Question

Swanson Brothers, Inc. is putting together a bid for a multi-year state project. The project will have a lifespan of 12 years. If successful, the state will pay Swanson $131,078 at the end of each year, increasing the payment by $28,943 each subsequent year. The project will have expenses of $46,352 per year. Part way through the project, Swanson will need to rent some special equipment at a cost of $2,985 per year, with the cost decreasing by 10% each subsequent year. Swanson will make the first payment on the special equipment at the end of year 6 and will need the equipment through the end of year 12.

If Swanson remains on schedule, the company will receive a bonus of $93,739 at the end of year 8. (Swanson plans on remaining on schedule.) Calculate the present worth of the project using an interest rate of 1% compounded yearly.

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

Answer 1

i = 1%

Present value of geometric series = C * [ 1 - (1+g)^n / (1+i)^n ] / (i-g)

Present value of rent cost at EOY 5 = 2985 * [ 1 - (1-0.1)^7 / (1+0.01)^7 ] / (0.01+0.1)

= 2985 * [ 1 - (0.9)^7 / (1.01)^7 ] / (0.11)

= 2985 * 5.035307

= 15030.39

Present value of contract = 131078 * (P/A, 1%,12) + 28943 * (P/G, 1%,12) - 46352 * (P/A, 1%, 12) - 15030.39 * (P/F, 1%,5) + 93739 * (P/F, 1%,8)

= 131078 * 11.255077 + 28943 * 60.598677 - 46352 * 11.255077 - 15030.39 * 0.951466 + 93739 * 0.923483

= 2778902.40