Question

1. In 2013, Barrick Gold, a Canadian mining company, adopted a plan to accumulate remediation beginning Aug. 2, 2018 at an estimated cost of $32 million. Barrick plans to make equal semiannual payments into a fund earning 5.2% interested compounded semiannually. The first deposit is scheduled for Aug. 1, 2013. Determine the required semiannual deposit. First determine how many payments Barrick will be making. Assume the last payment is made on Feb. 1, 2018 but the funds are not needed until Aug. 1, 2018.

N =            I/Y =               PV =                PMT =             FV =

2. Assume the same facts as in part 1, except on Feb. 1, 2016, due to financial problems, Barrick deposit nothing in the fund. After this date, they resume and make sufficient equal payments to meet their goal of $32 million on Aug. 1, 2018. In other words, they make the same amount of payments in the fund as part 1 from Aug. 1, 2013-Aug. 1, 2015. Determine the first set of required payments and the second set of required payments. Show your work.

3. Barrick is comparing two gold mines.

Mine A:

The mine is expected to make $3.5 billion in year 1, $4.5 billion in year 2, and $5.5 billion in years 3-6 and $4.25 billion in years 7-10. At the end of year 10, Barrick will need to spend $202 million on environmental clean-up costs and expects the residual value to be $200 billion.

Mine B:

The mine is currently in operation and produces $4.1 billion per year. At the end of 10 years the residual value would be $200 billion and no environmental clean-up costs would be necessary.

Which mine should Barrick buy for $142 billion. (To simplify things, assume Net Income is earned one time per year at the end of the year.) The appropriate discount rate is 6.22% compounded quarterly. Show your work.

Answer 1

1). Payments which Barrick needs to make to reach a goal of $32 million by Aug 1, 2018:

Number of payments N = 10

Interest (semi-annual) = Annual interest/2 = 5.2%/2 = 2.6%

Present Value = 0; Future Value = 32 million

Using PMT function (annuity due) in excel, semi-annual payment = $2,771,148.96

2). From Aug .1, 2013 till Aug.1, 2015, Barrick makes semi-annual payments of $2,771,148.96

Calculate the total amount accumulated till Aug.1, 2016

N = 4; I = 2.6%; PMT = $2,771,148.96; FV = $11,824,072.33 (again, using annuity due)

This is the amount collected till Feb.1, 2016. One more compounding period will be there from Feb.1, 2016 to Aug.1, 2016

Total amount collected till Aug.1, 2016 = $11,824,072.33*(1+2.6%) = $12,131,498.21

So, PV = $12,131,498.21; N = 4; I = 2.6%; FV = 32,000,000 (using annuity due)

PMT = $4,349,055.96

Barrick will have to make payments of $4,349,055.96 from Aug.1, 2016 to Feb.1, 2018 to reach $32 million by Aug.1, 2018.

c). Mine A NPV:

Formula	Year (n)	Cash flow (CF) (In USD billion)	Discount factor 1/(1+d)^n	PV of CF (CF*discount factor)
	0	-142	1.000	-142.000
	1	3.5	0.941	3.295
	2	4.5	0.886	3.988
	3	5.5	0.834	4.589
	4	5.5	0.786	4.321
	5	5.5	0.740	4.068
	6	5.5	0.696	3.829
	7	4.25	0.655	2.786
	8	4.25	0.617	2.623
	9	4.25	0.581	2.469
(Cash inflow-cleanup cost+residual value)	10	204.048	0.547	111.601
			NPV	1.569

Mine B NPV:

Formula	Year (n)	Cash flow (CF) (In USD billion)	Discount factor 1/(1+d)^n	PV of CF (CF*discount factor)
	0	-142	1.000	-142.000
	1	4.1	0.941	3.860
	2	4.1	0.886	3.634
	3	4.1	0.834	3.421
	4	4.1	0.786	3.221
	5	4.1	0.740	3.032
	6	4.1	0.696	2.855
	7	4.1	0.655	2.687
	8	4.1	0.617	2.530
	9	4.1	0.581	2.382
(Cash inflow+residual value)	10	204.1	0.547	111.630
			NPV	-2.748

Mine B has a negative NPV so Barrick should buy Mine A.

Note: The discount rate used here is 6.22% p.a. as it is not stated whether it is annual or quarterly. If this is quarterly discount rate, then annual rate of (1+6.22%)^4 -1 = 27.3% should be used.