1. Capital Budgeting: Refinements
Dr. C. Bulent Aybar
Professor of International Finance

2. Topics Covered
Projects with unequal lives and Annualized NPV
Risk Adjusted Discount Rate
Capital Rationing

3. Projects with Unequal Lives
If projects are independent, comparing projects with unequal lives is not critical because any project with positive NPV can be pursued.
But when unequal-lived projects are mutually exclusive, the impact of differing lives must be considered because they do not provide service over comparable time periods.
This is particularly important when continuing service is needed from the projects under consideration

4. Projects with Unequal Lives
A commonly used method in comparative analysis of NPVs is Annualized NPV.
The ANPV approach converts the NPV of unequal-lived mutually exclusive projects into an equivalent (in NPV terms) annual amount that can be used to select the best project.
Calculate the NPV of each project over its life using the appropriate cost of capital.
Divide the NPV of each positive NPV project by the PVIFA at the given cost of capital and the project’s live to get the ANPV for each project.
Select the project with the highest ANPV.

5. Example
The AT Company, a regional cable-TV firm, is evaluating two projects, X and Y. The projects’ cash flows is given below.

6. Project NPVs
The projects’ resulting NPVs at a cost of capital of 10% is given below.

7. Calculator and Excel Solutions to Project NPVs

8. Ignoring the difference in their useful lives, both projects are acceptable (have positive NPVs).
However, if the projects were mutually exclusive, project Y would be preferred over project X.
Would this conclusion stand if we assumed that 3 year project is renewed? Under this assumption we could repeat the analysis and see how the NPV of X would change.
Annualized NPV approach is another way to draw direct comparisons.

9. Choosing between Mutually Exclusive Projects
As described earlier we first calculated the NPV for projects X and Y at 10%.
NPVX = $11,248; NPVY = $18,985.
Then we calculate the ANPV for Projects X and Y.
ANPVX = $11,248/PVIFA10%,3 years = $4,523
ANPVY = $18,985/PVIFA10%,6 years = $4,359
Choose the project with the higher ANPV.

10. Risk Adjusted Discount Rates
In generic CB process, we assumed that all projects considered by the firm can be evaluated by using firm’s weighed average cost of capital.
However, this approach would be correct only when the projects have similar risk profiles as the firm. In other words, when the projects under consideration are not distinctly safer or riskier than firm’s general line of business, discounting project cash flows at the cost of capital makes sense.
However, when projects have different risk profiles, using a cost of capital may under or overestimate the risks involved in the project.

11. How do we make risk adjustments in the discount rate?
How do we account for varying levels of risk in the respective projects?
One approach is to measure project beta as a reflection of its level of risk, and use CAPM to calculate required rate of return. Although it presents some computational challenges, this method can be implemented with careful considerations.
When projects are located in foreign markets, some additional adjustments are necessary!

12. CAPM and Risk Adjustments: An Example
Adjusted Equity
Market Risk
Premium
Project/Operating
Beta
US Risk Free Rate
Sovereign Spread

13. Risk Adjustment Models
Another approach is to develop internal risk assessment and enumeration models, and implement these models to account for risk associated with a particular project.
Energy Multinational AES developed this system to estimate required returns from its overseas generation plant investments.
AES identified 7 risk factors and assigned a weight to each risk factor. Subsequently each factor was rated from 1 to 3, 1 being the least risky.
AES calculated a risk score for each project. Each risk point required 5% compensation. For instance a project with a Risk Score of 3, would require a 15% risk adjustment over weighted average cost of capital.

