KLM will finance a project at its target D/E of 0.25. Comparable businesses have equity beta 0.95 and D/E 0.8. Debt is risk-free at 3%, the market risk premium is 6% and the corporate tax rate is 30%. Assume the Hamada/MM tax-shield convention and equal operating risk.
Equity beta = 0.715545.
WACC = 6.25%. Use it for project operating free cash flows.
ABC will finance a project at its target D/E of 1. Comparable businesses have equity beta 1.15 and D/E 0.4. Debt is risk-free at 3%, the market risk premium is 6% and the corporate tax rate is 30%. Assume the Hamada/MM tax-shield convention and equal operating risk.
Equity beta = 1.527344.
WACC = 7.13%. Use it for project operating free cash flows.
BAC will finance a project at its target D/E of 0.6. Comparable businesses have equity beta 1.25 and D/E 0.8. Debt is risk-free at 3%, the market risk premium is 6% and the corporate tax rate is 30%. Assume the Hamada/MM tax-shield convention and equal operating risk.
Equity beta = 1.137821.
WACC = 6.93%. Use it for project operating free cash flows.
SPD will finance a project at its target D/E of 1.5. Comparable businesses have equity beta 0.85 and D/E 0.8. Debt is risk-free at 3%, the market risk premium is 6% and the corporate tax rate is 30%. Assume the Hamada/MM tax-shield convention and equal operating risk.
Equity beta = 1.116987.
WACC = 5.14%. Use it for project operating free cash flows.
SVE will finance a project at its target D/E of 2.2. Comparable businesses have equity beta 1.5 and D/E 1. Debt is risk-free at 3%, the market risk premium is 6% and the corporate tax rate is 30%. Assume the Hamada/MM tax-shield convention and equal operating risk.
Equity beta = 2.241176.
WACC = 6.58%. Use it for project operating free cash flows.
Grill & Steak is evaluating a 4-year project. Equipment costs 120,000.00, annual straight-line depreciation is 30,000.00, and expected terminal sale proceeds are 12,000.00. The corporate tax rate is 30.00%. Operating working capital equals 20.00% of sales, is invested at each year-end and fully recovered in the last year. Tax losses can offset other taxable profits immediately. Additional costs include 25,000 marketing in each of years 1–2 and 20,000 annual foregone rent. The firm is all-equity financed, asset beta is 0.8, the risk-free rate is 2% and the market premium is 3%, giving r = 4.4%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Revenue | 100,000.00 | 110,000.00 | 120,000.00 | 130,000.00 |
| Cash operating costs | 40,000.00 | 44,000.00 | 48,000.00 | 52,000.00 |
| Additional incremental costs | 45,000.00 | 45,000.00 | 20,000.00 | 20,000.00 |
The appropriate discount rate is 4.40%. Additional costs include 25,000 marketing in each of years 1–2 and 20,000 annual foregone rent. The firm is all-equity financed, asset beta is 0.8, the risk-free rate is 2% and the market premium is 3%, giving r = 4.4%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| EBIT | -15,000.00 | -9,000.00 | 22,000.00 | 28,000.00 |
| Tax | 4,500.00 | 2,700.00 | -6,600.00 | -8,400.00 |
| Operating cash flow | 19,500.00 | 23,700.00 | 45,400.00 | 49,600.00 |
| Change in NWC | 20,000.00 | 2,000.00 | 2,000.00 | -24,000.00 |
| Year | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Free cash flow | -120,000.00 | -500.00 | 21,700.00 | 43,400.00 | 82,000.00 |
| Discount factor | 1.0000 | 0.9579 | 0.9175 | 0.8788 | 0.8418 |
| Present value | -120,000.00 | -478.93 | 19,909.43 | 38,140.66 | 69,025.86 |
NPV = 6,597.03. Accept.
