Question

an investor has a budget of $5 million. he can invest in the projects shown above. if the cost of capital is 7%, what investment or investments should he make?

Initial Investment Cash flow Project A $5 million $2 million per year for four years Project B 53 million $1 million per year for five years Project C $2 million $1 million per year for four years Project D $3 million $1.5 million per year for three years An investor has a budget of $5 million. He can invest in the projects shown above. If the cost of capital is 7%, what inve O A. Project O B. Project B OC. Project B and Project C OD. Project C and Project D

Answer 1

NPV = PV of Cash Inflows - PV of Cash Outflows

NPV(A) = [$2,000,000 * {(1 - 1.07^-4) / 0.07}] - $5,000,000

= [$2,000,000 * {0.2371 / 0.07}] - $5,000,000

= [$2,000,000 * 3.3872] - $5,000,000

= $6,774,422.51 - $5,000,000 = $1,774,422.51

NPV(B) = [$1,000,000 * {(1 - 1.07^-5) / 0.07}] - $3,000,000

= [$1,000,000 * {0.2870 / 0.07}] - $3,000,000

= [$1,000,000 * 4.1002] - $3,000,000

= $4,100,197.44 - $3,000,000 = $1,100,197.44

NPV(C) = [$1,000,000 * {(1 - 1.07^-4) / 0.07}] - $2,000,000

= [$1,000,000 * {0.2371 / 0.07}] - $2,000,000

= [$1,000,000 * 3.3872] - $2,000,000

= $3,387,211.26 - $2,000,000 = $1,387,211.26

NPV(D) = [$1,500,000 * {(1 - 1.07^-3) / 0.07}] - $3,000,000

= [$1,500,000 * {0.1837 / 0.07}] - $3,000,000

= [$1,500,000 * 2.6243] - $3,000,000

= $3,936,474.07 - $3,000,000 = $936,474.07

Project B and C together have greater NPV than what the Project A individually provides. they also fully exhaust the budget.

So, Project B and C should be selected and hence, Option "C" is correct.