Question

Suppose Appin coal mine values their coal extraction benefits as:

Amount $18,000(YEAR 1)

$23,000(YEAR 2)

$27,000(YEAR 3)

$30,000 (YEAR 4)

$32,000 (YEAR 5)

a. Find the net present value of their extraction benefit when the discount rate is 12%. b. Now suppose the discount rate changes to 2%, find the new net present value and explain what Appin coal mine will do as a result of this change and why.

Answer 1

a)

Expected cash flow in year1=CF1=$18000

Expected cash flow in year2=CF2=$23000

Expected cash flow in year3=CF3=$27000

Expected cash flow in year4=CF4=$30000

Expected cash flow in year5=CF5=$32000

Rate of interest=i=12%

Present value of coal extraction=CF1/(1+i)^1+CF2/(1+i)^2+CF3/(1+i)^3+CF4/(1+i)^4+CF5/(1+i)^5

Present value of coal extraction =18000/(1+0.12)^1+23000/(1+0.12)^2+27000/(1+0.12)^3+30000/(1+0.12)^4+32000/(1+0.12)^5

=$90848.16

b)

Rate of interest=i=2%

Present value of coal extraction=CF1/(1+i)^1+CF2/(1+i)^2+CF3/(1+i)^3+CF4/(1+i)^4+CF5/(1+i)^5

Present value of coal extraction =18000/(1+0.02)^1+23000/(1+0.02)^2+27000/(1+0.02)^3+30000/(1+0.02)^4+32000/(1+0.02)^5

=$121895.39

Present worth of expected coal extraction has increased. Appin coal company may offer extraction rights as higher price.