Answer to Question #263331 in Microeconomics for Tumi443

Question

Abridge will cost P5m to build and P200 000.00 per year to maintain. The life span of the bridge is forty years, Benefits to the driving public is P900 000.00 per year. Damage costs associated with noise pollution are estimated at P250 000.00 per year.

i)Given market interest rates at four percent (4%) calculate the present value/present worth of the benefits of the bridge. (3 marks)

ii)Calculate the present value/worth of the cost of the bridge. (3 marks)

iii)Would you recommend the construction of the bridge or not? Explain your reasoning.(3 marks)

iv) if the interest rate is increased to 11% how does that affect the present values? (2 marks

Answer 1

Solution:

i.). Present value of the benefits of the bridge:

Benefits to the driving public = 900,000

Years = 40 years

Market interest rate = 4%

Present value factor = (1 – (1 + r)^-n ÷ r = (1 – (1 + 0.04)^-40 ÷ 0.04 = 19.7928

Present value                                              = 900,000 x 19.7928 = 17,813,520

Less Initial investment                                                                 =   5,000,000  

Net present value                                                                        =  12,813,520

The present value/present worth of the benefits of the bridge = P12,813,520

 

ii.). Present value/worth of the cost of the bridge:

Total costs:

Maintenance costs = 200,000

Pollution costs = 250,000

Total costs per year = 200,000 + 250,000 = 450,000

Total benefits per year = 900,000

Net benefits = 900,000 – 450,000 = 450,000

Present value = 450,000 x 19.7928                     = 8,906,760

Less Initial investment (costs)                           = 5,000,000

The present value/worth of the cot of the bridge = 3,906,760

iii.). Yes, I would recommend the construction of the bridge since it will generate positive benefits to the society.

 

 

iv.). Present value of the benefits of the bridge:

Benefits to the driving public = 900,000

Years = 40 years

New market interest rate = 11%

Present value factor = (1 – (1 + r)^-n ÷ r = (1 – (1 + 0.11)^-40 ÷ 0.11 = 8.9511

Present value                                              = 900,000 x 8.9511  =  8,055,990

Less Initial investment                                                                 =   5,000,000  

Net present value                                                                        =  3,055,990

The present value/present worth of the benefits of the bridge = P3,055,990

 

Present value/worth of the cost of the bridge:

Total costs:

Maintenance costs = 200,000

Pollution costs = 250,000

Total costs per year = 200,000 + 250,000 = 450,000

Total benefits per year = 900,000

Net benefits = 900,000 – 450,000 = 450,000

Present value = 450,000 x 8.9511                     =  4,027,995

Less Initial investment (costs)                           = 5,000,000

The present value/worth of the cost of the bridge = (972,005)

 

With the increased interest rate, the present worth of the benefits of the bridge will reduce massively and the present value/worth of the cost of the bridge will be negative.

Therefore, the bridge should not be constructed with increased interest rates as it will result in negative benefits.