14. Project Specific (Idiosyncratic) Risks
Business / Project
Country
Const.
Operatioal
Regulatory
Currency
Counterparty
Contract
Commodity
Andres
Dominican Republic 3
Caracoles
Argentina 2 - 1
Drax
United Kingdom
Eletropaulo
Brazil
Gener
Chile
Haripur
Bangladesh
Kelvin
South Africa
Lal Pir
Pakistan
Los Mina
OPGC
India
Ottana
Italy
Red Oak
USA
Rivnoblenergo
Ukraine
Telasi
Georgia
Uruguaiana

15. Idiosyncratic Project Risk Premiums

16. Problems with Risk Adjustments
Risk scoring systems with elegant designs often lack theoretical consistency and justification. They tend to be logical and ad hoc adjustments.
A problem with these adjustments is over or underestimation of risk.
It is always prudent to check if the adjustments make any sense. One approach to such assessment is to discount the cash flows at risk free rate under various assumptions. For instance an AES project yielded an NPV that was inferior to NPV calculated by discounting 50% of the cash flows at the risk free rate.

17. Capital Rationing
Firm’s often operate under conditions of capital rationing—they have more acceptable independent projects than they can fund.
In theory, capital rationing should not exist—firms should accept all projects that have positive NPVs.
However, research has found that management internally imposes capital expenditure constraints to avoid what it deems to be “excessive” levels of new financing, particularly debt.
Thus, the objective of capital rationing is to select the group of projects within the firm’s budget that provides the highest overall NPV or IRR.

18. Tate Company, a fast growing plastics company with a cost of capital of 10%, is confronted with six projects competing for its fixed budget of $250,000. The initial investment and IRR for each project are shown below:

19. IRR and NPV of the Projects
According to IRR rule, projects B, C and E would be accepted!

20. NPV Rule Project NPV Investment C 45,000 100,000 B 42,000 70,000 A
20,000
80,000 E
19,000
60,000 F
16,500
110,000 D
(4,000)
40,000
According to NPV rule projects C, B and A make the cut! Although
Managers find IRR method more compelling, from a shareholder
Wealth maximization perspective NPV method should be used.

21. Budget Constraint and Acceptable Projects

22. Weighted Average Marginal Cost of Capital
Definition: The cost of the next dollar of capital that the firm raises.
As we discussed in the class earlier, components of cost of capital remains flat when the range of capital raised does not dramatically change the risks taken by capital providers.
However, as investors provide more capital, changing exposure to cash flows, changing of nature of firm assets or a combination of both change the expected returns by capital providers. This causes jumps in WACC.
The jumps in WACC is called break points.

23. Breakpoints Break Points can be calculated as follows:
Where wi is the share of given component in the capital structure.
Example: Assume that company finances its investments with 40% debt and 60% equity.
Company can raise debt capital up to $1,000,000 at a cost of 10%. After 1,000,000 each debt dollar raised costs 13%.
The example suggests that the company has a possible breakpoint at 1,000,000/0.4=$2,500,000.
In order to find WAMCC breakpoints, we need to calculate WACC between breakpoints.

24. Example
A company has a current dividend of $1, the current stock price is $10.40, and the company is expected to grow at a rate of 4%.
The company is financed with 75% equity and 25% debt, where the debt costs 6% in interest per year (tax rate = 40%).
Assume the cost of debt remains fixed for all levels of capital.
The company is expected to generate $75,000 in net income this year with a dividend payout ratio of 40%.
Assuming 20% floatation costs, what should be the MWACC schedule of the firm?

25. Step-1: Find the Breakpoint:
R/E=75,000 x (1-0.4)=45,000
This means that company can fund $60,000 of capital budget without incurring external fund raising costs.
Step-2; Find the cost of internal equity (up to 60,000 total funding)
After external equity is issued (when more than 60,000 is needed)

26. Step-3: Find Cost of debt:
Step-4: Find MWACC
After the breakpoint:

27. MWACC
13.28%
11.40%

28. Investment Opportunity Schedule
Suppose that the company has the following investment opportunities.
Given company’s MWACC schedule which projects should the firm consider investing?

29. MCC/IOS Schedule - Example
If we combine the following Investment Opportunity Schedule with the earlier MCC Schedule:

30. MCC/IOS Schedule - Example
In this instance we would invest in projects C and A, but not in B and D.
The cost of the last dollar invested in B exceeds the project’s expected return. Investment in this project is likely to destroy value!

