Question

I want decision answer please

if it is required to install a new substation to meet a continuous load growth that currently require only 1 x 25MVA transformer while within four years the load growth will require2 x 25 MVA transformers. Utility planners have to choose between two options. Either to build a substation with one transformer now and spend $1,000,000, then add the second transformer after four years and pay another $642,000 (a total expenses of $1,642,000). Or, they can decide to build the substation with two transformers now and spend a total of only $1,400,000.

Answer 1

Extra Cost to be paid after 4 years is $642000, Extra cost to be paid now is $1,400,000- $1,000,000= $400,000

If Present Value of $642,000 is less than $400,000 then it is better to buy the transformer later. Lets find the interest rate at which Present Value of $642,000 is equal to $400,000

Present Value= Future Value/ (1+r)^n

n=4

4000000= 642000/ (1+r)^4

Or, (1+r)^4= 642000/400000

Or, (1+r)^4= 1.605

Or, 1+r = 1.605^(1/4)

Or 1+r = 1.1256

Or, r= 1.1256-1

Or, r= 0.1256 i.e 12.56%

Hence at rate 12.56% Present Value of $642,000 is equal to $400,000.

If Discount Rate is below 12.56%, the Present value will be more than $400,000 and if Discount Rate is above 12.56%, the Present value will be less than $400,000.

Hence, if Discount Rate is above 12.56% it is better to add the transformer later. At 12.56% discount rate anything can be done it is indifferent. And if Discount Rate is below 12.56% it is better to add the transformer now.