Capital Budgeting Decision to Open Gold Mine Now or Later - CA Final SFM

Question: - XYZ Ltd owns an unused Gold Mine that will cost Rs. 10, 00, 000 to reopen. If XYZ Ltd opens the mine, XYZ expect to be able to extract 1,000 ounces of Gold a year for each of three years. After that the deposit will be exhausted. The Gold Price is currently Rs. 5000 an ounces, and each year the price is likely to rise or fall by Rs. 500 from its level at start of year. The extraction cost is Rs. 4600 an ounces and the discount rate is 10 percent.

Should XYZ Ltd open the mine or delay one year in the hope of a rise in the Gold Price? 

Solution: -

When XYZ Ltd opens Gold Mine Now

Cash Inflows are when Gold Mine opened now

First Year		Second Year		Third Year
Joint Probability	Annual Cash Inflow	Joint Probability	Annual Cash Inflow	Joint Probability	Annual Cash Inflow
.50	5500	.50*.50 =.25	6000	.50*.50*.50=.125	6500
.50	4500	.50*.50 =.25	5000	.50*.50*.50=.125	5500
		.50*.50 =.25	5000	.50*.50*.50=.125	5500
		.50*.50 =.25	4000	.50*.50*.50=.125	4500
				.50*.50*.50=.125	5500
				.50*.50*.50=.125	4500
				.50*.50*.50=.125	4500
				.50*.50*.50=.125	3500
Annual Cash Inflow	5000	Annual Cash Inflow	5000	Annual Cash Inflow	5000
Annual Cash Outflow	4600	Annual Cash Outflow	4600	Annual Cash Outflow	4600
Net Cash Inflow	400	Net Cash Inflow	400	Net Cash  Inflow	400
PV Factor	.909	PV Factor	.826	PV Factor	.751
Total Net Cash Inflow Per Ounce			994.8
Total Net Cash Inflow			1000*994.8 =994800
Initial Cash Outflow			(1000000)
NPV			Rs. (5200)

XYZ Ltd should not Open Mine now because NPV = (Rs. 5200).

When Gold Mine is opened one year later

When Gold Mine is opened one year later than we should calculate NPV at Y1 and then we discount NPV at PV Factor for one year

First Year		Second Year		Third Year
Joint Probability	Annual Cash Inflow	Joint Probability	Annual Cash Inflow	Joint Probability	Annual Cash Inflow
.50	6000	.50*.50 =.25	6500	.50*.50*.50=.125	7000
.50	5000	.50*.50 =.25	5500	.50*.50*.50=.125	6000
		.50*.50 =.25	5500	.50*.50*.50=.125	6000
		.50*.50 =.25	4500	.50*.50*.50=.125	5000
				.50*.50*.50=.125	6000
				.50*.50*.50=.125	5000
				.50*.50*.50=.125	5000
				.50*.50*.50=.125	4000
Annual Cash Inflow	5500	Annual Cash Inflow	5500	Annual Cash Inflow	5500
Annual Cash Outflow	4600	Annual Cash Outflow	4600	Annual Cash Outflow	4600
Net Cash Inflow	900	Net Cash Inflow	900	Net Cash  Inflow	900
PV Factor	.909	PV Factor	.826	PV Factor	.751
Total Net Cash Inflow Per Ounce			2238.3
Total Net Cash Inflow			1000*2238.3 = 2238300
Initial Cash Outflow			(1000000)
NPV at Y1			Rs. 1238300
NPV at Y0			1238300*.909 = 1125615
Total NPV at Y0			(1125615*.50) + (0*.50)# = Rs. 562807

XYZ Ltd should Open Mine at one year later because NPV = Rs. 562807.

# Expiation: - When Gold mine is opened one year later than there is equal chance that price will Rs. 5500 and Rs. 4500, when gold price is Rs. 4500 than XYZ ltd will not open the Gold Mine in such Case NPV will be Rs. 0 at Y1.  

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