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Can someone pls help me with this question
A vehicle distributor plans to buy a piece of land on which to park his vehicles. The land will cost $1m.The net cash inflows before tax are $100000 in yr1, $200000 in yr2 and $250000 every yr in perpetuity from year 3 onwards.
The tax on the additional funds generated will be 30% of the net cash inflow, paid 1 yr in arrears.
The distributors cost of capital is 10%.
Calculate the present value of this proposal.
Give your answer to the nearest $Hi j4son!
The present value of the proposal is referred to as the net present value. It is the difference between the present value of the investment (or rather the initial cost of the investment) and the present value of future benefits in this case future cash in -flows. And it is easy to calculate as shown below. For better presentation let’s use the following abbreviations:I=initial investment
Yr=year
Interest factor= 1/(1+r)^n =IF where n is the number of years
Present value =PV
Net present value=NPV
Net Cash inflows =NCFs
Interest rate =cost of capital=rPV of I= I x IF in Yr zero
= 1,000,000 X 1
= $1,000,000Present value of NCFs
Yr 1; 100,000(1-0.3)(IF)
=70,000( 0.9091)
= $63, 637Yr 2; 200,000(1-0.3)(IF)
=140,000(0.8264)
= $115,696Yr 3; [(250,000)(1-0.3)]/0.1)(IF)
= 1,750,000(0.8264)
= $1,446,200The total PV of NCFs=63,637+115,696+1,446,200=$1,625,533
Therefore the NPV of the proposal = PV of NCFs – PV of I
= 1,625,533-1,000,000
= $625,533Take note that the perpetuity is a constant cash flow that that’s has an indefinite period. To determine its present value the constant value is divided by the interest rate or cost of capital . In our case we will first adjust for tax by geting the amount after tax then divide by 10%. it will be [250,000(1-0.3)/0.1= 1,750,000. This amount is the PV of the perpetuity at the beginning of year 3 or at the end of year 2. Remember that the perpetuity starts from year 3 and not after year 3. So the cash in flows in year 3 are part of the perpetuity. That’s why I said its present value is at the beginning of year 3 or at the end of year 2, just one day difference.
But to find the PV of the perpetuity today ie year zero, we have to discount the 1,750,000. Over the period of 2 years. This will be :
1,750,000 X (1+0.1)^-2
=1,750,000X(0.8264)
=1,446,200Also, note that the cash inflow values used should be after tax .
And overall if you were asked to advise the company, the company should accept the investment since NPV>0 ie $625,533 is greater than zero .
I hope you found this to be helpful. Good Luck!!!!
Hi- Thanks for your help – just a reminder though that this is the ‘Ask the Tutor’ forum.
Student discussions should be posted on the student forums.
However, the answer given is very detailed and correct.
My only comment would be for straightforward discount rates – such as 10% – you can use the discount tables provided in your exam -this is quicker than calculating the discount rate each time yourself via 1/(1+r)^n
Kindest Regardsm
CathHi,
Well it was a fantastic answer so hope I’ve not dampened your enthusiasm!… the cima student discussion forums can be found at link below:
https://opentuition.com/forum/cima-forums/
Kindest Regards,
Cath
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