Question

A firm is considering purchasing equipment costing $32,000. It has a useful life of 5 years, and anticipated after-tax maintenance costs for years 1-5 as given below. The firm expects to use straight line depreciation and expects to be able to deduct the full amount of depreciation each year. The firm's WACC is 8%, its marginal tax rate is 20%. 3 4 5 Round all numbers in the solution space to the nearest dollar t=0 1 2 Investment 32,000 After-tax maintenance costs 7,500 7,800 Tax Benefit of Depreciation Net costs of ownership 8,000 9,500 10,000 Extra rows can be used for PV calculations a) Calculate the annuity factor for the given values of n and r ( WACC): (round to 3 decimals) Show the formula to be used with all variable values b) Calculate the (total) Present Value of the Net Cost of Ownership: c) Calculate the Effective Annual Cost of this asset: (round to nearest dollar) Show all work

Please show any and all work or sub-calculations.

Answer 1

(a)

Annuity factor for each year = 1 / (1 + r)ⁿ,

where r = WACC, and n = number of years.

(b)

Net cost of ownership in each year = maintenance cost - tax benefit of depreciation.

Tax benefit of depreciation = annual depreciation * tax rate.

Annual depreciation = Investment / depreciable life = $32,000 / 5 = $6,400.

Present value of net cost of ownership = net cost of ownership each year * annuity factor.

Total present value of net cost of ownership = $60,660.

A B C D Ε F G | 21 H 5 Total 1 4 32,000 2 Investment 3 Maintenance Cost 4 Tax benefit of depreciation 5 Net cost of ownership 7,500 1,280 6,220 7,800 1,280 6,5206 8,000 1,280 ,720 9,500 1,280 8,220 10,000 1,280 8,720 32,000 6 7 Annuity factor 8 PV of net cost of ownership 1.000 32,000 0.926 5,759 0.857 5,590 0.794 5,335 0.735 6,042 0.681 5,935 60,660

А D Total 2 Investment 32000 3 Maintenance Cost 7500 4 Tax benefit of depreciation =($B$2/5)*20% 5 Net cost of ownership =B2 =C3-C4 6 7 Annuity factor =1/(1+8%)^B1 =1/(1+8%)^C1 8 PV of net cost of ownership =B5*B7 =C5*C7 7800 = ($B$2/5)*20% =D3-D4 8000 =($B$2/5)*20% =E3-E4 9500 =($B$2/5)* 20% =F3-F4 10000 =($B$2/5)*20% =G3-64 =1/(1+8%)^D1 =1/(1+8%)^E1 =D5*D7 =E5*E7 =1/(1+8%)^F1 =F5*F7 =1/(1+8%)^G1 =G5*G7 =SUM(B8:58)

(c)

Effective annual cost = (total present value * r) / (1 - (1 + r)^-n)

Effective annual cost = ($60,660 * 0.08) / (1 - (1 + 0.08)^-5)

Effective annual cost = $15,193