Question

Question 4 a) Tiga projek kerja-kerja awam yang saling eksklusif, Alpha, Gamma dan Beta kini sedang dipertimbangkan bagi menyediakan prasarana kemudahan awam melalui peruntukan Rancangan Malaysia Kesebelas, RMK11. Kos dan faedah masing- masing projek dimasukkan ke dalam Jadual S4(a) di bawah. Setiap projek mempunyai hayat berguna selama 50 tahun, dan MARR adalah 10% setahun. Projek yang manakah antara projek-projek ini harus dipilih sebagai project terbaik mengikut peruntukan yang disediakan? (Nota: Gunakan prosedur nisbah B-C peningkatan) Three mutually exclusive alternative public-works projects; Alpha, Gamma and Beta are currently under consideration in providing the public infrastructure facilities via Eleventh Malaysia Plan budget. Their respective costs and benefits are included in Table Q4(a) below. Each of the projects has a useful life of 50 years, and MARR is 10% year. Which, if any of these projects should be selected as the best project that follows the provided budget? Note: Use incremental B-C ratio procedure). Jadual S4(a)/Table Q4(a Alpha Gamma Beta Pelaburan kapital Capital investment Kos penyelenggaraan tahunan Annual operating and maintenance costs Nilai pasaran Market value Faedah tahunan Annual benefit RM8,500,000RM10,000,000 RM12,000,000 operasi dan M750,000RM725,000 RM1,250,000 RM1,750,000 RM2,000,000 RM2,150,000RM2,265,000RM2,500,000 RM700,000 (8 markahlmarks)

Answer 1

	Alpha	Gamma	Beta
Capital Investment	8,500,000	10,000,000	12,000,000
Annual O $ M Cost	750,000	725,000	700,000
Annual Benefits	2,150,000	2,265,000	2,500,000
Net Annual Benefits(Benefits – O&M Cost)	1,400,000	1,540,000	1,800,000
Market Value	1,250,000	1,750,000	2,000,000

MARR = 10% per year

Life all the alternatives = 50 years

For calculating incremental Benefit cost ratio, first we have to calculate the Incremental Cash flows.

First

Calculating the Incremental cash flow between Gamma and Alpha

(Cash Flows of Gamma – Cash Flows of Alpha)

	Alpha	Gamma	ICF of Gamma and Alpha
Capital Investment	8,500,000	10,000,000	1,500,000
Net Annual Benefits(Benefits – O&M Cost)	1,400,000	1,540,000	140,000
Market Value	1,250,000	1,750,000	500,000

Present Worth of the Benefits = 140,000 (P/A, 10%, 50)

Present Worth of the Benefits = 140,000 (9.9148) = 1,388,072

Present Worth of the Cost = 1,500,000 – 500,000 (P/F, 10%, 50)

Present Worth of the Cost = 1,500,000 – 500,000 (0.0085) = 1,495,750

Incremental B-C Ratio = PW of incremental Benefits / PW of Incremental Costs

Incremental B-C Ratio = 1,388,072 / 1,495,750 = 0.928

Incremental B-C Ratio of Gamma and Alpha is less than one, SELECT the lowest cost alternative, ALPHA.

Second

Now calculate the incremental Cash flow between BETA and ALPHA

(Cash Flows of Beta – Cash Flows of Alpha)

	Alpha	Beta	ICF of Beta and Alpha
Capital Investment	8,500,000	12,000,000	3,500,000
Net Annual Benefits(Benefits – O&M Cost)	1,400,000	1,800,000	400,000
Market Value	1,250,000	2,000,000	750,000

Present Worth of the Benefits = 400,000 (P/A, 10%, 50)

Present Worth of the Benefits = 400,000 (9.9148) = 3,965,920

Present Worth of the Cost = 3,500,000 – 750,000 (P/F, 10%, 50)

Present Worth of the Cost = 3,500,000 – 750,000 (P/F, 10%, 50)

Present Worth of the Cost = 3,500,000 – 750,000 (0.0085) = 3,493,625

Incremental B-C Ratio = PW of incremental Benefits / PW of Incremental Costs

Incremental B-C Ratio = 3,965,920 / 3,493,625 = 1.135

Incremental B-C Ratio of Beta and Alpha is MORE than one, SELECT the HIGHEST cost alternative, BETA.

Finally Select the alternative BETA.