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.

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$)$ $ $370,000$ $ $570,000$

Annual revenues and costs:

Sales revenues $ $400,000$ $ $480,000$

Variable expenses $ $180,000$ $ $214,000$

Depreciation expense $ $74,000$ $ $114,000$

Fixed out$-$of$-$pocket operating costs $ $88,000$ $ $68,000$

The company$$s discount rate is $20\%$

Click here to view Exhibit $14$B$-1$ and Exhibit $14$B$-2,$ to determine the appropriate discount factor using tables.

This is a great review problem that reinforces the individual concepts covered using a comprehensive example.

To answer the questions, you must first calculate the annual net cash inflows as follows: Sales revenue minus variable expenses minus fixed out$-$of$-$pocket operating costs.

Then you will calculate the following: payback period $($even flows$),$ net present value $($NPV$),$ internal rate of return $($IRR$)$ and profitability index.

$1.$ Calculate the payback period for each product.

$2.$ Calculate the net present value for each product.

$3.$ Calculate the internal rate of return for each product.

$4.$ Calculate the profitability index for each product. EXHIBIT $14$B$-1$

Present Value of $$1$;

$1$

$($

$1$

$+$

$$

$)$

$$

Periods $4\%5\%6\%7\%8\%9\%10\%11\%12\%13\%14\%15\%16\%17\%18\%19\%20\%21\%22\%23\%24\%25\%$

$10\mathrm{.}9620\mathrm{.}9520\mathrm{.}9430\mathrm{.}9350\mathrm{.}9260\mathrm{.}9170\mathrm{.}9090\mathrm{.}9010\mathrm{.}8930\mathrm{.}8850\mathrm{.}8770\mathrm{.}8700\mathrm{.}8620\mathrm{.}8550\mathrm{.}8470\mathrm{.}8400\mathrm{.}8330\mathrm{.}8260\mathrm{.}8200\mathrm{.}8130\mathrm{.}8060\mathrm{.}800$

$20\mathrm{.}9250\mathrm{.}9070\mathrm{.}8900\mathrm{.}8730\mathrm{.}8570\mathrm{.}8420\mathrm{.}8260\mathrm{.}8120\mathrm{.}7970\mathrm{.}7830\mathrm{.}7690\mathrm{.}7560\mathrm{.}7430\mathrm{.}7310\mathrm{.}7180\mathrm{.}7060\mathrm{.}6940\mathrm{.}6830\mathrm{.}6720\mathrm{.}6610\mathrm{.}6500\mathrm{.}640$

$30\mathrm{.}8890\mathrm{.}8640\mathrm{.}8400\mathrm{.}8160\mathrm{.}7940\mathrm{.}7720\mathrm{.}7510\mathrm{.}7310\mathrm{.}7120\mathrm{.}6930\mathrm{.}6750\mathrm{.}6580\mathrm{.}6410\mathrm{.}6240\mathrm{.}6090\mathrm{.}5930\mathrm{.}5790\mathrm{.}5640\mathrm{.}5510\mathrm{.}5370\mathrm{.}5240\mathrm{.}512$

$40\mathrm{.}8550\mathrm{.}8230\mathrm{.}7920\mathrm{.}7630\mathrm{.}7350\mathrm{.}7080\mathrm{.}6830\mathrm{.}6590\mathrm{.}6360\mathrm{.}6130\mathrm{.}5920\mathrm{.}5720\mathrm{.}5520\mathrm{.}5340\mathrm{.}5160\mathrm{.}4990\mathrm{.}4820\mathrm{.}4670\mathrm{.}4510\mathrm{.}4370\mathrm{.}4230\mathrm{.}410$

$50\mathrm{.}8220\mathrm{.}7840\mathrm{.}7470\mathrm{.}7130\mathrm{.}6810\mathrm{.}6500\mathrm{.}6210\mathrm{.}5930\mathrm{.}5670\mathrm{.}5430\mathrm{.}5190\mathrm{.}4970\mathrm{.}4760\mathrm{.}4560\mathrm{.}4370\mathrm{.}4190\mathrm{.}4020\mathrm{.}3860\mathrm{.}3700\mathrm{.}3550\mathrm{.}3410\mathrm{.}328$

$60\mathrm{.}7900\mathrm{.}7460\mathrm{.}7050\mathrm{.}6660\mathrm{.}6300\mathrm{.}5960\mathrm{.}5640\mathrm{.}5350\mathrm{.}5070\mathrm{.}4800\mathrm{.}4560\mathrm{.}4320\mathrm{.}4100\mathrm{.}3900\mathrm{.}3700\mathrm{.}3520\mathrm{.}3350\mathrm{.}3190\mathrm{.}3030\mathrm{.}2890\mathrm{.}2750\mathrm{.}262$

$70\mathrm{.}7600\mathrm{.}7110\mathrm{.}6650\mathrm{.}6230\mathrm{.}5830\mathrm{.}5470\mathrm{.}5130\mathrm{.}4820\mathrm{.}4520\mathrm{.}4250\mathrm{.}4000\mathrm{.}3760\mathrm{.}3540\mathrm{.}3330\mathrm{.}3140\mathrm{.}2960\mathrm{.}2790\mathrm{.}2630\mathrm{.}2490\mathrm{.}2350\mathrm{.}2220\mathrm{.}210$

$80\mathrm{.}7310\mathrm{.}6770\mathrm{.}6270\mathrm{.}5820\mathrm{.}5400\mathrm{.}5020\mathrm{.}4670\mathrm{.}4340\mathrm{.}4040\mathrm{.}3760\mathrm{.}3510\mathrm{.}3270\mathrm{.}3050\mathrm{.}2850\mathrm{.}2660\mathrm{.}2490\mathrm{.}2330\mathrm{.}2180\mathrm{.}2040\mathrm{.}1910\mathrm{.}1790\mathrm{.}168$

$90\mathrm{.}7030\mathrm{.}6450\mathrm{.}5920\mathrm{.}5440\mathrm{.}5000\mathrm{.}4600\mathrm{.}4240\mathrm{.}3910\mathrm{.}3610\mathrm{.}3330\mathrm{.}3080\mathrm{.}2840\mathrm{.}2630\mathrm{.}2430\mathrm{.}2250\mathrm{.}2090\mathrm{.}1940\mathrm{.}1800\mathrm{.}1670\mathrm{.}1550\mathrm{.}1440\mathrm{.}134$

$100\mathrm{.}6760\mathrm{.}6140\mathrm{.}5580\mathrm{.}5080\mathrm{.}4630\mathrm{.}4220\mathrm{.}3860\mathrm{.}3520\mathrm{.}3220\mathrm{.}2950\mathrm{.}2700\mathrm{.}2470\mathrm{.}2270\mathrm{.}2080\mathrm{.}1910\mathrm{.}1760\mathrm{.}1620\mathrm{.}1490\mathrm{.}1370\mathrm{.}1260\mathrm{.}1160\mathrm{.}107$