Question

6. The equivalent annual annuity approach - Evaluating projects with unequal lives Aa Aa E Evaluating projects with unequal lives Bidget Corp. is a Canadian firm that wants to expand its business internationally. It is considering potential projects in both Spain and Ukraine, and the Spanish project is expected to take six years, whereas the Ukrainian project is expected to take only three years. However, the firm plans to repeat the Ukrainian project after three years. These projects are mutually exclusive, so Bidget Corp.'s CFO plans to use the equivalent annual annuity approach to analyze both projects. The expected cash flows for both projects follow: If Bidget Corp.'s cost of capital is 10%, what is the NPV of the Spanish project? Project: Year 0: Year 1: Year 2: Year 3: Year 4: Year 5: Year 6: Spanish -$1,120,000 $370,000 $390,000 $420,000 $330,000 $220,000 $95,000 Project: Ukrainian Year 0: -$490,000 Year 1: $250,000 Year 2: $265,000 Year 3: $275,000 $256,359 $296,837 $283,345 $269,852

Answer 1

Solution :

If Bidget Corp.'s cost of capital is 10 %, the NPV of the Spanish project is = $ 269,852.0570

= $ 269,852 ( when rounded off to the nearest whole number )

If Bidget's Corp.'s cost of capital is 10 %, the NPV of the Ukranian project is = $ 162,892.5620

= $ 162,892.56 ( when rounded off to two decimal places )

The EAA of the Ukraine project is = $ 65,501.5106

= $ 65,501.51 ( when rounded off to two decimal places )

The EAA of the Spanish project is = $ 61,960.0239

= $ 61,960.02 ( when rounded off to two decimal places )

If the CFO uses the EAA approach to decide which project to undertake, he should choose the Ukranian Project as it has the higher EAA.

Please find the attached screenshot of the excel sheet containing the detailed calculation for the solution.

19.03.2020 - Excel File Home Insert Page Layout Formulas Data Review View Help ? Tell me what you want to do R23 fix : x B r C A D E F G H I J K L M N O 1 (3) (3) Statement showing calculation of Net Present value and Equivalent annual annuity of the Spanish Project Sl.No. Particulars Expected Cash Year PV Factor Discounted Cash Flows (2) @ 10% Flows (1) (4)=(1) * (3) 1 Cash outflow Year 0 $ 1,120,000.00 0 1.0000l $ 1.120.000.0000 Total of Cash Outflows (A) $ 1,120,000.0000 3 Cash Inflow Year 1 $ 370,000.00 110.90911 $ 336.363.6364 4 Cash Inflow Year 2 $ 390,000.00 2 0 .8264 $ 322,314.0496 5 Cash Inflow Year 3 $ 420,000.00 3 0.75131 $ 315.552.2164 6 Cash Inflow Year 4 | $ 330,000.00 4 0.68301 $ 225.394.4403 7 Cash Inflow Year 5 $ 220,000.00 5 0 .62091 $ 136,602.6911 8 Cash Inflow Year 6 $ 95,000.00 6 0 .56451 $ 53,625.0234 9 Total of Discounted Cash Inflows (B) $1,389,852.0570 10 Net Present Value = (B) - (A) $ 269,852.0570 PVIFA at 10 % for 6 years $ 4.3553 12 EAA = (10) / (11) = NPV / PVIFA at 10 % for 6 years $ 61,960.0239 Statement showing calculation of Net Present value and Equivalent annual annuity of the Ukranian Project Sl.No. Particulars Expected Year PV Factor Discounted Cash Cash Flows (2) @ 10% Flows (4)=(1) * (3) 1 Cash outflow Year 0 $ 490,000.00 0 1.0000 $ 490,000.0000 Total of Cash Outflows (A) $ 490,000.0000 3 Cash Inflow Year 1 $ 250,000.00 1 0.9091 $ 227,272.7273 4 Cash Inflow Year 2 $ 265,000.00 2 0.8264 $ 219,008.2645 5 Cash Inflow Year 3 $ 275,000.00 3 0.7513 $206,611.5702 Total of Discounted Cash Inflows (B) $ 652,892.5620 Net Present Value = (B) - (A) $ 162,892.5620 PVIFA at 10 % for 3 years 2.4869 9EAA = (7) / (8) = NPV / PVIFA at 10 % for 3 years / $ 65,501.5106