DISCOUNTING AND PRESENT VALUE: Please Help Me Calculate the Cost of this Project

[Mil]

Company X wants to build a new plant. The total cost of the construction of the plant is: $900,000. Construction of the Plant will take two years to build and d get ready for operation, because the previous owner of the land first needs to clear the land and make it ready for use. 20% of the cost of constructing the plant would be paid one year after the decision to go ahead; 25% would be paid after a further 6 months; and the remainder would be payable when the plant is ready for operation, at the end of the two-year period. The interest rate is 5.7%. The useful life of the plant will be 20 years. Please help me figure out how to get the NPV of the construction cost.
Should I discount it? If so why?

 

[Ishuda]

Company X wants to build a new plant. The total cost of the construction of the plant is: $900,000. Construction of the Plant will take two years to build and d get ready for operation, because the previous owner of the land first needs to clear the land and make it ready for use. 20% of the cost of constructing the plant would be paid one year after the decision to go ahead; 25% would be paid after a further 6 months; and the remainder would be payable when the plant is ready for operation, at the end of the two-year period. The interest rate is 5.7%. The useful life of the plant will be 20 years. Please help me figure out how to get the NPV of the construction cost.
Should I discount it? If so why?

"Net present value is the present value of the cash inflows minus the present value of the cash outflows. ..."
http://www.accountingcoach.com/blog/net-present-value
So, you need to bring everything to the present.

First of all you have to fix the date "after the decision to go ahead". You can fix that at the present date and then, if you want to change it, work from there. So, bring the 20% back one year, the 25% back 18 months, and the remainder (55%) back two years. The sum would be the NPV of the cost (a negative number). The NPV of the plant requires more information.

 

[Mil]

"Net present value is the present value of the cash inflows minus the present value of the cash outflows. ..."
http://www.accountingcoach.com/blog/net-present-value
So, you need to bring everything to the present.

First of all you have to fix the date "after the decision to go ahead". You can fix that at the present date and then, if you want to change it, work from there. So, bring the 20% back one year, the 25% back 18 months, and the remainder (55%) back two years. The sum would be the NPV of the cost (a negative number). The NPV of the plant requires more information.

Please tell me if this is correct

0 (Go-ahead Decision)	1	End of Year 2
No Payment	One Year After Go-Ahead Decision	At 1.5 Years	0.55*900,000 =495,000
0.20*900000 =180,00	0.25*900000 =225,000
	180,000/(1+0.057) =170,293.29	225,000/(1+0.057)^1.5 =297,047.52	495,000/(1+0.057)^2 =443,052.53

 

[Ishuda]

I didn't check the actual numbers but the formulas look right. Your table kind of got mixed up so to re-write it
1.0 year: 0.20 * 90000 / (1+.057)^1.0
1.5 year: 0.25 * 90000 / (1+.057)^1.5
2.0 year: 0.55 * 90000 / (1+.057)^2.0

 

[Mil]

I didn't check the actual numbers but the formulas look right. Your table kind of got mixed up so to re-write it
1.0 year: 0.20 * 90000 / (1+.057)^1.0
1.5 year: 0.25 * 90000 / (1+.057)^1.5
2.0 year: 0.55 * 90000 / (1+.057)^2.0

I used the formulas above. Please guide me on how to do this next bit. I know how to do the NPV Table:

Investment - ₤910,393.34
Revenues
Variable Costs
Depreciation
Total Income (Revenue-Variable Costs-Fixed Costs-Depreciation)
Taxes
After Tax Total Income
Depreciation

Company B has made an investment of ₤910,393.34 to construct a new bottling plant in England. The variable cost per month is: 9,000. The annual tax depreciation charge (i.e. annual depreciation charge allowable by tax authorities against taxable profits): £28,000. The annual fixed costs of operating the plant are £140,000 and include lease of land. The estimated useful life is 20 years. The bottling plant will have a production capacity of 100,000 bottles per month which will lead to monthly revenues of 50,000. B Ltd think that ample demand exists for the expanded output. In fact, B’s management think that the market for their drinks will expand further in the future. They are currently selling all of the bottled drinks that they produce, and their current plants are operating at full capacity. The discounting rate is 5.7%.

Please help me calculate the NPV for this project.

Do I need to include growth in the answer. If so how do I do it?

I am not too sure about my approach. Do I need to discount monthly or yearly? What assumptions should I make? I'd really appreciate your help.

 

[Ishuda]

To calculate an internal rate of return, you need to bring every thing to the time you want the IRR. Typically that time is the present so we need a NPV. Even if it isn't the present, if we do it for the present then it is easy to do it for any other point in time.

So, to answer the questions "Do I need to include growth in the answer." No (I assume you mean growth in sales other than the operating at full capacity plant being considered) since "B Ltd think that ample demand exists for the expanded output."

As far as the interest rate goes, it can either be monthly or annually. Generally for an IRR, it doesn't make a lot of difference as long as you are consistent across projects. If you compute an IRR for two projects, use the same methods for both projects although actual rates may vary. Since the number of computations in determining an IRR tend to be about linear in n (more time periods), I think I would tend to use annual interest rates unless told differently. That is, I would bring the monthly revenue, variable costs, etc to a yearly basis first and then compute the NPV for that year.

To review more about computing an IRR you might look at
http://www.mathsisfun.com/money/internal-rate-return.html