Mining Economics

Discounted Cash Flow & NPV

The time value of money — discounting future cash to the present and judging a mine project by its net present value.

PART 1

Topic Breakdown & Traps

The Engineering Principle

A rupee received in the future is worth less than one today, because money can earn a return in the meantime. Discounting brings each future cash flow back to its present value by dividing by

(1 + i)^{n}

. A project's net present value (NPV) is the sum of all discounted inflows minus the initial investment; a positive NPV means the project earns more than the discount rate and is worth pursuing.

The Core Formula Matrix

Present value of a single future amount:

P V = \frac{F V}{( 1 + i ) ^{n}}

i

= discount rate per period,

n

= number of periods.

Net present value:

N P V = - C_{0} + t = 1 \sum n \frac{C F _{t}}{( 1 + i ) ^{t}}

C_{0}

= initial investment,

C F_{t}

= cash flow in year

t

The ‘IIT Traps’

⚠
Discount each year by its own exponent. Year 3 cash divides by $(1 + i)^{3}$ , not $(1 + i)$ ; using a single year understates the discounting.
⚠
**Subtract the initial outlay $C_{0}$ .** NPV is *net* — forgetting $- C_{0}$ turns it into a gross present value.
⚠
Rate as a decimal. $i = 10%$ means $0.10$ ; mixing percent and decimal corrupts $(1 + i)^{n}$ .

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

At a discount rate of

10%

, the present value of

₹ 1100

received one year from now is:

Q2MEDIUM2 Marks · NAT

The present value of

₹ 1000

to be received in

3

years at a discount rate of

10%

is ₹______. (Round off to two decimal places.)

₹

Q3HARD2 Marks · NAT

A project costs

₹ 1000

today and returns

₹ 500

at the end of each of the next

3

years. At a discount rate of

10%

, the NPV is ₹______. (Round off to two decimal places.)

₹