Question

Question 3 Sebuah syarikat utiliti mengunakan generator kuasa diesel untuk membekalkan kuasa tunggu sedia kepada stesen pengepaman. Wujud peluang bagi syarikat untuk mengunakan gas asli dalam membekalkan kuasa bagi generator-generator, tetapi syarikat harus menunggu beberapa tahun lagi bagi gas asli dapat dibekalkan ke kawasan pendalaman. Syarikat menganggarkan dengan bertukar pada sumber gas asli, mereka dapat menjimatkan kos sebanyak RM13,000 setahun untuk tempoh 10 tahun, mulai 3 tahun dari sekarang. Bagi kadar faedah sebanyak 6%, dapatkan A utility company provides standby power to pumping stations using diesel-powered generators. An alternative has arisen whereby the utility could use natural gas to power the generators, but it will be few years before the gas is available at remote sites. The utility estimates that by switching to gas, it will save RM13,000 per year for 10 years, starting 3 years from now. At an interest rate of 6% per year, determin a) Nilai kini dan nilai tahunan untuk tempoh 12 tahurn The present worth and the annual worth over 12 years (4 markah/marks) b) Sebagai pilihan, syarikat utiliti boleh membeli sebuah generator kuasa diesel yang baru. Kirakan nilai kini untuk generator yang mempunyai kos pertama (kos beli) sebanyak RM52,000, jangka hayat 10 tahun, dan kos operasi tahunan sebanyak RM13.000 untuk 4 tahun pertama, bertambah dengan kadar 10% setahun selepas itu. Alternatively, the utility company could invest on a new diesel powered generator Calculate the present worth for the diesel-powered generator that has an initial cost of RM52,000, a life of 10 years, and an annual operating cost of RM13,000 for the first 4 years, increasing by 10% per year thereafter. (6 markah/marks) c) Syarikat berkeputusan untuk mengantikan generator beberapa tahun kemudian. Syarikat ingin menyimpan RM40,000 ke dalam akaun pelaburan dan berharap umlah akan bertambah kepada RM60,000 pada masa anya diperlukan (andaikan harga generator kuasa diesel baru yang akan dibeli berharga sekitar RM60,000 beberapa tahun kemudian). Berapa lamakah masa di ambil untuk pelaburan mencecah jumlah yang diharapkan jika kadar faedah ialah 12% setahun? The company decided to replace the generator several years later. The company would like to put aside RM40,000 into the investment account and would like the amount to reach RM60,000 during that time (assuming the price of the new diesel powered generator will be around this price several years later). How long did it take for the investment to reach the desired amount if the interested rate is 12% per year? (4 markah/marks)

Answer 1

(a) Present value (PV) or Present worth is the current value of a future sum of money or stream of cash flows given a specified rate of return.

The formula for calculating present worth is as follows:-

PV = FV/(1+I)ⁿ

= RM 13000/(1+0.06)12

= RM 13000/0.497

= RM 26157

Now, let us calculate the Annual Worth. Before calculating Annual Worth, let us discuss the term briefly:-

Annual Worth (AW) Analysis is defined as the equivalent uniform annual worth of all estimated receipts (income) and disbursements (costs) during the life cycle of a project. It is defined as the cost /year of owning and operating an asset over its lifetime. The Annual Worth is calculated as follows:-

ANNUAL WORTH = P{i(1+i)ⁿ/(1+i)ⁿ-1}

= 26157{0.06(1+0.06)¹²/(1+0.06)¹² -1}

= 26157 (0.06*2.01/2.01-1)

= 26157(0.1206/1.01)

= RM 3123 (approx)

(b) The net present worth in case of new diesel power generator can be calculated as follows:

Initial Cost = RM 52000

Annual Operating Cost = RM 13000

Let us prepare a statement of cash flows in the following manner:-

YEAR	CASH FLOWS	PVF@6%	PRESENT VALUE
1	13000	0.943	12259
2	13000	0.890	11570
3	13000	0.840	10920
4	13000	0.792	10296
5	14300	0.747	10682
6	15730	0.705	11090
7	17303	0.665	11506
8	19033	0.627	11934
9	20937	0.592	12395
10	23031	0.558	12851

The sum total of present value is equal to RM 115503. So, the Present worth can be calculated in the following manner:-

Present Worth = PV of cash inflows -Initial Cash Outflow

=RM 115503 - RM 52000 = RM 63503

(c) In this part, the Present Value is given as RM 40000 and the Future value is given as RM 60000 and the rate of interest is 12% per year. In order to calculate the time period in which the investment will reach the desired amount can be calculated by putting these values in the Present Value formula as follows:-

PV = FV/(1+i)ⁿ

40000 = 60000/ (1+0.12)ⁿ

60000/40000 = (1.12)ⁿ

1.5 = (1.12)ⁿ

(1.12)⁴ = (1.12)ⁿ

So, n=4 years  

Thus, it will take 4 years for the investment to reach to RM 60000 if the interest rate is 12% per year.