# Capital Budgeting for Project NPV

Project NPV

1. Suppose a firm is considering the following project, where all of the dollar figures are in thousands of dollars. In year 0, the project requires $37,500 investment in plant and equipment, is depreciated using the straight-line method over seven years, and there is a salvage value of $5,600 in year 7. The project is forecast to generate sales of 5,700 units in year 1, rising to 24,100 units in year 5, declining to 8,200 units in year 7, and dropping to zero in year 8. The inflation rate is forecast to be 1.5% in year 1, rising to 2.8% in year 5, and then leveling off. The real cost of capital is forecast to be 9.3% in year 1, rising to 10.6% in year 7. The tax rate is forecast to be a constant 42.0%. Sales revenue per unit is forecast to be $15.30 in year 1 and then grow with inflation. Variable cost per unit is forecast to be $9.20 in year 1 and then grow with inflation. Cash fixed costs are forecast to be $7,940 in year 1 and then grow with inflation. What is the project NPV?

2. Consider the same project as problem 1, but modify it as follows. Suppose that Direct Labor, Materials, Selling Expenses, and Other Variable Costs are forecast to be $5.20, $3.70, $2.30, and $0.80, respectively, in year 1 and then grow with inflation. Lease Payment, Property Taxes, Administration, Advertising, and Other cash fixed costs are forecast to be $4,100, $730, $680, $1,120, and $730, respectively, in year 1 and then grow with inflation. What are the Total Variable Cost / Unit, the Total Cash Fixed Costs, and the project NPV?

Cost -Reducing Project

1. Suppose a firm is considering a labor-saving investment. In year 0, the project requires a $11,700 investment in equipment (all figures are in thousands of dollars). This investment is depreciated using the straight-line method over five years and there is salvage value in year 5 of $4,500. With or without the cost-reducing investment, all cash flows start in year 1 and end in year 5. The inflation rate is 2.6% in year 2 and declines to 1.4% in year 5. The real growth rate is 21.3% in year 2 and declines to 9.5% in year 5. The tax rate is 41.0% in all years. The real cost of capital is 8.7% in year 1 and declines to 7.5% in year 5. Without the cost-reducing investment, the firm's existing investments will generate year 1 revenue, labor costs, other cash expenses, and depreciation of $15,200, $4,100, $5,300, and $3,300, respectively. With the cost-reducing investment, the firm's year 1 labor costs will be $1,600 and revenues and other cash expenses will remain the same. What is the cost-reducing project NPV?

2. For the same cost-reducing project as problem 1, analyze the sensitivity of the Project NPV to the assumed With Investment Labor Costs.

Break-Even Analysis

1. A project has a fixed cost of $73,000, variable costs of $9.20 per unit, and generates sales revenue of $15.40 per unit. What is the break-even point in unit sales, where accounting profit exactly equals zero, and what is the intuition for it?

2. Suppose a firm is considering the following project, where all of the dollar figures are in thousands of dollars. In year 0, the project requires $24,490 investment in plant and equipment, is depreciated using the straight-line method over seven years, and there is a salvage value of $5,800 in year 7. The project is forecast to generate sales of 4,800 units in year 1 and grow at a sales growth rate of 72.0% in year 2. The sales growth rate is forecast to decline by 12.0% in years 3, to decline by 15.0% in year 4, to decline by 18.0% in year 5, to decline by 23.0% in year 6, to decline by 29.0% in year 7. Unit sales will drop to zero in year 8. The inflation rate is forecast to be 2.7% in year 1 and rising to 3.5% in year 7. The real cost of capital is forecast to be 10.2% in year 1, rising to 11.9% in year 7. The tax rate is forecast to be a constant 38.0%. Sales revenue per unit is forecast to be $12.20 in year 1 and then grow with inflation. Variable cost per unit is forecast to be $7.30 in year 1 and then grow with inflation. Cash fixed costs are forecast to be $6,740 in year 1 and then grow with inflation. What is the project NPV? What is the NPV Break-Even Point in Year 1 Unit Sales, where NPV equals zero? What is the NPV Break-Even Point in the Year 2 Sales Growth Rate, where NPV equals zero? What is the NPV Break-Even Contour in the two-dimensional space of Year 1 Unit Sales and Year 2 Sales Growth Rate?

Three Valuation Methods

1. A firm has the opportunity to do a one-shot project. It requires a date 0 initial outlay for new investment of $250,000. During the initial five-years, it will generate the following before-tax cash flows: date 1 = $380,000, date 2 = $430,000, date 3 = $520,000, date 4 = $460,000, date 5 = $280,000, and $120,000 each year thereafter. The project's tax rate is 36.0%, its unlevered cost of capital is 11.6%, and the riskfree rate (= cost of debt) is 3.7%. The company has precommitted to a particular quantity of debt on the following dates to support this project: date 0 = $130,000, date 1 = $220,000, date 2 = $270,000, date 3 = $240,000, date 4 = $150,000, and $70,000 each year thereafter. What is the project's NPV as calculated using the APV method? What is the present value of future cash flows to both debt and equity?

2. Given the same firm and same project as problem 1, calculate the project's NPV using the Flows To Equity method. Compare this result to the APV result. On each date, calculate the present value of future cash flows to both debt and equity. Verify that this result is the same as the APV case.

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#### Solution Summary

Capital budgeting for a projects NPV. Three valuation methods are determined.

Capital budgeting projects: NPV, IRR, PI, MIRR, payback

B6. (Investment criteria) Consider the cash flows for the two capital budgeting projects given

here. The cost of capital is 10%.

a. Calculate the NPV for both projects.

b. Calculate the IRR for both.

c. Calculate the PI for both.

d. Calculate the MIRR for both.

e. Calculate the payback for both.

f. Which is the better project? Why?

YEAR 0 1 2 3 4

Project A −25,000 10,000 10,000 10,000 10,000

Project B −12,500 5,000 5,000 5,000 5,000