Question 3: An investment company is considering the following independent proje

Question

Question 3: An investment company is considering the following independent projects having 20 years uwet lives. In terms of initial investments, the current budget for this company allows no more than be spent. Use the B-C ratio method and the annual worth to decide which project or a should be selected assuming an interest rate of 20% per year. diann 00.000 to ol Projeet Initial Investment Annual Costs Annual Benefits 15,000,000 12,000,000 S10,000,000 $2,500,000 2500,000 $5,000,000 -?? S1,700,000 $1,500,000 $4,700,000 $3,700,000

Explanation / Answer

(A) Conventional B/C Ratio (BCR) = PV of annual benefit / (Initial investment + PV of annual cost)

BCR, Project A: [$5,000,000 x PVIFA(20%, 20)] / [$15,000,000 + $2,500,000 x PVIFA(20%, 20)]

= ($5,000,000 x 4.8696**) / [$15,000,000 + ($2,500,000 x 4.8696**)]

= 24,348,000 / (15,000,000 + 12,174,000) = 24,348,000 / 27,174,000 = 0.896

BCR, Project B: [$4,700,000 x PVIFA(20%, 20)] / [$12,000,000 + $1,700,000 x PVIFA(20%, 20)]

= ($4,700,000 x 4.8696**) / [$12,000,000 + ($1,700,000 x 4.8696**)]

= 22,887,120 / (12,000,000 + 8,278,320) = 22,887,120 / 20,278,320 = 1.13

BCR, Project C: [$3,700,000 x PVIFA(20%, 20)] / [$10,000,000 + $1,500,000 x PVIFA(20%, 20)]

= ($3,700,000 x 4.8696**) / [$10,000,000 + ($1,500,000 x 4.8696**)]

= 18,017,520 / (10,000,000 + 7,304,400) = 18,017,520 / 17,304,400 = 1.04

Since project B and project C each has a BCR > 1 and total outlay is within budget ($12,000,000 + $10,000,000 = $22,000,000 < $23,000,000), projects B and C should be selected.

(B) Annual worth (AW) of all projects are computed below. Here, Net annual benefit = Annual benefit - Annual cost.

AW, Project A ($): - 15,000,000 x A/P(20%, 20) + (5,000,000 - 2,500,000)

= - 15,000,000 x 0.2054** + 2,500,000 = - 3,081,000 + 2,500,000 = - 581,000

AW, Project B ($): - 12,000,000 x A/P(20%, 20) + (4,700,000 - 1,700,000)

= - 12,000,000 x 0.2054** + 3,000,000 = - 2,464,800 + 3,000,000 = 535,200

AW, Project C ($): - 10,000,000 x A/P(20%, 20) + (3,700,000 - 1,500,000)

= - 10,000,000 x 0.2054** + 2,200,000 = - 2,054,000 + 2,200,000 = 146,000

Since project B and project C each has a positive AW of net benefits and total outlay is within budget ($12,000,000 + $10,000,000 = $22,000,000 < $23,000,000), projects B and C should be selected.

**Using PVIFA and A/P Factor tables.

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