Help me with Example 1: Optimal capital budget

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LECTURE 8B (OUTLINE) OTHER TOPICS IN CAPITAL BUDGETING [CHAPTER 10 & 11] I. SPECIAL ISSUES 1. Unequal Lives A. Why is it a problem? B. What to do? Two oft-suggested methods: a. Replacement Chain Method b. Annual Annuity Method: 2. Optimal Capital Budget and Capital Rationing A. Optimal Capital Budget: MCC and IOS Schedules B. Capital Rationing a. Definition b. Effect of Capital Rationing on the Firm's Investment Decision c. Why does capital rationing exist? C. Making Decision under Capital Rationing a. Objective b. A Suggested Approach D. Mukherjee and Hingorani's Article on Capital Rationing 3. Adjusting for Inflation A. How does inflation Introduce bias in Capital Budgeting Decision? B. Ways to handle the Inflation-introduced Bias II. REAL OPTIONS [CHAPTER 11] 1. Definition 2. Types of real options A. B. C. D. Investment Timing Growth Abandonment Flexibility 3. Valuing Real Options LECTURE 8B: OTHER TOPICS IN CAPITAL BUDGETING 1. UNEQUAL LIVES A. Why is it a problem? When two mutually exclusive projects have different lives and we need the project on a permanent (or long term) basis, we will make a biased selection decision if we just look at the original life of each machine. NPV and IRR may give different ranking: NPV favoring the longer life Project and IRR favoring the shorter life project. An example: Two projects with unequal lives Life (Years) 0 1 2 3 4 5 6 NPV @(10%) IRR Project A -180 75 75 75 75 0 0 $57.75 24% Project B -255 75 75 75 75 75 75 $71.63 19% NPV favors B, IRR favors A. B. What to do? Two oft-suggested methods: a. Replacement Chain Method: Shoot for a common denominator (life) by repeating each project (for example repeat 'A' 3 times and 'B' 2 times making both lives equal to 12). b. Equivalent Annual Annuity Method (EAA): (i) Find the NPV of each project: $57.75 (A) and $71.63 (B). (ii) Divide the NPV by respective PVIFA: (iii) $57.75 = $18.221 for A 3.17 $71.63 =$16.441 for B 4.357 If both projects have the same required rate of return, select the one with higher "annual annuity," which is Project B. If the projects have different RRRs divide each annuity figure by its respective RRR and choose the one with the highest value. 2. OPTIMAL CAPITAL BUDGET AND CAPITAL RATIONING A. OPTIMAL CAPITAL BUDGET a) Definition: The amount that a firm should invest in a given year to maximize the value of the firm. b) Determining the Optimal Capital Budget Step 1. Draw the MCC schedulefrom the lowest to the highest WACC Step 2. Draw the IOS scheduleFrom the highest to the lowest IRR Step 3. Accept the projects whose IRRs are higher than their relevant WACCs. (When a project is partly funded at a WACC less than the IRR and partly above the IRR, compute the average WACC of this project and determine if this average is below or above its IRR.) Step 4. Usually, the optimal capital budget is the amount where MCC and IRR schedules intersect. EXAMPLE 1: OPTIMAL CAPITAL BUDGET Here are some data on the Schwab Company: 1) 2) 3) 4) 5) 6) 7) The target capital structure is 40% debt and 60% equity; Projected retained earnings = $6 million; New bonds can be issued to yield 10%; Applicable marginal tax rate = 30%; Cost of retained earnings = 15.5%; Cost of New Common Stock = 16.5%; The following four capital projects have been identified. They are all of average risk, independent, and non-divisible. Computation for MCC Schedule COMPONENT WEIGHT MCC1 MCC2 $_____ to_______ Over $________ DEBT EQUITY MCC Investments Opportunities Project Cost IRR A B C D $2.5 mill $5.0 mill $2.5 mill $2.5 mill 14.0% 13.6% 13.5% 12.4% Determining the optimal capital budget? COC & IRR (%) Capital ($) EXAMPLE 2: OPTIMAL CAPITAL BUDGET The following information is given: a. The optimal capital structure is debt 30%, Preferred stock 10%, and common equity is 60%. b. A maximum of $9 million of debt can be issued at a cost of 6.3%. The firm's cost of c. debt (after-tax) goes up to 7.3%, If it wants to raise more than $9 million in debt. c. Yield on preferred stock is 10%. The floatation costs for issuing new preferred is 5%. d. The cost of retained earnings is 16%, and the cost of new common stock is 18% e.The amount available in retained earnings is $12 million. f. The firm has the following investment opportunities this year: Investment IRR ($ Million) (% )__ A 8 16 B 6 20 C 14 14 D 12 14.5 E 10 15 Given the above info, find the optimal capital budget. MCC Computation: COMPONENT WEIGHT MCC1 $0 TO $______ MCC2 FR $_______ TO$_______ MCC3 OVER$_______ COC & IRR (%) Capital ($) The optimal capital budget is _________________________. 