I used PW = - PW( initial cost)*Capital tac factor + PW(Savings from rent)*(1- t

Question

I used PW = - PW( initial cost)*Capital tac factor + PW(Savings from rent)*(1- tax%)+ PW(Tax savings) + PW(Salvage value)*Capital salvage factor

Are these the right formulas to use ? if not please provide it

The Shell Corporation has a 34% tax rate and owns a piece of petroleum-drilling equipment that costs $138,600 and will be depreciated at a CCA rate of 30%. Shell will lease the equipment to others and each year receive $34,600 in rent. At the end of five years, the firm will sell the equipment for $34,000. All values are presented in todays dollars. Calculate the overall present worth of these cash flows with tax effects if market interest rate is 10% and annual inflation rate is 2%.

Explanation / Answer

Soln : Please refer the table, here considering the given data, revenue has been taken by using the inflation of 2% each year, salvage value = 34000*1.02^5, as inflation adjusted. depreciation is CCA based i.e. 30% of remaining value each year and each year cost is reduced by the value of depreciation.

In the last column you will see year =5 as it is calculated for salvage value, which will show the value at the end of 5th year and capital gain = 34000*1.02^5 - 23294.50 = 14244.25, there after tax is calculated normally.

We can see here the Tax = 0 in 1st 2 years as we will carry forward the losses in first 2 years until it is positive, and in 3rd year the tax will be applied on amount = 15623.64+6186-6980 = 14829.64.

Kindly refer this solution and let me know in case you find it difficult to understand.

Year,t 0 1 2 3 4 5 5 Cost 138600 97020 67914 47539.8 33277.86 23294.5 Revenue,r 34600 35292 35997.84 36717.8 37452.15 Salvage Value,s 37538.75 Depreciation,d 41580 29106 20374.2 14261.94 9983.358 Income I = (r-d) -6980 6186 15623.64 22455.86 27468.79 14244.25 Tax @ 34%,T 0 0 5042.078 7634.991 9339.39 4843.043 Net income, P = I-T -6980 6186 10581.56 14820.87 18129.4 9401.202 Discount factor,D = 1/1.1^t 0.91 0.83 0.75 0.68 0.62 0.62 PW = P*D -6345.45 5112.397 7950.084 10122.85 11256.93 5837.407 NPW 33934.22

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