Question

When discounting future costs and benefits, anyone performing a benefit-cost analysis will use an interest rate or a discounting rate, which is shown as i in the following equation:

1. Explain why the net present value of most projects rises when i decreases. (1)

2. Imagine that a project will yield $20M in benefits immediately, but will result in $200B in damaged at the end of 500 years. Using a rate of i=0.03 or 3% to discount the future damages, calculate the present value of the future damages and the net present value of this project. (1)

3. What does your answer from part B suggest about discounting and intergenerational equity? Explain. (1)

Answer 1

*15. A) A decrease in i increases the discounting factor making net present value of most projects to rise.

*B).Present value of future damages equals $76,281.20

Net Present value of this project is $19,923,718.80

C).The part B suggests that the discounting lowers the current value of a future cash flow.

It also predicts the intergenerational equity through cash flow changes and worth of people in different generations.

Explanation:

*15. A).Discounting the future costs and benefits is done through the equation:

PV=$X/(1+i)ⁿ or

PV=$X(1+i)^-n

Based on the equation, the net present value of most projects rise when i decreases. A decrease in i increases the discounting factor making net present value to increase. The discounting factor equals the (1+i)^-n. Most investors therefore prefer projects with lower i that will have higher the net present value. A higher net present value is an indicator of profitable project.

*B).The discounting is done at i=0.03 or 3%:n=500 years

Present value of future damages: PV=$X/(1+i)ⁿ

X=200B =200,000,000,000

PV =200,000,000,000/(1+0.03)⁵⁰⁰

=$76,281.20

Net Present value of project=current net benefits-present value of damages

=20M-76,281.20

=20,000,000-76,281.20

=$19,923,718.80

*C).The part B suggests that the discounting lowers the current value of a future cash flow. The discounting approach provides a clear value of an investment that has projected future benefits. This guides investors when it comes to implementation of project.

It also predicts the intergenerational equity through cash flow changes and worth of people in different generations. Through discounting, net present value of future generations can be projected based on the current and expected financial benefits. The changes in interest, i and the number of years between generations will have a direct impact on the integenerational equity.