Question

Your firm is considering leasing a new computer. The lease lasts for 9 years. The lease calls for 10 payments of $1,000 per year with the first payment occurring immediately. The computer would cost $7,650 to buy and would be straight-line depreciated to a zero salvage value over 9 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 8%. The corporate tax rate is 30%.

What would the after-tax cash flow in year 9 be if the asset had a residual value of $500 (ignoring any possible risk differences)?

-$605

-$955

-$1,455

-$1,305

None of these

Answer 1

Annual installments under buy & borrow option:

Annual installments = Cost / ((1 - (1/(1+r)^n)) /r)

r = 8% or 0.08, n = 9 years

Annual installments = $7650 / ((1 - (1/(1+0.08)^9)) / 0.08

Annual installments = $7650 / ((1 - 0.5003)/0.08)

Annual installments = $7650 / 6.2463 = $1225

Now, interest calculation:

Years	Opening(Opening - Principal	Interest @ 8% (Opening * 8%)	Principal (Installment @ $1225 - Interest)
1	$7650	$612	$613
2	$7037 (ie. 7650 - 613)	$563	$662
3	$6375 (ie. 7037 - 662)	$510	$715
4	$5660	$453	$772
5	$4888	$391	$834
6	$4054	$324	$900
7	$3153	$252	$973
8	$2180	$174	$1051
9	$1129	$96	Nil

Calculation of 9th year after tax cash flow :

After tax cash flow(9th year) = Annual Installment - (Tax shield on depriciation & interest of 9th year) - Residual value (after tax)

Here,

i) Depriciation (straight line)= Cost/years = $7650/9

Depriciation = $850

ii) Interest (9th year) = $96

iii) Tax shield on depriciation & interest = ($850 + $96) * 30% = $284

iv) Residual value (after tax) = $500 * (1 - 0.30)

Residual value (after tax) = $500 * 0.70 = $350

Now,

After tax cash flow (9th year) = $1225 - $284 - $350 = $591

Ans : Net cash flow - $605

Note: Here difference is due to decimal rounding off.