Ecodevelopment Company has two mutually exclusive construction projects to evaluate. Each type of project can be duplicated repeatedly in different geographic locations around the country, but each requires a very different set of assets to construct. Thus, Ecodevelopment uses the equivalent annual annuity method to evaluate such projects. Project type A costs $6 million initially and generates expected end-of-year cash flows of $3 million, $5 million, and then $10 million when it is sold after 3 years. Project type B costs $9 million initially and has projected end-of-year cash flows of $3, $3, $6, and $6 million in Year 1 through Year 4, and then $10 million in Year 5. The project types are equally risky and the firm's cost of capital is 12 percent. What is the EAA of the higher valued project type?
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A. B. C. D. E.C
Calculate each project's original life NPV:
NPV(A) = $3.0(PVIF(12%,1)) + $5.0(PVIF(12%,2)) + $10.0(PVIF(12%,3)) - $6.0
= $3.0(0.8929) + $5.0(0.7972) + $10.0(0.7118) - $6.0
= $2.6787 + $3.9860 + $7.1180 - $6.0
= $7.7827 million = $7,782,700.
NPV(B) = $3.0(PVIFA(12%,2)) + $6.0(PVIFA(12%,2))(PVIF(12%,2))
+ $10.0(PVIF(12%,5)) - $9.0
= $3.0(1.6901) + $6.0(1.6901)(0.7972) + $10.0(0.5674) - $9.0 =
$5.0703 + $8.0841 + $5.6740 - $9.0
= $9.8284 million = $9,828,400.
Calculate the equivalent annual annuity:
NPV(A) = $7,782,700 = EAA(A)(PVIFA(12%,3))
EAA(A) = $7,782,700/2.4018 = $3,240,361.40.
NPV(B) = $9,828,400 = EAA(B)(PVIFA(12%,5))
EAA(B) = $9,828,400/3.6048 = $2,726,475.81.