Question

Swanson Brothers, Inc. is putting together a bid for a multi-year state project. The project will have a lifespan of 10 years. If successful, the state will pay Swanson $116,193 at the end of each year, increasing the payment by $31,646 each subsequent year. The project will have expenses of $49,293 per year. Part way through the project, Swanson will need to rent some special equipment at a cost of $3,112 per year, with the cost decreasing by 8% each subsequent year. Swanson will make the first payment on the special equipment at the end of year 5 and will need the equipment through the end of year 10.

If Swanson remains on schedule, the company will receive a bonus of $79,177 at the end of year 7. (Swanson plans on remaining on schedule.) Calculate the present worth of the project using an interest rate of 2% compounded yearly.

Notes: The first payment and the first year of expenses will occur at the end of year 1.

Be sure to count the years carefully when calculating the years for the cost of renting the special equipment.

Answer 1

Present Worth of the project = 1,889,366.10

Formula	Year (n)	0	1	2	3	4	5	6	7	8	9	10
Increasing by $31,646 p.a.	Payment (P)		116193	147839	179485	211131	242777	274423	306069	337715	369361	401007
	Expenses ('E)		-49293	-49293	-49293	-49293	-49293	-49293	-49293	-49293	-49293	-49293
RCn-1*(1-8%)	Rent cost (RC)						-3112.00	-2863.04	-2634.00	-2423.28	-2229.41	-2051.06
	Bonus (B)								79177.00
P+E+RC+B	Total (T)		66900.00	98546.00	130192.00	161838.00	190372.00	222266.96	333319.00	285998.72	317838.59	349662.94
1/(1+2%)^n	Discount factor @ 2%	1.000	0.980	0.961	0.942	0.924	0.906	0.888	0.871	0.853	0.837	0.820
T*Discount factor	Present Value of T (PV)	0	65588.24	94719.34	122682.83	149513.30	172425.79	197366.70	290174.25	244097.16	265953.11	286845.40
Sum of all PVs	Present Worth	1889366.10