Lou Barlow, a divisional manager for Sage Company, has an opportunity to manufacture and sell one of two new products for a five-year period. His annual pay raises are determined by his division?s return on investment (ROI), which has exceeded 18% each of the last three years. He has computed the cost and revenue estimates for each product as follows:
Product A Product B
Initial investment:
Cost of equipment (zero salvage value) $ 170,000 $ 380,000
Annual revenues and costs:
Sales revenues $ 250,000 $ 350,000
Variable expenses $ 120,000 $ 170,000
Depreciation expense $ 34,000 $ 76,000
Fixed out-of-pocket operating costs $ 70,000 $ 50,000
The company?s discount rate is 16%.
Required:
1. Calculate the payback period for each product. (Round your answers to 2 decimal places.)
2. Calculate the net present value for each product. (Round discount factor(s) to three decimal places.)
3. Calculate the internal rate of return for each product. (Round percentage answer to 1 decimal place. i. e. 0.1234 should be considered as 12.3%.)
4. Calculate the project profitability index for each product. (Round discount factor(s) to three decimal places. Round your answers to 2 decimal places.)
5. Calculate the simple rate of return for each product. (Round percentage answer to 1 decimal place. i. e. 0.1234 should be considered as 12.3%.)

1) Payback Period = Initial investment / Cash flows

       - Product A  = 170,000/60,000

                            = 2.83 Years

      - Product B   = 380,000/130,000

                            =2.92 Years

2) Net Present Value

   - Product A = 28,566.78 +33,137.47 + 38439.46 +44,589.77 + 51,724.14 -170,000 = $26,457.62

  - Product B =61,894.69 + 71,797.84 +83,284.50 +96,611.18 +112,068.97 -380,000 = $45,657.18

3) Internal Rate of Return

   - Product A =22.5%

   - Product B = 21.1%

4) Profitability Index  = Present Value of future Cash flows/ initial investment

      -Product A = $196,457.62/170,000  = 1.16

      -Product B = $425,657.18/380,000 =1.12

5) Simple Rate of Return = (incremental Revenue - Incremental expenses)/initial investment

therefore the formula can be expressed Net income /initial investment

   - Product A = $26,000/170,000 =15.3%

   -Product B = 54,000/380,000 = 14.2%

Explanation:

                                          PRODUCT A      PRODUCT B

Revenues                         $250,000            $350,000

Variable expenses         -$120,000            -$170,000

Depreciation                  -$34,000              -$76,000

Fixed operating costs   -$70,000              -$50,000

Net Income                     $26,000               $54,000

Add Depreciation          $34,000                $76,000

Cash Flow                      $60,000                $130,000

Payback period with same annual cash flows is calculated by dividing the initial investment by the cash flow.

To Compute NPV we take cash flows divide by (1+r)^n

the we deduct initial investment from the total of Present value cash flows of five years.

For IRR after getting NPV we use financial calculator to calculate is press down shift and IRR/YR

The Discount Factors :

Year 0 = 1

Year 1 = 0.862

Year 2 =0.743

Year 3 = 0.641

Year 4 = 0.552

Year 5 = 0.476

(1) payback period Product A 2.83 years, Product B 2.92 years (2) NPV Product A $26,464, Product B $45,672, (3) IRR Product A 25%, Product B 20%, (4) Profitability index Product A 1.15, Product B 1.12, (5) Simple rate of return Product A 15.3%, Product B 14.2%

Explanation:

To calculate the pay back period

Product A. Product B

Sales 250,000. 350,000

Less:

Variable cost 120,000. 170,000

Depreciation. 34,000. 76,000

Fixed operating cost 70,000. 50,000

Net income. 26,000. 54,000

Add: Depreciation. 34,000. 76,000

Net cash inflow. 60,000. 130,000

Pay back period = initial investment / Annual cash inflow

For product A

Initial investment = $170,000, Annual cash inflow =$60,000

=170,000/60,000

=2.83 years

For product B

Initial investment =$380,000, Annual cash inflow =$130,000

=380,000/130,000

=2.92 years

To calculate NPV for each product

For product A

Initial investment = $170,000, Annual cash inflow =$60,000

Discount Factor = 16% for 5 years

DF = 1 - (1 + i) ∧-n / i

= 1 - (1 + 0.16)∧-5 / 0.16

= 1- (1.16)∧-5 / 0.16

= 1- 0.4761 / 0.16

= 0.5239/0.16

=3.2744

PV of cash inflow = 60,000 × 3.2744 = $196,464

NPV of Product A = PV of cash inflow - PV of cash outflow

= $196,464 - 170,000

= $26,464

For product B

Initial investment =$380,000, Annual cash inflow =$130,000

DF = 16% for 5years = 3.2744

PV of cash inflow = $130,000 × 2.2744 = $425,672

NPV of Product B = PV of cash inflow - PV of cash outflow

$425,672 - $380,000

=$45,672

To calculate the IRR

DF = 25% for 5years using the formula 1 - (1 + i )∧-n / i

= 1 - (1 + 0.25)∧-5 / 0.25

= 1 - (1.25)∧-5 / 0.25

= 1 - 0.3277 / 0.25

= 0.6723/ 0.25

=2.6892

PV of cash inflow =$60,000 × 2.6892 = $161,352

NPV of Product A = PV of cash inflow - PV of cash outflow

= $161,352 - $170,000

=-$8,648

For product B

DF = 20% for 5 years using the above formula

1 - ( 1 + 0.2)∧-5 / 0.2

= 1 - (1.2)∧-5 / 0.2

=1 - 0.4019 / 0.2

= 0.5981/0.2

=2.9905

PV of cash inflow =$130,000 × 2.9905 = $388,765

NPV of Product B = PV of cash inflow -PV of cash outflow

= $388,765 -$380,000

=$8,765

Therefore IRR Product A =25%, Product B =20%

To calculate the profitability index

PI = PV of cash inflow / initial investment

For product A

= PV of cash inflow = $196,464, initial investment = $170,000

= $196,464 / $170,000

=1.15

For product B

PV of cash inflow =$425,672, initial investment = $380,000

= $425,672/$380,000

=1.12

To calculate simple rate of return

Simple rate of return = Annual income / initial investment

For product A

Annual income =$26,000, initial investment =$170,000

=$26,000 / $170,000

=0.1529 × 100

= 15.29

=15.3% Approximately

For product B

Annual income =$54,000, initial investment =$380,000

=$54,000/ $380,000

=0.142 × 100

= 14.2%

Payback period choose Product A

NPV choose Product B

IRR choose Product A

PI choose Product A

Simple rate of return choose Product A

88 because 4 plus 4 equals 8. 40 plus 40 equals 80. 80 plus 8 equals 88