Saggio is evaluating a 4-year project. Equipment costs 4,500.00, annual straight-line depreciation is 900.00, and expected terminal sale proceeds are 500.00. The corporate tax rate is 30.00%. Operating working capital equals 10.00% of sales, is invested at each year-end and fully recovered in the last year. Tax losses can offset other taxable profits immediately. Foregone rent is 250 per year; only 100 of the 200 annual cannibalisation loss is caused by the project. The other 100 occurs anyway. With equity weight 60%, debt weight 40%, equity beta 1.10, risk-free debt 3% and market premium 5%, cost of equity is 8.5% and WACC = 0.60 × 8.5% + 0.40 × 3% × 0.70 = 5.94%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Revenue | 3,000.00 | 3,300.00 | 3,600.00 | 3,900.00 |
| Cash operating costs | 1,500.00 | 1,650.00 | 1,800.00 | 1,950.00 |
| Additional incremental costs | 350.00 | 350.00 | 350.00 | 350.00 |
The appropriate discount rate is 5.94%. Foregone rent is 250 per year; only 100 of the 200 annual cannibalisation loss is caused by the project. The other 100 occurs anyway. With equity weight 60%, debt weight 40%, equity beta 1.10, risk-free debt 3% and market premium 5%, cost of equity is 8.5% and WACC = 0.60 × 8.5% + 0.40 × 3% × 0.70 = 5.94%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| EBIT | 250.00 | 400.00 | 550.00 | 700.00 |
| Tax | -75.00 | -120.00 | -165.00 | -210.00 |
| Operating cash flow | 1,075.00 | 1,180.00 | 1,285.00 | 1,390.00 |
| Change in NWC | 300.00 | 30.00 | 30.00 | -360.00 |
| Year | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Free cash flow | -4,500.00 | 775.00 | 1,150.00 | 1,255.00 | 2,370.00 |
| Discount factor | 1.0000 | 0.9439 | 0.8910 | 0.8410 | 0.7939 |
| Present value | -4,500.00 | 731.55 | 1,024.66 | 1,055.51 | 1,881.52 |
NPV = 193.23. Accept.
Bradley, Betts & Holt is evaluating a 5-year project. Equipment costs 21,000.00, annual straight-line depreciation is 4,200.00, and expected terminal sale proceeds are 4,200.00. The corporate tax rate is 35.00%. Operating working capital equals 10.00% of sales, is invested at each year-end and fully recovered in the last year. Tax losses can offset other taxable profits immediately. Sales volumes are 85, 98, 106, 114 and 93 thousand units; monetary totals are in thousands, consistently with equipment cost 21,000 and annual fixed costs 900. Price per unit is 325 and variable cost 240. Comparable equity beta 1.2 at D/E 0.8 is unlevered as 1.2/[1+0.65×0.8], then relevered at target D/E 1. Risk-free and debt rates are 3%, market premium 4.5%. This gives equity beta 1.302632, equity cost 8.8618% and WACC 5.4059%.
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Revenue | 27,625.00 | 31,850.00 | 34,450.00 | 37,050.00 | 30,225.00 |
| Cash operating costs | 20,400.00 | 23,520.00 | 25,440.00 | 27,360.00 | 22,320.00 |
| Additional incremental costs | 900.00 | 900.00 | 900.00 | 900.00 | 900.00 |
The appropriate discount rate is 5.41%. Sales volumes are 85, 98, 106, 114 and 93 thousand units; monetary totals are in thousands, consistently with equipment cost 21,000 and annual fixed costs 900. Price per unit is 325 and variable cost 240. Comparable equity beta 1.2 at D/E 0.8 is unlevered as 1.2/[1+0.65×0.8], then relevered at target D/E 1. Risk-free and debt rates are 3%, market premium 4.5%. This gives equity beta 1.302632, equity cost 8.8618% and WACC 5.4059%.
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| EBIT | 2,125.00 | 3,230.00 | 3,910.00 | 4,590.00 | 2,805.00 |
| Tax | -743.75 | -1,130.50 | -1,368.50 | -1,606.50 | -981.75 |
| Operating cash flow | 5,581.25 | 6,299.50 | 6,741.50 | 7,183.50 | 6,023.25 |
| Change in NWC | 2,762.50 | 422.50 | 260.00 | 260.00 | -3,705.00 |
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Free cash flow | -21,000.00 | 2,818.75 | 5,877.00 | 6,481.50 | 6,923.50 | 12,458.25 |
| Discount factor | 1.0000 | 0.9487 | 0.9001 | 0.8539 | 0.8101 | 0.7686 |
| Present value | -21,000.00 | 2,674.19 | 5,289.63 | 5,534.53 | 5,608.74 | 9,574.85 |
NPV = 7,681.94. Accept.
