Consider the following cash flows for two mutually exclusive capital investment projects. the required rate of return is 12%. use this information for the next 5 questions.

year project a cash flow project b cash flow
0 -$32,400 -$14,400
1 9,600 4,200
2 9,600 4,200
3 9,600 4,200
4 8,400 3,600
5 8,400 3,600
6 6,000 3,600

1. what is the irr of project a?

a) 18.69% c) 10.05% e) 16.58%
b) 12.97% d) 16.32%

2. what is the payback period of project a?

a) 3.5 years c) 4.57 years e) 3.8 years
b) 3.43 years d) 3.57 years

3. what is the profitability index of project a?

a) 1.128 d) 1.09
b) 1.045 e) 1.117
c) .98

4. calculate the net present value of project b. a) $1,842 d) $1,415
b) $3,802 e) $2,223 c) $3,471

1. d) 16.32%

2. b) 3.43 years

3. e) 1.117

a) $1,842 

Explanation:

The IRR is the discount rate that equates the after tax cash flows from an investment to the amount invested.

The IRR for project A.

Using a financial calculator:

Cash flow for year zero = $-32,400

Cash flow each year from year 1 to 3 = $-9,600

Cash flow each year for year 4 and 5 =$8,400

Cash flow for year six = $6,000

IRR = 16.32%

The payback period measures how long it takes for the amount invested to be recouped from the cumulative cash flows.

Explanations on how the payback period for project A is calculated can found in the attached image.

Profitability index = present value of cash flows / amount invested

Present value of cash flows can be calculated using a financial calculator.

Cash flow for year zero = 0

Cash flow each year from year 1 to 3 = $-9,600

Cash flow each year for year 4 and 5 =$8,400

Cash flow for year six = $6,000

I = 12%

PV = $36,202.10

profitability index = $36,202.10 / $32,400 = 1.117

Net present value is the present value of after tax cash flows substracted from the amount invested.

The NPV of project B using a financial calculator:

Cash flow for year zero = $-14,400

Cash flow each year from year one to three = $4200

Cash flow each year from year four to six = $3600

I = 12 %

NPV =$1842.17

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