Problem 8-23 Comprehensive Problem LO8-1, LO8-2, L08-3, Lo8-5, Lo8-6) manager fo

Question

Problem 8-23 Comprehensive Problem LO8-1, LO8-2, L08-3, Lo8-5, Lo8-6) manager for Sage Company, has an opportunity to manufacture and sell one of two new products for a five-year Lou Barkow, a divisional period. His annual pay raises are determined by his division's return on investment (ROn. which has exceede years. He has computed the cost and revenue estimates for each product as follows Initial investment Cost of equipment (zero salvage value) Annual revenues and costs: Sales revenues $290.000 s 500.000 $ 450,000 5 210,000 Variable expenses Depreciation expense Fixed out-of-pocket operating costs $350,000 $160,000 S 58.000 S 80,000 S 100,000 S 60,000 The company's discount rate is 16%. Click here to view Exhibit 88-1 and Exhibit RB-2, to determine the appropriate discount factor using tables Required 1. Calculate the payback period for each product (Round your answers to 2 decimal places.) Product A Product B Payback period ayear years

Explanation / Answer

Step 1 Calculation of payback period

Step 2 - Calculatation of net present value

Cumulative annuity @ 16% for 5 years

Formula = [1/(1+r)]n = [1/1.16]5

Where r = 16% or 0.16 and n = 5 years

Step 3 - Calculation of Internal rate of return (IRR) (Rate at which present value of cash inflows equals the cash outflow)

Since Cummulative factor required is 2.63 and 2.78 (payback period) for product A and B

Product A

Cumulative factor 2.63 apporoximate 26% hence :-

Assumption lower rate is 25% and higher rate is 27%

IRR = lower rate + [(Cummulative annuity of lower rate - 2.63)/cummulative annuity of lower rate - Higher rate annuity)] * (Higher rate - lower rate)

Here = Higher rate assumed = 27%

Lower rate assumed = 25%

Cumulative annuity @27% for 5 years = 2.583

Cumulative annuity @25% for 5 years = 2.689

Product B

Cumulative factor of 2.78 year is required to calculate IRR.

Cumulative annuity at @23% and 24% approximate 2.78.

Assumed lower rate = 23%

Higher rate = 24%

Cumulative annuity @23% for 5 years = 2.803

Cumulative annuity @24% for 5 years = 2.745

IRR = 23% + [(2.803 - 2.78)/(2.803 - 2.745)] * (24 - 23)

IRR = 23.4%

Step 4 - Calculation of profitability Index

Step 5 - Calculation of Simple rate of return

Simple rate of return

(Net income / Investment)

Particulars Product A Product B Sales $350000 $450000 Less. : Variable cost $160000 $210000 Fixed cost $80000 $60000 Net annual cash inflow $110000 $180000 Initial Investment $290000 $500000 Payback period (cash outflow/Average annual cash inflow) 2.63 years 2.78 years

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