BiancoLatte is evaluating a 4-year project. Equipment costs 100,000.00, annual straight-line depreciation is 20,000.00, and expected terminal sale proceeds are 15,000.00. The corporate tax rate is 30.00%. Operating working capital equals 17.00% of sales, is invested at each year-end and fully recovered in the last year. Tax losses can offset other taxable profits immediately. Cannibalisation costs 15,000 per year. Receivables are 15% of sales, inventory 8%, payables 10% of cash operating costs, so NWC = (15%+8%−10%×60%) of sales = 17%. Comparable equity beta 1.1 at D/E 1 is unlevered by dividing by 1.70, then relevered at target D/E = 0.20/0.80 = 0.25. Risk-free and debt rates are 3%, market premium 6%. WACC = 6.469412%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Revenue | 80,000.00 | 96,000.00 | 115,200.00 | 138,240.00 |
| Cash operating costs | 48,000.00 | 57,600.00 | 69,120.00 | 82,944.00 |
| Additional incremental costs | 15,000.00 | 15,000.00 | 15,000.00 | 15,000.00 |
The appropriate discount rate is 6.47%. Cannibalisation costs 15,000 per year. Receivables are 15% of sales, inventory 8%, payables 10% of cash operating costs, so NWC = (15%+8%−10%×60%) of sales = 17%. Comparable equity beta 1.1 at D/E 1 is unlevered by dividing by 1.70, then relevered at target D/E = 0.20/0.80 = 0.25. Risk-free and debt rates are 3%, market premium 6%. WACC = 6.469412%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| EBIT | -3,000.00 | 3,400.00 | 11,080.00 | 20,296.00 |
| Tax | 900.00 | -1,020.00 | -3,324.00 | -6,088.80 |
| Operating cash flow | 17,900.00 | 22,380.00 | 27,756.00 | 34,207.20 |
| Change in NWC | 13,600.00 | 2,720.00 | 3,264.00 | -19,584.00 |
| Year | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Free cash flow | -100,000.00 | 4,300.00 | 19,660.00 | 24,492.00 | 70,291.20 |
| Discount factor | 1.0000 | 0.9392 | 0.8822 | 0.8286 | 0.7782 |
| Present value | -100,000.00 | 4,038.72 | 17,343.38 | 20,293.16 | 54,701.79 |
NPV = -3,622.95. Reject.
McKinnon is evaluating a 4-year project. Equipment costs 200,000.00, annual straight-line depreciation is 50,000.00, and expected terminal sale proceeds are 0.00. The corporate tax rate is 30.00%. Operating working capital equals 10.00% of sales, is invested at each year-end and fully recovered in the last year. Tax losses can offset other taxable profits immediately. Treat all stated amounts in one common currency; no exchange-rate information is supplied. The initial cost buys a four-year mining concession. Existing underused machinery has no stated incremental cost or alternative use. Debt weight is 80%, target D/E 4; comparable beta 1.5 at D/E 3 gives asset beta 0.483871. Risk-free and debt rates are 2%, market premium 5%, and relevered beta 1.838710 gives WACC 3.358710%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Revenue | 100,000.00 | 70,000.00 | 65,000.00 | 50,000.00 |
| Cash operating costs | 30,000.00 | 21,000.00 | 19,500.00 | 15,000.00 |
| Additional incremental costs | 0.00 | 0.00 | 0.00 | 0.00 |
The appropriate discount rate is 3.36%. Treat all stated amounts in one common currency; no exchange-rate information is supplied. The initial cost buys a four-year mining concession. Existing underused machinery has no stated incremental cost or alternative use. Debt weight is 80%, target D/E 4; comparable beta 1.5 at D/E 3 gives asset beta 0.483871. Risk-free and debt rates are 2%, market premium 5%, and relevered beta 1.838710 gives WACC 3.358710%.
| Year | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| EBIT | 20,000.00 | -1,000.00 | -4,500.00 | -15,000.00 |
| Tax | -6,000.00 | 300.00 | 1,350.00 | 4,500.00 |
| Operating cash flow | 64,000.00 | 49,300.00 | 46,850.00 | 39,500.00 |
| Change in NWC | 10,000.00 | -3,000.00 | -500.00 | -6,500.00 |
| Year | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Free cash flow | -200,000.00 | 54,000.00 | 52,300.00 | 47,350.00 | 46,000.00 |
| Discount factor | 1.0000 | 0.9675 | 0.9361 | 0.9056 | 0.8762 |
| Present value | -200,000.00 | 52,245.23 | 48,956.18 | 42,882.37 | 40,305.98 |
NPV = -15,610.24. Reject.