The cash flow diagram of Option-3 is shown in Fig. 2.9.

Fig. 2.9 Cash flow diagram of Option-3

For Option-3, the annual operating cost is in the form of a positive uniform gradient series with gradient starting from end of year ‘6’. The annual operating cost can thus be split into the uniform base amount of Rs.35000 and the gradient amount in multiples of Rs.2000 starting from end of year ‘6’ (shown in Fig. 2.10).

The equivalent present worth of the gradient series for the annual operating cost starting from end of year ‘6’ will be located at the end of year ‘4’. Further the present worth of this amount at time ‘0’ will be determined by multiplying the equivalent present worth ‘Pg’ (shown in Fig. 2.10)at the end of year ‘4’ with the single payment present worth factor (P/F, i, n). 

Fig. 2.10 Cash flow diagram of Option-3 with annual operating cost split into uniform base amount and gradient amount

The equivalent present worth (in Rs.) of Option-3 is obtained as follows;
PW₃ = - 2700000 - 35000 (P/A, 8%, 10) - Pg(P/F, 8%, 4) + 140000 (P/A, 8%, 10) + 650000 (P/F, 8%, 10)
Now in the above expression, Pg will be replaced by G (P/G, i, n) i.e. 2000 (P/G, 8%, 6).
PW₃ = - 2700000 - 35000 (P/A, 8%, 10) - 2000(P/G, 8%, 6) (P/F, 8%, 4) + 140000 (P/A, 8%, 10) + 650000 (P/F, 8%, 10)
PW₃ = - 2700000 + (140000 - 35000) (P/A, 8%, 10) - 2000(P/G, 8%, 6) (P/F, 8%, 4) + 650000 (P/F, 8%, 10)
Now putting the values of different compound interest factors in the above expression, the value of PW₃ is given by;
PW₃= - 2700000 + 105000 X 6.7101 - 2000 X 10.5233 X 0.7350 + 650000 X 0.4632
PW₃= - 2700000 + 704561 - 15469 + 301080
PW₃ = - Rs.1709828

From the comparison of equivalent present worth of all the three mutually exclusive alternatives, it is observed that Option-3 shows lowest negative equivalent present worth as compared to other options. Thus Option-3 will be selected for the purchase of the dump truck.