Question

Please use the following table, which represents the costs and benefits of a new bridge.

	1st year	2nd year	3rd year	4th year
Costs	100	200	0	0
Benefits	0	0	200	200

Now consider the following interest rates 0%, 10% and 50%. Calculate

A the net benefits with all interest rates

B the benefit-cost ratio with all interest rates     

Answer 1

	1st year	2nd year	3rd year	4th year
Costs	100	200	0	0
Benefits	0	0	200	200

At i=0%, 10% and 50%

..

PV = FV/ (1+i)n

..

A. Net benefit with 0% interest rate

Total cost in 1st and 2nd year = 100+200= 300

Total benefits in the 3rd anf 4th year = 200+200= 400

NPV = 100

..

Net benefit with 10% interest rate

Total cost in 1st and 2nd year = 100+200 (1+0.1)2= 100+ 165.29 = 265.29

Total benefits in the 3rd anf 4th year = 200(1+0.1)3+200(1+0.1)4= 150.26 + 136.60 = 286.86

NPV = 286.86 - 265.29 = 21.57

..

Net benefit with 0% interest rate

Total cost in 1st and 2nd year = 100+200 (1+ 0.5)2= 100+88.88 = 188.89

Total benefits in the 3rd anf 4th year = 200(1+ 0.5)3+200(1+ 0.5)4= 59.25 + 39.51 = 98.76

NPV = 98.76 - 188.89 = -90.13

..

B. The benefit-cost ratio with all interest rates

Benefit-Cost ratio = Present value of benefit from the project/ Present value of cost of the project

at i = 0%

Present value of benefit from the project = 400

Present value of cost of the project = 300

B-C ratio = 400/300 = 1.33

..

at i =10%

Present value of benefit from the project = 286.86

Present value of cost of the project = 265.29

B-C ratio = 286.86/265.29 = 1.08

..

at i=50%

Present value of benefit from the project = 98.76

Present value of cost of the project = 188.89

B-C ratio = 98.76/188.89 = 0.52