Question

question 20 Albernie LTD purchase a CCA class 8 (CCA rate of 20%) item of equipment for $90000 the equipment was the only item in the class 8 capital cost allowance pool the equipment is expected to generate savings in the amount of $40000 per year the company uses straight line depreciation estimates a 3 year useful life with $20000 salvage value for the new equipment the tax rate is 35% and albernie has a required rate of return of 9% 1-what is the net present value of the albernie ltd investment in equipment ? 1-$1480 2-$9382 3-$(1075) 4-$89799 5-$8357 2-what is present value of the after tax savings that albernie ltd expects during the useful life of the equipment ? 1-$101252 2-$42188 3-$50370 4-$65814 5-$81257

Answer 1

To calculate the present value of the investment, we use the present value of an annuity formula and the tax shield formula:

1.The NPV of Albernie Ltd's investment is:

NPV of investment = PV of the cash flow + PV of tax shield - Initial Cost of investment + Salvage Value

2.The cash inflow, in this case, an annuity, is the after-tax savings, which can be calculated using formula:

= Annual savings x (1-Tax rate) x PV of annuity

= $40000 x (1-0.35) x (2.531294666)

= $65,813.66132

= $65,814(approx)

Therefore we choose option 4.

In the above calculation, PV of annuity is calculated using formula:

PV of annuity = P[1-(1+r)-n]/r

For P = $1, r = 9%, n= 3

PV of annuity = $1x [1-(1+0.09)-3]/0.09 = 2.531294666

3. Next we need to calculate the tax shield using formula :

PV tax shield on CCA = [CdT / (d+r)] x [(1+0.5r ) /(1+r)] - [SdT / (d+r)] x [1/ (1+r)n]   

where C= Cost of investment

d= CCA tax rate

T= Corporate tax rate

r= discount rate

n= No.of periods in the project

S= Salvage value

PV tax shield on CCA = [($90000)(20%)(35%) / (20%+9%)] x [1+0.5(9%) / (1+9%)] - [($20000)(20%) (35%) /(20% + 9%)] x [1/(1+9%)3]

= $21724.1379 x 0.958715596 - $4827.58621x [1/(1.09)3]

= $20827.2698 - $3727.78232

= $17099.4875

4. The salvage value can be calculated as the present value of income using formula:

=Salvage value x PV of $1

= $20000 x 0.77218348

= $15443.6696

In th above calculation, PV of $1 using formula:

PV = FV/ (1+r)n

For FV = $1, r = 9%, n= 3

PV = $1/(1+0.09)3 = 0.77218348

5. Therefore, the NPV of the investment is:

NPV of investment = $65813.66132 + $17099.4875 - $90000 + $15443.6696

= $8356.81842

= $8375(approx)

Therefore we choose option 5.