Question

The HVAC engineer for a company constructing one of the world's tallest buildings (Shanghai Financial Center in the Peoples' Republic of China) has requested that $500,000 be spent now during construction on software and hardware to improve the efficiency of the environmental control systems. This is expected to save $10,000 per year for 10 years in energy costs and $700,000 at the end of 10 years in equipment refurbishment costs.

a-)Draw cash-flow diagram.
b-)Find PW when MARR = 5%. Is this project financially acceptable ?
c-)Determine the IRR. Is this project financially acceptable if the MARR = 5% ?

Answer 1

a)   Cash flow Diagram as under:
arrows to represent the inflows (arrows pointing from the line) or outflows (arrows pointing to the line) of cash.

As we can see in the above diagram of cash flow which starts as 0 means at the time of initial investment (Cash outflow) which $500,000 shows downward and cash inflows (cost savings) at each year shows upward in the diagram.
I have made this diagram in the system, if any further query please let me know.

b)   Given:
Initial investment: $500,000
Cash inflow (saving in energy cost) for 10 years: $ 10,000 per year
Cash inflow (saving in equipment refurbishment costs) at the end of year 10: $700,000

Present Worth: formula of present worth is
PW =    CF0   +    CF1   +    CF2   +    …   +    CFN
   (1 + r)0       (1 + r)1       (1 + r)2               (1 + r)N

Where: PW is Present Worth
CF is Cash flow
r is MARR(Minimum Acceptable Rate of Return)
A   B   C     
Year   Cash flows ($)   Present vale factor (5%)   Present value (B*C)
0   -$5,00,000.00    1   -$5,00,000.00
1   $10,000.00    0.952380952   $9,523.81
2   $10,000.00    0.907029478   $9,070.29
3   $10,000.00    0.863837599   $8,638.38
4   $10,000.00    0.822702475   $8,227.02
5   $10,000.00    0.783526166   $7,835.26
6   $10,000.00    0.746215397   $7,462.15
7   $10,000.00    0.71068133   $7,106.81
8   $10,000.00    0.676839362   $6,768.39
9   $10,000.00    0.644608916   $6,446.09
10   $7,10,000.00    0.613913254   $4,35,878.41
       Present Worth   $6,956.63
now we are calculating Present Worth by below table presentation:

c)   IRR: Internal Rate of Return is where Net present worth is Zero.
Internal rate of return is to calculate by hit and trail method when cash flows are uneven. Firstly we should calculate present value with the two different discount rate are as
A   B   C   D   E   F
Year   Cash flows ($)   Present vale factor (5%)   Present value (B*C)   Present vale factor (10%)   Present value (B*E)
1   $10,000.00    0.952   $9,523.81    0.909   $9,090.00
2   $10,000.00    0.907   $9,070.29    0.826   $8,260.00
3   $10,000.00    0.864   $8,638.38    0.751   $7,510.00
4   $10,000.00    0.823   $8,227.02    0.683   $6,830.00
5   $10,000.00    0.784   $7,835.26    0.564   $5,640.00
6   $10,000.00    0.746   $7,462.15    0.513   $5,130.00
7   $10,000.00    0.711   $7,106.81    0.466   $4,660.00
8   $10,000.00    0.677   $6,768.39    0.424   $4,240.00
9   $10,000.00    0.645   $6,446.09    0.386   $3,860.00
10   $7,10,000.00    0.614   $4,35,878.41    0.35   $2,48,500.00
       Total   $5,06,956.63       $3,03,720.00

IRR   =   Discount rate where present worth is more than initial investment   X   higher Present value (-) initial investment    X   Difference in Discount rates
               higher Present value (-) lower present value at other discount rate      

=   5%   X   (506956-500000)   X   5
           (506956-303720)      

Then IRR Would be 5.17%
Yes, this project financially acceptable if the MARR is 5%. As we can see IRR > then MARR.