2B. CAPITAL RATIONING a) Definition: Capital rationing refers to the situation where a budget constraint is imposed, and the firm may not invest in all acceptable projects. Although theoretically capital rationing should not exist, in practice many surveys have shown it does. Generally it arises because of internally imposed constraints on the amount of external funds a firm will raise, or because of dollar limits imposed on capital expenditure divisions of firms and undertake. b) Internal vs. External Capital Rationing c) Why is Internal Capital Rationing Common SEE MUKHERJEE and HINGORANI'S ARTICLE ON CAPITAL RATIONING d) Effect of Capital Rationing on the Firm's Investment Decision If there are no capital constraints, the firm would accept Projects N, A, Z, and P. With capital constraints (as shown by solid vertical line) the firm would accept A and N only. That's why it is said that when capital rationing exists value of the firm is less than optimal (maximum). e) Example: Cumulative _Project_Net Inv.___NPV_______ PI___ Net Investment__ P $100,000 $25,000 1.25 $100,000 R 150,000 33,000 1.22 250,000 S 175,000 36,750 1.21 425,000 U 100,000 20,000 1.20 525,000 T 50,000 9,000 1.18 575,000 V 75,000 12,500 1.17 650,000 Q 200,000 30,000 1.15 850,000 W 50,000 -10,000 .80 900,000 Cumulative NPV______ $25,000 58,000 94,750 114,750 123,750 136,250 166,250 156.250 In the absence of capital rationing the firm should select all projects except project W. However, the firm has imposed a capital limit of $550,000. In this situation the capital falls short of $850,000 needed to implement all acceptable projects. What do we do? f) Objective: The object should be to select projects subject to the capital constraint, such that the sum of the projects' NPV is maximized. g) One of the recommended procedures for optimum solution Beginning with the highest PI, proceed down through the list and accept projects have PI's is equal to or greater than 1 until the entire budget has been utilized. On the initial observation, given the constraints, the firm should select P, R, S and U utilizing $525,000. Project T cannot be accepted, since this would require an additional outlay of $25,000. Management should give another look at the projects and consider other alternatives such as Alternative 1: It should attempt to find other combinations that would fully utilize the capital and give even higher NPV. For example, P, R, S, T, and V combination utilizes $550,000 and yields and NPV of $116,250. Alternative 2: Increase the cap budget by $25,000 and accept P, R, S, U and T resulting in an NPV of $123, 750. If management does not want to increase the budget, alternative 1 is best. h) Mukherjee & Hingorani discuss two major hypotheses explaining the prevalence of internal capital rationing among U.S. firms. Explain these two hypotheses. Which one of the two hypotheses they find to provide stronger explanation for capital rationing? How do they arrive at the conclusion? 3. ADJUSTING FOR INFLATION n CF t (1 RRR )t NPV= t 0 In general, the cost of capital (RRR) used as discount rate in capital budgeting analysis is based on the market-determined nominal costs of debt and equity. But, it is not uncommon for firms to estimate CF in constant (base year) dollars throughout the analysis. When the cost of capitaL includes an inflation premium, but the cash flows are all stated in constant dollars, then the calculated NPV will be downward biased. Two ways to adjust for inflation: Express cost of capital in real terms (unadjusted for inflation). Adjust cash flows to reflect expected inflation. EXAMPLE: II. REAL OPTIONS 1. Definition: Opportunities for managers to respond to changing circumstances and influene the outcome of a project. They are known as Real, as opposed to Financial option, because they involve real assets. 