Determine the following: i) Payback period ii) Net present value iii) Which project will you recommend?

The payback period is the time it takes for the cumulative cash inflows to equal the initial investment.
Initial Investment ($C_0$) = 100 Thousand Leones.
Cumulative cash flows for Project A:

• Year 1: 20
• Year 2: $20 + 25 = 45$
• Year 3: $45 + 30 = 75$
• Year 4: $75 + 35 = 110$ The initial investment of 100 Thousand Leones is recovered between Year 3 and Year 4. Amount remaining to be recovered after Year 3 = $100 - 75 = 25$ Thousand Leones. Cash flow in Year 4 = 35 Thousand Leones. Fraction of Year 4 needed = $\frac{25}{35} \approx 0.714$ years. Payback Period for Project A = $3 + 0.714 = \boxed{\text{3.714 years}}$.

Initial Investment ($C_0$) = 100 Thousand Leones.
Cumulative cash flows for Project B:

• Year 1: 30
• Year 2: $30 + 35 = 65$
• Year 3: $65 + 35 = 100$ The initial investment of 100 Thousand Leones is recovered exactly at the end of Year 3. Payback Period for Project B = $\boxed{\text{3.000 years}}$.

The formula for NPV is $NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - C_0$.
Given $C_0 = 100$ Thousand Leones and $r = 0.10$.

$$NPV_A = \frac{20}{(1.10)^1} + \frac{25}{(1.10)^2} + \frac{30}{(1.10)^3} + \frac{35}{(1.10)^4} + \frac{40}{(1.10)^5} + \frac{25}{(1.10)^6} + \frac{10}{(1.10)^7} - 100$$ $$NPV_A = 18.18 + 20.66 + 22.54 + 23.91 + 24.84 + 14.11 + 5.13 - 100$$ $$NPV_A = 129.37 - 100 = \boxed{\text{29.37 Thousand Leones}}$$

Given $C_0 = 100$ Thousand Leones and $r = 0.10$.

$$NPV_B = \frac{30}{(1.10)^1} + \frac{35}{(1.10)^2} + \frac{35}{(1.10)^3} + \frac{40}{(1.10)^4} + \frac{40}{(1.10)^5} + \frac{40}{(1.10)^6} + \frac{15}{(1.10)^7} - 100$$ $$NPV_B = 27.27 + 28.93 + 26.30 + 27.32 + 24.84 + 22.58 + 7.71 - 100$$ $$NPV_B = 164.95 - 100 = \boxed{\text{64.95 Thousand Leones}}$$

To recommend a project, we compare the payback periods and NPVs.

• Project A: Payback Period = 3.714 years, NPV = 29.37 Thousand Leones.
• Project B: Payback Period = 3.000 years, NPV = 64.95 Thousand Leones.

Project B has a shorter payback period (3.000 years vs. 3.714 years), indicating quicker recovery of the initial investment. Project B also has a higher Net Present Value (64.95 Thousand Leones vs. 29.37 Thousand Leones), indicating it is expected to generate more wealth. Based on both criteria, Project B is the more favorable investment.