3 A process costing 24000 results in a reduction in costs of

(3) A process costing $24000 results in a reduction in costs of $8000 every year for years. The process is depreciated straight line to a book value of $8000 and is sold for $1500. If the tax rate is 20%, and the cost of capital is 25% find the NPV and the IRR of this cost cutting process s 500-01500-8000 1500+1300 2300

Solution

Annual Depreciation = (purchase price - salvage value)/no. of years = ($24,000 - $8,000)/8 = $16,000/8 = $2,000

Cashflow Year 0 = -$24,000

Cashflow Year 1 to 8:

= (Reduction in Costs - Depreciation)(1 - t) + Depreciation

= ($24,000 - $2,000)(1 - 0.20) + $2,000

= $17,600 + $2,000 = $19,600

After Tax Salvage Value Year 8 = MV + (BV – MV)TC

= $1,500 + ($8,000 - $1,500)0.20 = $1,500 + $1,300 = $2,800

NPV = present value of cash inflows - present value of cash outflows

=$15,680 + $12,544 + $10,035.20 + $8,028.16 + $6,422.53 + $5,138.02 + $4,110.42 + $3,288.33 + $469.76 - $24,000

= $41,716.42

IRR is the rate at which NPV is 0.

Hence,

0 = $19,600/(1 + r)¹ + $19,600/(1 + r)² + $19,600/(1 + r)³ + $19,600/(1 + r)⁴ + $19,600/(1 + r)⁵ + $19,600/(1 + r)⁶

+ $19,600/(1 + r)⁷ + $19,600/(1 + r)⁸ + $2,800/(1 + r)⁸ - $24,000

To solve this equation, we need to input the following values in the financial calculator;

CF0 = -24,000; C01 = 19,600; F01 = 7; C02 = 22,400; F02 = 1;

Press IRR, then CPT, which gives 81.04%