2. Types of real options: Abandonment a. Economic Life vs. Physical Life b. Why should Abandonment Option be considered? The abandonment option should be considered in the capital budgeting process because there are cases, where recognizing this option can change a project from unacceptable to acceptable. This type of analysis helps determine a project's economic life (as opposed to physical life), which is the life that maximizes the project's NPV and thus maximizes shareholder wealth. It should be also considered for on-going projects. c. The Decision Rule: As a general rule, any project should be abandoned if its abandonment value is greater than the present value of all cash flows beyond the abandonment year, discounted to the abandonment decision point. A. Growth A growth option allows a company to increase its capacity if market conditions are better than expected----increase capacity of an existing product line, to expand into new geographic markets or add new products. Ex: B. Investment Timing Ability to delay (wait) decision on a project. Ex: C. Flexibility Ability to alter operations depending on how conditions change during the life of the project. Ex. 3. Valuing Real Options: Alternative Methods: A. B. C. D. E. Apply DCF, ignoring option values DCF + QUALITATIVE recognition of real option Decision tree Standard model for a financial option Financial engineering techniques PRACTICE QUESTIONS/PROBLEMS QUESTIONS 1. In the EAA method, the lives of projects are made equal to ___________, while in the Replacement Chain method they are made equal to 2. _________________________________. In theory, capital rationing runs counter to a firm's value-maximizing principle because_____________________________________ ____________________________________________________. 3. Mukherjee and Hingorani article provides two informationasymmetry based explanation for the prevalence of capital rationing. What are they? Explain. _____________________________________________________ 3-1. Inflation introduces a bias in capital budgeting decisions because _____________________________________________________ 4. How do we reduce the inflation induced bias? _____________________________________________________ 5. Define optimal capital budget. How is it different from optimal capital structure? _____________________________________________________ 6. Define real option. How is it different from financial option? List the type of real option facing businesses with example of each. PROBLEMS I. UNEQUAL LIVES 1. P & Q are two mutually exclusive projects. P's life 4 years, and Q's life is 5 years. The project is needed for a long time. You have computed the NPVs of the two competing projects using 10% as the cost of capital. The NPVs are $200 and $227 respectively for P and Q, while their IRRs are 20% and 18% respectively. Which one would you choose? 2. A & B are two mutually exclusive projects. Whichever is selected will be needed for a long time. The cost of capital is 10%.Initial life of A and B are 4 and 5 respectively. Which one would you choose? 0 1 2 3 4 5 Project A -190 75 75 75 75 - Project B -225 75 75 75 75 75 NPV@(10%) IRR II. OPTIMAL CAPITAL BUDGET 3. (1) (2) (3) (4) (5) (6) (7) (8) The target capital structure is debt 30%, preferred stock 20%, and common equity 50%. Projected retained earnings ARE $6 million. Up to $9 million can be raised via bond at 10% YTM. If more than $9 million, is raised via debt, the YTM rises to 11%. Applicable tax rate is 40%. An unlimited amount can be raised through preferred at 9% yield to investors (floatation cost 5%). The common stock dividend has is expected to grow at 7% for a very long time. Common stock dividend is $2.00 in the most current period. Common stocks are selling for $50.00 a share. The floatation cost for new common stocks is 10%. The following four capital projects have been identified. They are all of average risk, independent, and non-divisible. Project A B C D ____Cost____ $10 million $10 million $ 7.5 million $10 million IRR 11.5% 12.6 11.0 12.8 A. Show the breaking points below: Breaking Points Because of the increase in this component cost B. Show your component cost computation and fill in the blanks below: Kb is (are Kps is: KRE is: Kncs is c. Show below your WACC computation for each interval (use the market value weight you computed above) by filling in the blanks in the table: COMPONENT WEIGHT MCC1 FR$______ TO $_____ MCC2 FR$______ TO $_____ MCC3 OVER$______ The optimal capital budget is $______________. Show your diagram with labels. COC & IRR (%) Capital ($) OPTIMAL CAPITAL BUDGET 4. OPTIMAL CAPITAL BUDGET a. The target capital structure is debt 