15.5)
- and the equity component,
CFE = the cash flow to equity, as Eqn 9.1:
CFE = [EBIT - DEBT.iD](1-Tc) + DEP&A – NINV
- repayment of the debt principal

11. (2) The capital cash flow (CCF) method (cont)
The CCF is then discounted using a weighted average (kAV) of shareholders’ cost of equity (kE) and bondholders’ cost of debt (kD) as defined by Eqn 8.4:
𝑘 𝐴𝑉 ≡ 𝑉 𝐸 𝑉 𝐸 + 𝑉 𝐷 𝑘 𝐸 + 𝑉 𝐷 𝑉 𝐸 + 𝑉 𝐷 𝑘 𝐷
Thus if for simplicity we imagine the above capital cash flow (CCF) in perpetuity, we have
𝑉 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 = 𝐶𝐶𝐹 𝑘 𝐴𝑉 (15.5)

12. (2) The capital cash flow (CCF) method (cont)
We observed in Chapter 14, that provided we allow that the appropriate rate with which to discount the tax savings due to debt (kTS) is the unlevered cost of equity (kU), kAV remains equal to kU independent of leverage, as Eqn 8.5:
kAV = kU
In this case, the CCF method has the advantage that the discount rate kAV remains fixed as kU.
For this reason, in the case of known but changing debt levels, the CCF method may be the preferred method.

13. Break time

14. Illustrative Example 15.1: Equivalence of the CCF and APV methods of discounting (demonstration of kAV = kU provided kTS = kU).
Company Stewart is a Scottish firm that manufactures steel rods for re-enforcing concrete. The company is considering an investment opportunity that will last 3 years and require $30 million of initial funding, which would be provided by a $30 million initial issue of debt.
The re-payment schedule for the loan would require repayments of $10 million at the end of Year 2 and $20 million at the end of Year 3.
The initial investment (of $30 million) would be depreciated in three equal payments of $10 million over each of the three years of the investment. The interest payments for the debt would be 10% over each of the three years repayments. The corporate tax rate is 30%. Both interest payments and depreciation costs are tax deductible.

15. Illustrative Example (cont)
The firm estimates that its unlevered cost of equity (kU) at 14%.
Company Stewart considers that the appropriate rate at which to discount the tax savings due to the tax deductibility of its interest payments is the unlevered cost of equity = kU (=14%).

16. Illustrative Example (cont)
The calculated project cash steams for the project over the 3 years duration of the project can be summarized as follows (numbers are millions of dollars):
Year 1
Year 2
Year 3
Revenue – earnings before costs, interest and tax, depreciation and amortization (EBITDA) 40 22
Operating Payments and Costs 20 10
Interest Payments 3 2
Tax
2.1
Loan repayment schedule

17. PART A Required:
(a) Show how the above (i) “interest payment” and (ii) “tax” items have been calculated.
(b) Assuming that the firm’s weighted average cost of the firm’s capital (kAV) with Eqn 8.4:
kAV ≡ 𝑉 𝐷 𝑉 𝐷 + 𝑉 𝐸 kD + 𝑉 𝐸 𝑉 𝐷 + 𝑉 𝐸 kE
can be determined as the unlevered cost of equty (= 14%), use the capital cash flow method (CCF) to calculate the NPV of the above investment opportunity.
(c) Assuming that Stewart goes ahead with the project, calculate the theoretical impact on the price of Stewart’s shares assuming that the project is fully communicated to the market. Stewart currently has 2 million shares outstanding.

18. Illustrative Example (cont)
SOLUTION:
(a) (i) interest payments:
= Debt x interest rate
year 1: $30 million x 0.1 = $3 million
year 2: $30 million x 0.1 = $3 million
year 3: $20 million x 0.1 = $2 million
(ii) tax = (Revenue – Operating payments – Interest payments - Depreciation) x tax rate
year 1: $( – ) x 0.3 = $2.1 million
year 2: $( – ) x 0.3 = $2.1 million
year 3: $(22 – 10 – ) x 0.3 = $0 million

19. . (b) We have: Year 1 Year 2 Year 3 Cash flow available to equity
Year 1
Year 2
Year 3
Cash flow available to equity
= $(40 – 20 – 3 – 10)(0.7) +10 = $14.9;
alternatively as:
(= 40 – – ) = $14.9 million
= $(40 – 20 – 3 – 10)(0.7) = $4.9;
(= 40 – – ) = $4.9
= $(22 – 10 – 2 – 10)(0.7)
= - $10.0; (=
-20) = - $10.0
Cash flow available to debt
3.0 million
(=3 + 0)
13.0 million
(=3+ 10)
22.0 million
(=2 +20)
Total cash flow
(add above two rows)
17.9 million
12.0 million
Discount factor, kAV = 14%
.877
.7695
.675
Present value of cash flows
15.7 million
13.8 million
8.1 million
Vproject (VD + VE) =
37.6 (37.575) million

20. Illustrative Example (cont)
Hence the total value of the cash flows including all required repayments to debt is $37.6 million.
(c) The repayments to debt have current value of $30 million.
The value of the project to the firm’s shareholders is therefore $ $30 = $7.6 million.
Hence the theoretical increase in share value is $7.6 million / 2 million = $3.8.

21. PART B Required: to calculate:
(d) Use the Adjusted Present Value Method (APV)
to calculate:
(i) the net present value of the above project and
(ii) the “corporate tax shield” of the present
value of the tax savings (PVTS) of the project.

22. (d) We have kU =14%. The calculations are therefore as follows.
Year 1
Year 2
Year 3
Unlevered cash flow (note, we subtract depreciation, but not the interest payments)
= $(40 – 20 –10)(0.7) +10 = $17.0 million
= $(22 – 10 –10)(0.7) +10 = $11.4 million
Discount factor, kU =14%
.877
.770
.675
Present value of cash flows assuming no debt
14.9 million
13.1 million
7.7 million
Total present value of cash flows
assuming no debt
35.69 million
Interest payments
3 million
2 million
Tax savings (TS )
= interest payment x TC
0.9 million
0.6 million
Present value of tax savings (TS)
0.80 million
0.69 million
0.405 million
Total present value of tax savings
1.89 million
Vproject (VD + VE) = =
= 37.6 (37.575)
million

23. Review
We have now developed four methods of discounting cash flows aimed at project valuation:
(1) the cash flow to equity (CFE) or discounting of dividends approach
(2) the WACC approach
(3) the adjusted present value (APV)
(4) the capital cash flow (CCF) methods in this chapter.

24. Review (cont)
Agreeably, the four methods are algebraically consistent with each other.
We recall from Chapter 9, that the WACC method represents the industry-favoured approach to discounting – provided the calculations are presented with the project NPV as a function of both (i) the discount rate and (ii) variation in the key input variables (rather than to commit to particular values). Such approach can of course be applied to the other methods.