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 $129,868 at the end of each year, increasing the payment by $31.525 each subsequent year. The project will have expenses of $48,172 per year. Part way through the project, Swanson will need to rent some special equipment at a cost of $3,937 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 $79,218 at the end of year 7. (Swanson plans on remaining on schedule.) Calculate the present worth of the project using an interest rate of 4% compounded yearly. Notes: The first payment and the first year of expenses will occur at the end of year 1. Be sure to count the years carefully when calculating the years for the cost of renting the special equipment. Enter your answer as: 1234 Round your answer. Do not use a dollar sign ("$"), any commas ()') or a decimal point("").

Answer 1

Life of the project = 10 years

Project Benefits in the first year = 129868

The benefits increase by 31525 in each subsequent year.

Project expenses = 48172 per year

Renting of equipments = 3937 at the end of 5^th year and decreases by 8% each year

Bonus = 79218 at the end of year 7

Calculate the Present Worth using interest rate of 4%

In the given question the benefits are

1. Project benefits

2. Bonus received

In the given question the costs are

1. Annual project expenses

2. Rent of equipments

Step 1

Calculate PW of project benefits

PW = 129868 (P/A, 4%, 10) + 31525 (P/G, 4%, 10)

PW = 129868 (8.11090) + 31525 (33.8814) = 2,121,457

PW of bonus

PW = 79218 (P/F, 4%, 7)

PW = 79218 (0.75992) = 60,199

Total Project benefits = 2,121,457 + 60,199 = 2,181,656

Step 2

Calculate PW of annual project expenses

PW = 48172 (P/A, 4%, 10)

PW = 48172 (8.11090) = 390,718

PW of renting of equipments

Renting of equipments = 3937 at the end of 5^th year and decreases by 8% each year

P = A1 [1 – (1 – g) ^N (1+i) ^–N ÷ i + g], where g = 8% and i=4% and n will be 6 years

P = 3937 [1 – (1 – 0.08) ⁶ (1 + 0.04) ^–6 ÷ 0.04 + 0.08] = 17,086

PW at 0^th year = 17,086 (P/F, 4%, 4)

PW at 0^th year = 17,086 (0.85480) = 14,605

Total PW of Cost = 390718 + 14605 = 405323

Step 3

Calculate Net Present Worth

NPW = PW of benefits – PW of cost

NPW = 2,181,656 – 405,323 = 1,776,333