30%, preferred stock 20%, and common equity 50%. b. Projected retained earnings are $6 million. c. Up to $9 million can be raised via bond at 10% YTM. If more than $9 million, is raised via debt, the YTM rises to 11%. Applicable tax rate is 40%. d. An unlimited amount can be raised via preferred at 12% yield to investors (floatation cost 5%). e. The common stock dividend has grown at 7% annual rate in the last 5 years. The same growth rate is expected to continue in the future. Current dividend is $.42. f. Common stocks are selling for $5 a share. The floatation cost for new common stocks is 10%. g. The following four capital projects have been identified. They are all of average risk, independent, and non-divisible. Project A B C D Cost_ IRR $5 million $10 million $ 7.5 million $10 million _ 13.0% 13.6 12.5 13.8 A. Show the breaking points below: Breaking Points Because of the increase in this component cost B. Show your component cost computation and fill in the blanks below: Kb is (are) Kps is: KRE is: (Implied g = ?) Kre = Kncs is C. Show below your WACC computation for each interval (use the market value weight you computed above) by filling in the blanks in the table: COMPONENT WEIGHT DEBT P/S C/E .3 .2 .5 D. MCC1 FR$_0 TO $12.0 MCC2 FR$12.0TO $30 MCC3 OVER $30 The optimal capital budget is $______________. Show your diagram with labels. COC & IRR (%) apital ($) 5. OPTIMAL CAPITAL BUDGET a. The target capital structure is debt 30%, preferred stock 20%, and common equity 50%. Projected retained earnings ARE $6 million. b. Up to $9 million can be raised via bond at 10% YTM. If more than $9 million, is raised via debt, the YTM rises to 11%. Applicable tax rate is 40%. c. An unlimited amount can be raised through preferred at 9% yield to investors (floatation cost 5%). d. The common stock dividend has is expected to grow at 7% for a very long time. Common stock dividend is $2.00 in the most current period. e. Common stocks are selling for $50.00 a share. The floatation cost for new common stocks is 10%. The following four capital projects have been identified. They are all of average risk, independent, and non-divisible. Project A B C D ____Cost____ I $20 million $20 million $5 million $ 7.5 million RR 10.0 9.5 11.0 10.5 A. Show the breaking points below: Breaking Points Because of the increase in this component cost B. Show your component cost computation and fill in the blanks below: Kb is (are Kps is: KRE is: Kncs is C. Show below your WACC computation for each interval (use the market value weight you computed above) by filling in the blanks in the table: COMPONENT WEIGHT MCC1 FR$______ TO $_____ MCC2 FR$______ TO $_____ MCC3 OVER$______ The optimal capital budget is $______________. Show your diagram with labels 6. OPTIMAL CAPITAL BUDGET Here are some data on the Schwab Company: The target capital structure is 40% debt and 60% equity; Projected retained earnings = $6 million; New bonds can be issued to yield 10%; Applicable marginal tax rate = 30%; Cost of retained earnings = 15.5%; Cost of New Common Stock = 16.5%; The following four capital projects have been identified. They are all independent, and non-divisible. Project Cost IRR A B C D $2.5 mill $5.0 mill $2.5 mill $2.5 mill 14.0% 13.6% 13.5% 12.4% of average 1. Computation for MCC Schedule COMPONENT WEIGHT DEBT EQUITY MCC .4 .6 MCC1 $ 0 to $10 MIL MCC2 Over $10 MILL Determining the optimal capital budget COC & IRR (%) Capital ($) risk, 7. GIVEN THE FOLLOWING INFO, FIND THE OPTIMAL CAPITAL BUDGET. a) The optimal capital structure is debt 30%, Preferred stock 10%, and common equity is 60%. b) A maximum of $9 million of debt can be issued at a cost of 6.3%. The firm's cost of debt (after-tax) goes up to 7.3%, If it wants to raise more than $9 million in debt. c) Cost of Pref Stock is 10% d) The cost of retained earnings is 16%, and the cost of new common stock is 18% e) The amount available in retained earnings is $12 million. f) The firm has the following investment opportunities this year: A B C D E Investment IRR best to worst CUMULATIVE ($ Million) 8 6 10 12 14 (%)___________________________ 16 B $8 8 20 A $6 14 15 C 10 24 14.5 D 12 36 14 E 14 50 g) The firm is in the 40% tax bracket. MCC Computation COMPONENT WEIGHT DEBT PS CS .3 .1 .6 MCC1 $0 TO -----MILL MCC2 FR -----MILL TO -------- MCC3 OVER----- MILL COC & IRR (%) Capital ($) The optimal capital budget is $50,000