The problem provides the initial investments and cash flows for two mutually exclusive projects, A and B. The firm's cost of capital is 0.1. We need to calculate the payback period for project A and project B, and the Net Present Value (NPV) of project A.

1. Problem Description

The problem provides the initial investments and cash flows for two mutually exclusive projects, A and B. The firm's cost of capital is 0.

1. We need to calculate the payback period for project A and project B, and the Net Present Value (NPV) of project A.

2. Solution Steps

Payback Period for Project A:

* Year 0: -$22,000

* Year 1: -$22,000 +$8,000 = -$14,000

* Year 2: -$14,000 +$8,000 = -$6,000

* Year 3: -$6,000 +$8,000 = $2,000

The payback period occurs between year 2 and year

3. To find the exact payback period, we calculate the fraction of year 3 needed to cover the remaining $6,

0

0

0. Payback period = 2 + ($6,000/$8,000) = 2 + 0.75 = 2.75 years

Payback Period for Project B:

* Year 0: -$28,000

* Year 1: -$28,000 +$9,000 = -$19,000

* Year 2: -$19,000 +$9,000 = -$10,000

* Year 3: -$10,000 +$9,000 = -$1,000

* Year 4: -$1,000 +$9,000 = $8,000

The payback period occurs between year 3 and year

4. To find the exact payback period, we calculate the fraction of year 4 needed to cover the remaining $1,

0

0

0. Payback period = 3 + ($1,000/$9,000) = 3 + 0.1111 = 3.1111 years

NPV for Project A:

The formula for NPV is:

$NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$

Where:

$CF_t$ = Cash flow at time t

r = discount rate (cost of capital)

n = number of periods

For Project A:

$NPV = \frac{-22000}{(1+0.1)^0} + \frac{8000}{(1+0.1)^1} + \frac{8000}{(1+0.1)^2} + \frac{8000}{(1+0.1)^3} + \frac{8000}{(1+0.1)^4}$

$NPV = -22000 + \frac{8000}{1.1} + \frac{8000}{1.21} + \frac{8000}{1.331} + \frac{8000}{1.4641}$

$NPV = -22000 + 7272.73 + 6611.57 + 6010.52 + 5464.11$

$NPV = -22000 + 25358.93 = 3358.93$

3. Final Answer

Payback period of project A: 2.75 years

Payback period of project B: 3.11 years (approximately)

NPV of project A: 3358.93