The problem provides the initial investments and cash flows for two projects, Project A and Project B. The goal is to find the payback period for each project, given that the firm's cost of capital is 0.09. The payback period is the time it takes for the cumulative cash flows to equal the initial investment. The cost of capital is not needed for the simple payback period calculation.

1. Problem Description

The problem provides the initial investments and cash flows for two projects, Project A and Project B. The goal is to find the payback period for each project, given that the firm's cost of capital is 0.

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9. The payback period is the time it takes for the cumulative cash flows to equal the initial investment. The cost of capital is not needed for the simple payback period calculation.

2. Solution Steps

First, we compute the payback period for Project A.

* Year 0: Cumulative cash flow = -$21,000

* Year 1: Cumulative cash flow = -$21,000 +$8,000 = -$13,000

* Year 2: Cumulative cash flow = -$13,000 +$8,000 = -$5,000

* Year 3: Cumulative cash flow = -$5,000 +$8,000 = $3,000

The initial investment of $21,000 is recovered sometime between year 2 and year

3. To find the exact payback period, we calculate the fraction of year 3 needed:

Payback period = 2 + ($5,000 /$8,000) = 2 + 0.625 = 2.625 years

Next, we compute the payback period for Project B.

* Year 0: Cumulative cash flow = -$26,000

* Year 1: Cumulative cash flow = -$26,000 +$9,000 = -$17,000

* Year 2: Cumulative cash flow = -$17,000 +$9,000 = -$8,000

* Year 3: Cumulative cash flow = -$8,000 +$9,000 = $1,000

The initial investment of $26,000 is recovered sometime between year 2 and year

3. To find the exact payback period, we calculate the fraction of year 3 needed:

Payback period = 2 + ($8,000 /$9,000) = 2 + 0.8889 = 2.8889 years

3. Final Answer

The payback period for project A is 2.625 years.

The payback period for project B is 2.8889 years.