The question begins this way: 

“The performance of your unit is not correct.”

Why?

“Because when I calculate the coil load from the stated conditions I do not get the capacity shown”

Answer:

When calculating the Total Capacity do not use Qt = 4.5 * cfm * (h₁ – h₂)

Because 4.5 is derived for standard air as follows:
ma = cfm * Density * 60 where the density of standard air = .075 lba/ft³

At 100 DB and 78 WB, the W = .015601 lbw/lba

h = ha + Whg = cpa*T + W*(1061 + .444*T) Btu/lba

h₁ =.24*100 + .015601*(1061 + .444*100) = 41.25 Btu/lba

At 57.50 DB and 57.30 WB, the W = .0099622 lbw/lba

h₂ = .24*57.50 + .0099622*(1061 + .444*57.50) = 24.62 Btu/lba

If you use this equation then you will get the following:

Qt = 4.5 * 15000 * (41.25 – 24.62) = 1,122,525 Btu/hr, or a perceived error of 8.3

At 100 DB and 78 WB, the W = .015601 lbw/lba, Density = .06914 ft³/lba

 h₁ = 41.25 Btu/lba from above

 At 57.50 DB and 57.30 WB, the W = .0099622 lbw/lba

 h₂= 24.62 Btu/lba above

 ma = CFM*Density*60 = 15000 * .06914 * 60 = 62,226 lba/hr

 Qt = ma * (h[1] – h[2]) = 62226*(41.25 – 24.62) = 1,034,818 Btu/hr

 
When calculating the sensible capacity do not use Qs = 1.1 CFM *(T₁-T₂):

 Because the 1.1 is derived from standard air as follows:

 m_{a *} C_pm = SCFM*Density_Std*(C_pa + W*C_pw)

 m_{a *} C_pm = SCFM *.075 * 60 * (.24 + .0093*.444) = 1.1*SCFM

 If you use this equation then you will get the following:

 Qs = 1.1 * 15000 * (100-57.50) = 701,250 Btu/hr                           

 Coil programs use actual conditions:

 At 100 DB and 78 WB, the W = .015601 lbw/lba, Density = .06914 ft³/lba

 At 57.50 DB and 57.30 WB, the W = .0099622 lbw/lba

 ma = CFM*Density*60 = 15000 * .06914 * 60 = 62226 lba/hr

 Cpm = (C_pa + W*C_pw)                  Btu/(lba – F)

 Qs = ma * Cpm * (T[1] – T[2])

 Qs = 622226*(.24+.015601*.444)*(100-57.5) = 652,988 Btu/hr

 The Total Latent Load is computed from:

 Q_L = Q_t – Q_s

 Using standard Air   Q_L = 1,034,818 - 701,250 = 333,568 Btu/hr

 Using actual air:  Q_L = 1,034,818 - 652,988 = 381,830 Btu/hr 

The above shows a sea level calculation.

The same equations apply for altitude however the true density must include DB, WB, and PB = altitude PB. PB altitude is calculated from the following equation:  PB = 14.696 * (1 - ALTITUDE*6.8753E-6)^5.2559