After-Tax Net Present Value and IRR (Non-MACRS Rules) eEgg is considering the pu
ID: 2460470 • Letter: A
Question
After-Tax Net Present Value and IRR (Non-MACRS Rules) eEgg is considering the purchase of a new distributed network computer system to help handle its warehouse inventories. The system costs $60,000 to purchase and install and $30,000 to operate each year. The system is estimated to be useful for four years. Management expects the new system to reduce by $62,000 a year the cost of managing inventories. The firm’s cost of capital is 10%.
Required
1. What is the net present value (NPV) of the proposed investment under each of the following independent situations?
a. The firm is not yet profitable and pays no taxes.
b. The firm is in the 30% income tax bracket and uses straight-line depreciation with no salvage value. Assume MACRS rules do not apply.
c. The firm is in the 30% income tax bracket and uses double-declining-balance depreciation with no salvage value. Assume MACRS rules do not apply.
2. What is the internal rate of return (IRR) of the proposed investment for situations 1(a) and 1(b) above?
***Please explain the math used to calculate the answers.***
Explanation / Answer
1) a) Year Cash outflow Cash Inflow Net Cash flow 0 -60000 -60000 1 -30000 62000 32000 2 -30000 62000 32000 3 -30000 62000 32000 4 -30000 62000 32000 39% NPV = CF * ( 1 - ( 1+ i)-n)/I - Initial investment CF = 32000 i = 10% =0.10 n = 4 NPV = 32000 * ( 1- (1+0.10)-4) / 0.10 - 60000 = 32000 * ( 1 - 0.6830)/0.10 -60000 = 32000 * 0.3170/0.10 - 60000 = 32000 * 3.17 - 60000 = 101440 - 60000 = 41440 b) Year Cash outflow Cash Inflow Net Cash flow Depriciation Operating Tax @ 30% Net cash flow profit A B C = A-B D =(60000/4) E = C-D F = E * 30% G = C - F 0 -60000 -60000 -60000 1 -30000 62000 32000 15000 17000 5100 26900 2 -30000 62000 32000 15000 17000 5100 26900 3 -30000 62000 32000 15000 17000 5100 26900 4 -30000 62000 32000 15000 17000 5100 26900 28% NPV = CF * ( 1 - ( 1+ i)-n)/I - Initial investment CF = 26900 i = 10% =0.10 n = 4 NPV = 26900 * ( 1- (1+0.10)-4) / 0.10 - 60000 = 26900 * ( 1 - 0.6830)/0.10 -60000 = 26900 * 0.3170/0.10 - 60000 = 26900 * 3.17 - 60000 = 85273 - 60000 = 25273 c) Year Cash outflow Cash Inflow Net Cash flow Depriciation Operating Tax @ 30% Net cash flow profit A B C = A-B D =(60000/4) E = C-D F = E * 30% G = C - F 0 -60000 -60000 1 -30000 62000 32000 0 32000 9600 22400 2 -30000 62000 32000 0 32000 9600 22400 3 -30000 62000 32000 0 32000 9600 22400 4 -30000 62000 32000 0 32000 9600 22400 NPV = CF1/( 1+i)1+CF2/(1+I)2 + CF3/(1 + i)3+CF4/(1+i)4 - Initial investment i = 10% =0.10 n = 4 NPV = 31400 /(1.10)1 + 26900/(1.1)2+26450/(1.1)3+26450/(1.1)4 - 60000 = 31400/1.1+ 26900 /1.21 + 26450/1.331 + 26450/1.4641 -60000 = 28545.45+22231.4+19872.28+18065.71 - 60000 = 88714.84 - 60000 = 28714.84 2) 1a) Year Net cash flow 0 -60000 1 32000 2 32000 3 32000 4 32000 IRR = 39% 1b) Year Net cash flow 0 -60000 1 26900 2 26900 3 26900 4 26900 IRR = 28%