Question

Please Post Equations for study and learning please.

1. Rand is considering a new project that requires an investment of $60 million in machinery. This is expected to produce sales of $94 million per year for 4 years and operating expenses of $71 million per year for 4 years. The machinery will be fully depreciated to a zero book value over 4 years using straight-line depreciation. They can sell it for $5 million at the end of 4 years. Working capital costs are negligible. The tax rate is 30%. The unlevered cost of capital is 12%.

1. Calculate the base-case NPV.
2. BONUS (5): The project will be financed with $20,000,000 in bonds. The bonds have a 4-year life, a coupon rate of 6% and a yield of 6%. Find the adjusted present value (APV).

Answer 1

a)

Depreciation = 60,000,000 / 4 = 15,000,000

After tax salvage value = 5,000,000*(1-tax)

= 5,000,000*(1-30%)

= 3,500,000

Net cash flows for years 1 to 3 = (sales - Operating expenses - Depreciation)*(1-tax) + depreciation

= (94,000,000 - 71,000,000 - 15,000,000)*(1-30%) + 15,000,000

= 20,600,000

For year 4 net cash flow = 20,600,000 + after tax salvage value

= 20,600,000+ 3,500,000

= $24,100,000

NPV = present value of future cash flows - initial cash outflow

= (20,600,000 / 1.12) + (20,600,000 / 1.12^2) + (20,600,000 / 1.12^3) + (24,100,000 / 1.12^4) - 60,000,000

= $4,793,709.81

b)

when it is financed with 20,000,000 bonds

WACC = (20,000,000 / 60,000,000)*6% + (40,000,000 / 60,000,000)*12% = 10%

we have to find NPV using above discount rate

NPV = (20,600,000 / 1.10) + (20,600,000 / 1.10^2) + (20,600,000 / 1.10^3) + (24,100,000 / 1.10^4) - 60,000,000

= 7,689,775.29

interest = 20,000,000 * 6% = 1,200,000

Tax shield on interest = 1,200,000 * 30% = 360,000

Present value of taxshield on interest = (360,000 / 1.10) + (360,000 / 1.10^2) + (360,000 /1.10^3)+(360,000/1.10^4)

= 1,141,151.56

APV = NPV + Present value of interest tax shield

= 7,689,775.29 + 1,141,151.56

= $8,830,926.85