We are given the cash flows for two projects, A and B, for years 4 and 5. We are asked to calculate the payback period, net present value (NPV), and profitability index for both projects. We are missing information about the initial investment and discount rate. Let's denote the initial investment for both projects as $I$ and the discount rate as $r$.

1. Problem Description

We are given the cash flows for two projects, A and B, for years 4 and

5. We are asked to calculate the payback period, net present value (NPV), and profitability index for both projects. We are missing information about the initial investment and discount rate. Let's denote the initial investment for both projects as $I$ and the discount rate as $r$.

2. Solution Steps

Payback Period:

Since we only have the cash flows for years 4 and 5, we need to make assumptions about earlier years. Let's assume that the initial investment $I$ is made at time 0 and there are no cash flows between time 0 and time

4. The payback period is the time it takes for the cumulative cash inflows to equal the initial investment.

Project A: The cash flows are $418000$ for year 4 and $418000$ for year

5. Project B: The cash flows are $300000$ for year 4 and $300000$ for year

5.

Without the value of $I$, we cannot calculate the payback period. We need to know how much has already been paid back from years 1-

3. If we assume the projects just have flows in years 4 and 5, then the flows in years 4 and 5 need to exceed $I$ to have a meaningful payback period calculation. We'll assume the initial investment I is such that it takes at least part of year 4 and part of year 5 to payback for Project A and Project B.

Net Present Value (NPV):

The NPV is the sum of the present values of all cash flows.

$NPV = -I + \frac{CF_4}{(1+r)^4} + \frac{CF_5}{(1+r)^5}$

where $CF_4$ is the cash flow in year 4 and $CF_5$ is the cash flow in year

5.

Project A: $NPV_A = -I + \frac{418000}{(1+r)^4} + \frac{418000}{(1+r)^5}$

Project B: $NPV_B = -I + \frac{300000}{(1+r)^4} + \frac{300000}{(1+r)^5}$

Without the values of $I$ and $r$, we cannot calculate the NPV.

Profitability Index (PI):

The profitability index is the present value of future cash flows divided by the initial investment.

$PI = \frac{\sum \frac{CF_t}{(1+r)^t}}{I}$

Project A: $PI_A = \frac{\frac{418000}{(1+r)^4} + \frac{418000}{(1+r)^5}}{I}$

Project B: $PI_B = \frac{\frac{300000}{(1+r)^4} + \frac{300000}{(1+r)^5}}{I}$

Without the values of $I$ and $r$, we cannot calculate the profitability index.

Since initial investment and discount rate are not given, the following calculations are done assuming a zero initial investment and a discount rate of

0.

Payback Period:

Assume $I=0$. Then the payback period would essentially be immediate as any cash flow greater than 0 would payback the initial investment.

Project A: Payback = Less than 4 years

Project B: Payback = Less than 4 years

Net Present Value (NPV):

Assume $I=0$ and $r=0$

Project A: $NPV_A = 418000 + 418000 = 836000$

Project B: $NPV_B = 300000 + 300000 = 600000$

Profitability Index (PI):

Assume $I=0$ and $r=0$

Project A: $PI_A = (418000 + 418000) / 0 = \infty$

Project B: $PI_B = (300000 + 300000) / 0 = \infty$

If we assume that the total initial investment is 600000, then project A could have a payback of 4+ years, and project B 4+ years.

If we use $r=0.1$,

$NPV_A = -600000 + 418000/1.1^4 + 418000/1.1^5 = -600000+285713.6+259739.7 = -54546.7$

$NPV_B = -600000 + 300000/1.1^4 + 300000/1.1^5 = -600000+204940.3+186842.6 = -208217.1$

$PI_A = (418000/1.1^4 + 418000/1.1^5)/600000 = (285713.6+259739.7)/600000 = 0.909$

$PI_B = (300000/1.1^4 + 300000/1.1^5)/600000 = (204940.3+186842.6)/600000 = 0.653$

3. Final Answer

Without knowing the initial investment $I$ and the discount rate $r$, it's impossible to give numerical answers. The calculations are only possible under assumptions.

Assuming I=0 and r=0:

Payback period of project A: Less than 4 years

Payback period of project B: Less than 4 years

Net present value of project A: $836000

Net present value of project B: $600000

Profitability index of project A: $\infty$

Profitability index of project B: $\infty$