Question

Your company has to obtain some new production equipment to be used for the next ten years, and leasing is being considered. You have been directed to perform an after-tax study of the leasing approach. The data information for the study is as follows: Lease cost: First year, S70,000; second year, S60,000; third through ten years, S50,000 per year. Assume that a 10-year contract has been offered by the lessor that fixes these costs over the 10- year period. Other costs (outside the contract) are $3,000 per year. The effective income tax rate is 30%. 1 Develop the Annual After-tax Cash Flow (ATCF's) for the leasing alternative. 2- If the Minimum Attractive Rate of Return (MARR) after taxes is 10%, what is the equivalant annual cost for the leasing alternative?

Answer 1

1) ATCF for the leasing alternative is following:

Lease period, t- 10 years 30% 10% tax-I MARR = | 10 -53,000 15,900 51,100-44,100 37,100-37,100l -37,100-37,10037,100-37,100-37,100 37,100 5 Year 6 Lease and other costs 7 Income tax 8 After-Tax Cash Flow 2 73,000-63,000 18,900 4 53,000 15,900 53,000 15,900 53,000 -53,000 15,900 53,000 15,900 53,000 15,900 53,000 21,900 15,900 15,900

EXCEL FORMULAS:

Lease period, t10 taxz 0.3 MARR 0.1 years 4 5 Year 6 Lease and other costs 7 Income tax 8 After-Tax Cash Flow 2 4 10 73000 63000 53000 53000 53000 53000 53000 53000 53000 53000 E6-E7 -F6-F7 -G6-G7 H6-H7 16-17 6-17 K6-K7

2)

Present Value is computed as below:

Lease period, t- 10 30% 10% years tax- MARR = | 10 5 Year 6 Lease and other costs 7 Income tax 8 After-Tax Cash Flow 2 4 000-53,000-5 53,000-53,000-53, 000-53,000-5 53,000-53,000 73,000-63,00053, 21,900-18, 51,100-44,100-37,1 900-15,90015, 90015,9001 15,90015,9001 -37,1 15,90015,90015, 100 37,100-37,100-37,100 100 37,100-37,100-37,100 10 11 (P/F,10%,t) 12 PWIt)"(P/F,10%,t) 13 14 Pw.ΣΡΝ(t)"(P/F,10%,t) 15 0.9091 0.82640.7513 0.6830 0.6209 0.5645 0.51320.4665 0.4241 0.3855 14,304 -46,455 6,446 -27,874-25,340 -23,03620,94219,038 -17,30715,7341 |-246,476

FORMULAS:

B. Lease period, t10 tax-0.3 MARR- 0.1 years 10 5 Year 6 Lease and other costs 7 Income tax 8 After-Tax Cash Flow 73000 63000 -C6"$852 -C6-C7 53000 53000 53000 53000 53000 -16 $B$2 -16-17 53000 53000 -G6-G7 -B6-B7 -D6-D7 -E6-E7 -F6-F7 -H6-H7 6-17 -K6-K7 10 11 (P/F,10%,t) 12 Pw(t)"(P/F,10%,t) 13 14 I Pw 2Pw(t) *(P/F,1096,t) EsUM(B12:K12) 15 1+$B$3 -B8 B11 -C8* C11 -G8 G11 -H8 H11 -D8 D11 E8 E11 -F8 F11 J8*111

For 10% MARR, Capital recovery factor = .1*1.1^10/(1.1^10-1) = 0.1627

Annual Worth = PV*Capital recovery factor

= -246476*0.1627

= $ -40,113