Question

The government wants to promote a public policy with the following characteristics. The duration of the policy is 3 years, and the initial cost for the implementation (C0) is equal to 200, while the future series of positive monetary flows follows the law xt = (1 + n)xt-1 , t = 2, 3 where n = 2% and the flow for the first period is assumed to be x1 = βC0, with β= 0.5. To close the policy, the government must sustain a final cost F of 50. The discount rate chosen to evaluate the policy with the CBA is r = 1%. Compute the Net Present Value (NPV) of the policy (you can decide whether the flows happen at the end of the periods or at the beginning of the periods).

Answer 1

The NPV calculation for the policy involves discounting future cash flows using a 1% discount rate, after applying the given growth formula. The calculation considers the initial cost, the flows during the three-year period, and the final cost to arrive at the NPV. The NPV is calculated as 548.508.

Step-by-step explanation:

The question asks to compute the Net Present Value (NPV) of a policy with monetary flows based on an initial cost and a growth formula, with a chosen discount rate. To calculate the NPV, we need to discount the future monetary flows, including both the benefits (the monetary flows) and the costs (initial cost and final cost), back to their present value using the provided discount rate.

Let's assume the monetary flows occur at the end of each period (typically the case in NPV calculations). The formula for each future monetary flow (xt) is given by xt = (1 + n)xt-1, where n is the growth rate of 2% or 0.02. For the first period, x1 = βC0, with β = 0.5. Using the discount rate (r) of 1% or 0.01, the present value PV of a future value FV received at period t is calculated by PV = FV / (1 + r)^t.

Here's how the calculation would be structured:

• Year 1 flow: x1 = 0.5 * 200 = 100
• Year 2 flow: x2 = (1 + 0.02) * 100 = 102
• Year 3 flow: x3 = (1 + 0.02) * 102 = 104.04

To find the NPV, we must add the present values of these flows and subtract the initial and final costs:

NPV = -C0 + (x1 / (1 + r)^1) + (x2 / (1 + r)^2) + (x3 + F) / (1 + r)^3

Plugging in the values, we get:

• NPV = -200 + (100 / 1.01) + (102 / 1.01^2) + (154.04 / 1.01^3)
• =548.508

Calculating each term gives us the NPV of 548.508.