Question

Problem (2): Consider the following three mutually exclusive alternatives. MARR is 10%. Alternative 1 10,000 Alternative 2 14,500 Alternative 3 20,000 $3,000 increasing by 500 each year thereafter negligible $5,000 Initial investment Annual yielded returns Salvage Value Service life $5,000 $5,000 negligible 6 a) Compute the payback (PB) period and discounted PB period of each alternative. Based on the PB period, which alternative do you recommend? b) Using Annual-worth analysis, which alternative do you recommend?

Answer 1

Question a: Calculation of Payback Period Alternative 1: Year Cash Flows Cumulative Cash Flows 0 -10000 -10000 1 5000 -5000 2 50000 3 10000 10000 Payback period for alternative 1 is 2 years Alternative 2: Year Cash Flows Cumulative Cash Flows 0 -14500 -14500 5000 -9500 5000 -4500 5000 500 5000 5500 5000 10500 6 5000 15500

Payback period for Alternative 2 = Years with full recovery + (balance unrecovered at the end of year / cash flow during the year) = 2 years +(4500/5000) = 2.9 years Payback period for the alternative 2 is 2.9 years 0 Alternative 3: Year Cash Flows Cumulative Cash Flows -20000 -20000 3000 -17000 3500 -13500 4000 -9500 4500 -5000 5000 5500 5500 Payback Period for the alternative 3 is 5 years

Payback period of Alternative 1 is lower than Alternative 2 and 3 hence Alternative 1 should be selected.

Calculation of Discounted Payback Period Altenative 1: Year Cash Flows Discount Factor @10% Discounted Cash Flows Cumulative Cash Flows A B / C = 1/(1+10%)^n D=B*C -10000 -10000 -10000 5000 0.909090909 4545.454545 -5454.545455 5000 0.826446281 4132.231405 -1322.31405 10000 0.751314801 7513.148009 6190.833959 w NP Payback Period for Alternative 1 = Years with full recovery + (balance unrecovered at the end of year / cash flow during the year) = 2 years +($1322.31405 / $7513.148009) = 2.176 years Therefore, Payback period for the Alternative 1 is 2.18 years

Alternative 2: Year Cash Flows Discount Factor @10% Discounted Cash Flows Cumulative Cash Flows C = 1/(1+10%)^n D=B*C - 14500 -14500 -14500 5000 0.909090909 4545.454545 -9954.545455 5000 0.826446281 4132.231405 -5822.31405 5000 0.751314801 3756.574005 -2065.740045 5000 0.683013455 3415.067277 1349.327232 5000 0.620921323 3104.606615 4453.933847 5000 0.56447393 2822.36965 7276.303497 Payback Period for Alternative 2 = Years with full recovery + (balance unrecovered at the end of year / cash flow during the year) = 3 years + ($2065.740045 / $3415.067277) = 3.60489 years Payback period for the alternative 2 is 3.60 years

Alternative 3: Year Cash Flows Discount Factor @10% Discounted Cash Flows Cumulative Cash Flows C = 1/(1+10%)^n D=B*C -20000 -20000 -20000 3000 0.909090909 2727.272727 -17272.72727 3500 0.826446281 2892.561983 -14380.16529 4000 0.751314801 3005.259204 -11374.90609 4500 0.683013455 3073.560549 -8301.345537 5000 0.620921323 3104.606615 -5196.738921 5500 0.56447393 3104.606615 -2092.132306 6 Payback Period for Alternative 3 = Years with full recovery + (balance unrecovered at the end of year / cash flow during the year) Payback period is more than project's life

Discounted Payback period of Alternative 1 is lower than 2 and 3 hence, Alternative 1 should be selected

Question b: Calculation of Net Present Value Alternative 1 Alternative 2 Alternative 3 Year Cash Flows Discount Factor @10% Discounted Cash Flows Cash Flows Discount Factor @10% Discounted Cash Flows Cash Flows Discount Factor @10% Discounted Cash Flows A B / C = 1/(1+10%)^n D=B*C F= 1/(1+10%)^n G=E*F H 1 = 1/(1+10%)^n J=H*1 0 -10000 -10000 -14500 -14500 -20000 -20000 5000 0.909090909 4545.454545 5000 0.909090909 4545.454545 3000 0.909090909 2727.272727 5000 0.826446281 4132.231405 5000 0.826446281 4132.231405 3500 0.826446281 2892.561983 10000 0.751314801 7513.148009 5000 0.751314801 3756.574005 4000 0.751314801 3005.259204 5000 0.683013455 3415.067277 4500 0.683013455 3073.560549 5000 0.620921323 3104.606615 5000 0.620921323 3104.606615 5000 0.56447393 2822.36965 5500 0.56447393 3104.606615 NPV 6190.833959 7276.303497 -2092.132306