Question

A cost benefit analysis of a new CD fence project indicates that the net benefits (B-C) of the project in each of the first three (3) years will be $-2,000,000 (-2 million dollars). Thereafter, the project will yield positive net benefits of $750,000 for the next 23yrs. Alternatively, an education project will yield net benefits of $-1,000,000 (-1 million dollars) for the first year, and positive net benefits of $6,000,000 for the next 10yrs, and $10,000,000 for another 15yrs.

1. Calculate the present value of net benefits of the projects when the social rate of discount is 5%. Which project merits approval? How would the present value of the net benefit change if the social rate of discount were 10%? Which project merits approval?

Would you approve the projects you did in (A), if instead you used the internal rate of return and the benefit cost ratio analysis under the two (2) different social discount rates that is 5% and 10%? The internal rate of return (IRR) is independent of the social rate of discount but the decisions will be based on these rates

Answer 1

Solution to part A

In this problem, we will make use of the financial calculator to keep things clearer and simpler. It is highly recommended to use a financial calculator for this question as it would be very tedious to perform calculations manually.

We have been asked to compute the present value of net benefits of the two projects at the given social rate of discount.

Project 1: CD Fence Project

The calculation for NPV will involve the use of the cash flow function of your financial calculator. We will input the following values to compute the net present value of benefits:

Step 1: Cash flow for year 0 (C00) = 0

Step 2: Cash flow for year 1 (C01) = -20,00,000

Step 3: Repeat value for 3 years (F01) = 3

Step 4: Cash flow for remaining 23 years (C02) = 7,50,000

Step 5: Repeat value for 23 years (F02) = 23

Step 6: Use CPT function to find NPV, where social rate of discount (I) = 5%

Step 7: NPV computed = 32,92,456.895

Net present value of benefits at 5% social rate of discount for the new CD Fence project is $32,92,456.90

Project 2: Education Project

We will compute the NPV of the net benefits of the education project using the same process as above.

Step 1: Cash flow for year 0 (C00) = 0

Step 2: Cash flow for year 1 (C01) = -10,00,000

Step 3: Repeat value for 1 year (F01) = 1

Step 4: Cash flow for next 10 years (C02) = 60,00,000

Step 5: Repeat value for 10 years (F02) = 10

Step 6: Cash flow for remaining 15 years (C03) = 100,00,000

Step 7: Repeat value for 15 years (F03) = 15

Step 8: Use CPT function to find NPV, where social rate of discount (I) = 5%

Step 9: NPV computed = 103,859,529.5

Net present value of benefits at 5% social rate of discount for the education project is $103,859,529.50

Answer: Looking at both the projects' net present value of benefits, clearly the project with the higher NPV should be approved. Considering this, the education project with the NPV of $103,859,529.50 should be approved as it is much higher than the new CD fence project.

Now, if the social rate of discount is increased from 5% to 10%, we will follow the same process as done above for each project. However, we will consider the discount rate (I) = 10% to compute the NPV. Upon calculation:

i) NPV of benefits for CD Fence project @ 10% social discount rate: $31,866.13

ii) NPV of benefits for education project @ 10% social discount rate: $592,655,74.33

Again, the project with the higher NPV should be approved. The doubling of the discount rate reduces the present value of net benefits for both the projects. Higher the discount rate, lower will be the NPV. Here, the education project should be approved with the NPV of $592,655,74.33 @ 10% social discount rate.

The thumb rule to follow when we are given the internal rate of return (IRR) and the net present value (NPV) is that we will select the project with the higher NPV over the IRR.