Question

question 8
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anglo coal is planning a new coal mine, which is expected to cost r430,000 to build, with the expenditure scheduled for next year. the mine is expected to generate annual cash inflows of r200,000 over the next seven years. it will then cost r170,000 to close down the mine over the following year. assume all cash flows occur at the end of the year. alternatively, lincoln coal may choose to sell the site today. what minimum price should lincoln set on the property, given a 16% required rate of return?
a. r234561
b. r283345

Explanation:

Step1: Calculate present - value of annual cash inflows

The annual cash inflow $A = R200,000$, $n = 7$ years, and $r=0.16$. Using the present - value of an ordinary annuity formula $PV = A\times\frac{1-(1 + r)^{-n}}{r}$, we have $PV_{inflows}=200000\times\frac{1-(1 + 0.16)^{-7}}{0.16}$.
First, calculate $(1 + 0.16)^{-7}=\frac{1}{(1 + 0.16)^{7}}\approx\frac{1}{2.825147}\approx0.354026$.
Then, $1-(1 + 0.16)^{-7}=1 - 0.354026 = 0.645974$.
$\frac{1-(1 + 0.16)^{-7}}{0.16}=\frac{0.645974}{0.16}\approx4.037337$.
So, $PV_{inflows}=200000\times4.037337 = R807467.4$.

Step2: Calculate present - value of the closing cost

The closing cost $F = R170,000$ occurs in year 8. Using the present - value formula $PV=\frac{F}{(1 + r)^{n}}$, with $n = 8$ and $r = 0.16$, we have $PV_{closing}=\frac{170000}{(1 + 0.16)^{8}}$.
$(1 + 0.16)^{8}=2.825147\times1.16\approx3.27716$.
$PV_{closing}=\frac{170000}{3.27716}\approx R51874.25$.

Step3: Calculate the net present value of the mine project

The initial cost $I = R430,000$.
The net present value $NPV=PV_{inflows}-I - PV_{closing}$.
$NPV = 807467.4-430000 - 51874.25=R325593.15$.

The minimum price to sell the site today should be equal to the net present value of the mine project.

Answer:

There seems to be an error in the provided options as the calculated value is R325593.15. But if we assume there are no calculation errors in the problem - setup and only consider the closest option to the calculated value among the given ones, we need to re - evaluate the calculations or check the problem statement for possible misunderstandings. If we go with the closest value concept, we need more options to make a proper selection. However, based on the correct NPV calculation process shown above, the minimum price should be the NPV value calculated.