Net present value (NPV), annual equivalent (AE): investor has 2 alternative projects

[mems]

An investor has two alternative projects to improve their property portfolio. Project ‘A’ would involve investing $700,000 now and the remainder of the work carried out in 5 years’ time at a cost of $1,500,000. In this alternative case, annual operating and maintenance charges will be $115,000 per year for the first 5 years and $105,000 per year thereafter. Project ‘B’involves a complete modernisation now of buildings which will cost $1,000,000 now. Annual operation and maintenance charges will amount to $100,000 per year. How do you calculate the net present value (NPV) and the annual equivalent (AE) of each project? The annual interest rate is 4% with an asset life of 25 years for both projects.

I am self-teaching myself and need help, please.

Thank you

 

[Denis]

Well, hard to help if we don't know "where you're at".
Can you answer this:
If you deposit $5000 now, then $1000 annually for 5 years,
how much will your account be worth after your last
deposit if the annual rate is 4%?

Do you have the answer available?
If so, what is it?

 

[mems]

Well, hard to help if we don't know "where you're at".
Can you answer this:
If you deposit $5000 now, then $1000 annually for 5 years,
how much will your account be worth after your last
deposit if the annual rate is 4%?

$11,616.24

 

[mems]

Well, hard to help if we don't know "where you're at".
Can you answer this:
If you deposit $5000 now, then $1000 annually for 5 years,
how much will your account be worth after your last
deposit if the annual rate is 4%?

$11,616.24

 

[Denis]

$11,616.24

Yes...if the 1st $1000 is deposited at same time as the $5000...
Would be 11,499.59 if 1 year later...agree?

I was asking if you had the answer available for YOUR problem.

 

[Denis]

Not important, but are you sure of your figures?

Project A total outlay: 700,000 + 115,000*5 + 1,500,000 + 105,000*20 = 4,875,000
Project B total outlay: 1,000,000 + 100,000*25 = 3,500,000

Also, 1,000,000 results in annual expenses of 100,000 (project B)
while 2,200,000 results in annual expenses of 105,000 (project A)

...well, at least easy to "see" which one is obvious

 

[Denis]

Hokay....here we go!
Basic formula is present value of annuity:
p = a[1-1/(1+i)^n]/i :
a = annuity amount, i = interest rate, n = number of periods

Project B
PV = 1000000 + 100000[1-(1/1.04^25]/.04 = ~2,562,208

Project A
PV = 700000 + 115000[1-(1/1.04^5]/.04
+ 1500000/1.04^5
+ {105000[1-(1/1.04^20]/.04}/1.04^5
= ~3,617,727

Soooo good ole B wins by a landslide!