31. Example
Forelli Products Company is a growing manufacturer of automobile accessories whose stock is actively traded on the over-the-counter (OTC) market.
During 2009, the Dallas-based company experienced sharp increases in both sales and earnings. Because of this recent growth, Kate Einhorn, the company's treasurer, wants to make sure that available funds are being used in their fullest.
The company policy is to maintain the current capital structure proportions of 30% long-term debt, 10% preferred stock, and 60% common stock equity for at least the next 3 years. The firm is in the 40% tax bracket.

32. Investment Opportunity IRR Initial Investment A 15% 400,000 B 22%
Forelli's division and product managers have presented several competing investment opportunities to Einhorn. However, because funds are limited, choices of which projects to accept must be made. The investment opportunities schedule (IOS) is shown in the table below
Investment Opportunity
IRR
Initial Investment A
15%
400,000 B
22%
200,000 C
25%
700,000 D
23% E
17%
500,000 F
19%
600,000 G
14%

33. To estimate the firm's weighted average cost of capital (WACC), Einhorn contacted a leading investment banking firm, which provided the financing cost data shown in the following table.
Financing Cost Data Forelli Prodcuts Company
 Long-term debt:
The firm can raise $450,000 of additional debt by selling 15-year,$1,000 par-value, 9% coupon interest rate bonds that pays annual interest. It expects to net $960 per bond after flotation costs. Any debt in excess of $450,000 will have a before-tax cost, of 13%.
 Preferred stock:
Preferred stock, regardless of the amount sold, can be issued with a $70 par value and a 14% annual dividend rate and will net $65 per share after flotation costs.
 Common stock equity
The firm expects dividends and earnings per share to be $0.96 and $3.20, respectively, in 2010 and to continue to grow at a constant rate of 11% per year. The firm's stock currently sells for $12 per share. Forelli expects to have $ 1,500,000 of retained earnings available in the coming year. Once the retained earnings have been exhausted, the firm can raise additional funds by selling new common stock, netting $9 per share after underpricing and flotation costs.

34. Breakeven Points Firm’s cost of debt changes after 450,000
Breakpoint-1: 450,000/0.3=1,500,000
Firm’s cost of equity changes when company issues external equity:
Breakpoint-2: 1,500,000/0.6=2,500,000
Firm’s cost of capital does not change until a total of 1.5m is raised. If the amount needed exceeds $1.5m, the cost makes a jump because of increasing cost of debt, but remains flat until the amount needed hits 2.5m.
To raise any dollar above 2.5m, company needs to issue external equity and be exposed to floatation costs.

35. WACC for Capital Raised<1,500,000
Par Value
1000
Coupon 9%
Net Price
960
YTM
9.51%
Maturity (N) 15
Price
$960.00
Preferred Par Value 70
Prefered Dividend
14%
Prefered Dividend in Dollars
9.8
Net Proceed 65
Cost of Preferred Stock
15.08%
Common Stock
Growth Rate
0.11
Dividend (D1)
0.96
Stock Price 12
Net Proceed from Stock Issue 9
Cost of Retained Earnings
19.00%
Cost of new issue
21.67%

36. Forelli’s MWACC If the amount needed <1,500,000

37. Investment Opportunity
IRR
Initial Investment
Cum. Investment
WAMCC C
25%
700,000
14.62% D
23%
400,000
1,100,000 B
22%
200,000
1,300,000 F
19%
600,000
1,900,000
15.25% E
17%
500,000
2,400,000 A
15%
2,800,000
16.85% G
14%
3,300,000

38. IOS and WMCC Schedule
Once we expand the fund raising to the extent to finance project “A”, company’s marginal cost of capital or corporate cost of capital climbs up to 16.8%. Since project A and G returns are lower than 16.8%, they are negative NPV projects and investing them destroys value!