Question

Please explain how to find the answers indicated below

A company is considering the acquisition of production equipment which will reduce both labour and material costs. The cost is $100,000 and it will be depreciated on a straight-line basis to zero over a four-year period. However, the useful life of the equipment is five years, and it will be sold for $20,000 at the end of the five years. Operating costs will be reduced by $30,000 in the first year and the savings will increase by $5,000 per year for years 2, 3 and 4. Due to increased maintenance costs, savings in year 5 will be $10,000 less than the year 4 savings. The equipment will also reduce net working capital by $5,000. Net working capital will revert back to normal at the end of the project’s life. The firm’s tax rate is 35% and the firm requires a 16% return.

1. Calculate the initial investment (CF₀) for this project. (-$95,000)
2. Calculate the cash flows in years 1 through 4. (CF₁=$28,250, CF₂= $31,500, CF₃= $34,750, CF₄= 38,000).
3. Calculate the terminal cash flow and the total cash flow in year 5. (TCF= $8,000, CF₅= $30,750)

Answer 1

Calculate the initial investment (CF₀) for this project. (-$95,000)

The initial investment at time t = 0 will have two components:

• The cost of equipment = - $ 100,000
• Reduction in net working capital = $ 5000
• Hence net initial investment CF₀ for this project = - $ 100,000 + $ 5,000 = - $ 95,000

Calculate the cash flows in years 1 through 4. (CF₁=$28,250, CF₂= $31,500, CF₃= $34,750, CF₄= 38,000).

Operating costs will be reduced by $30,000 in the first year and the savings will increase by $5,000 per year for years 2, 3 and 4.

Annual depreciation = Cost of equipment / 4 years = 100,000 / 4 = 25,000

Tax rate, T = 35%

Depreciation tax shield per year = Annual depreciation x T = 25,000 x 35% = 8,750.

Please see the table below. Please see the column titled "Linkage" to understand how each row has been calculated.

Year	Linkage	1	2	3	4
Cost reduction & savings (pre tax)	A	30,000	35,000	40,000	45,000
Post tax cost reduction and savings (= pre tax figures x (1-Tax rate)	B = A x (1 - tax rate)	19,500	22,750	26,000	29,250
Depreciation	D	25,000	25,000	25,000	25,000
Depreciation tax shield	C= D x Tax rate	8,750	8,750	8,750	8,750
Incremental annual cash flows	B + D	28,250	31,500	34,750	38,000

Calculate the terminal cash flow and the total cash flow in year 5. (TCF= $8,000, CF₅= $30,750)

The terminal cash flow will have two components:

• Post tax salvage value
  • Pre tax salvage value = $ 20,000
  • Tax basis at the of year 5 = 0 as the asset is fully depreciated by then
  • Gain on sale of the equipment = Salvage value - tax basis = 20,000 - 0 = 20,000
  • Tax on gain on sale = Tax rate x Gain on sale = 35%x 20,000 = 7,000
  • Post tax salvage value = Pre tax salvage value - tax on gain on sale = 20,000 - 7,000 = 13,000
• Working capital comes back to the normal level. So the reduction in working capital will go away. Working capital will increase by $ 5000

Hence terminal cash flow = TCF = Post tax salvage value - Increase in working capital = 13,000 - 5,000 = $ 8,000

Total Cash flow for year 5

• Due to increased maintenance costs, savings in year 5 will be $10,000 less than the year 4 savings. Pre tax savings = Savings in year 4 - 10,000 = $ 45,000 (please see the table above) = 10,000 = $ 35,000
• Post tax savings = 35,000 x (1 - Tax rate) = 35,000 x (1 - 35%) = $ 22,750
• Add to this, the terminal cash flow calculated above of $ 8,000
• Hence total cash flow for year 5 = $ 22,750 + 8,000 = $ 30,750