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 $147,656 at the end of each year, increasing the payment by $34,885 each subsequent year. The project will have expenses of $47,147 per year. Part way through the project, Swanson will need to rent some special equipment at a cost of $3,373 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 12. If Swanson remains on schedule, the company will receive a bonus of $76,049 at the end of year 8. (Swanson plans on remaining on schedule.) Calculate the present worth of the project using an interest rate of 5% compounded yearly. Notes: The first payment and the first year of expenses will occur at the end of year 1. Be sure to count the years carefully when calculating the years for the cost of renting the special equipment. Enter your answer as: 1234 Round your answer. Do not use a dollar sign ("$"), any commas (")') or a decimal point ("").

Answer 1

i = 5%

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

Present value of rent cost at EOY 4 = 3373 * [ 1 - (1-0.08)^8 / (1+0.05)^8 ] / (0.05+0.08)

= 3373 * [ 1 - (0.92)^8 / (1.05)^8 ] / (0.13)

= 3373 * 5.020255

= 16933.32

Present value of contract = 147656 * (P/A, 5%,12) + 34885 * (P/G, 5%,12) - 47147 * (P/A, 5%, 12) - 16933.32 * (P/F, 5%,4) + 76049 * (P/F, 5%,8)

= 147656 * 8.863252 + 34885 * 43.624052 - 47147 * 8.863252 - 16933.32 * 0.822702 + 76049 * 0.676839

= 2450203.51 ~ 2450204 (Nearest Dollar)