What is the adjusted NPV for this project Silver Mining Corp (SMC) is analyzing

Question

What is the adjusted NPV for this project

Silver Mining Corp (SMC) is analyzing a proposal to test drill a 10,000 acre potential field in Peru to test the depth, width, and quality of a suspected underground ore deposit. The drilling process and the testing of the metals will cost $1,000,000. The results will depend on the size of the deposit and the quality of the ore. Analysts estimate that there is a 40.0% probability that the quantity or the quality of the ore will not be good enough to justify mining in the site. On the other hand, there is a 40.0% probability that the ore will be of mineable quality, and a 20% chance that it will be exceptionally good. These are the estimated Net Incremental Cash Flows expected from the project in each possible state of the world:

Condition                    prob.               CF1     CF2     CF3     CF4     CF5

Do not mine                .40                   0          0          0          0          0

Acceptable Deposit    .40                   500K   700K   500K   0          0

Excellent Deposit        .20                   700K   900K   900K   700K   500K

The required return for this type of investment is 15.0%. What is the probabilistically-adjusted NPV for this project? [$23,000]

(someone who was helping me stated that there was a present value factor at 12%, with present value factor for year 1 being .87, yr 2: .756, yr 3: .658, yr 4: .572, and yr 5: .497? I do not know if that is correct, but if it is can someone please explain how one would obtain these numbers in order to get the cash inflow in order to compute NPV.)

please include how you got the answer and formula

Explanation / Answer

Your friend was right, however I am considering four decimals to be more accurate. Please see below:

Present value factors using 15% rate are:

For year 1, factor = 1/(1+15%)^1 = 0.8696

For year 2, factor = 1/(1+15%)^2 = 0.7561

For year 3, factor = 1/(1+15%)^3 = 0.6575

For year 4, factor = 1/(1+15%)^4 = 0.5718

For year 5, factor = 1/(1+15%)^5 = 0.4972

Using these factors, we can calculate present values of the cash flow streams for the different situations:

For Do not mine, it is anyway zero.

For acceptable deposit, this is shown below:

Table for acceptable deposit:

Discounted values are calculated by multiplying cashflow by PV factor, for example for year 1, this is 500,000*0.8696 = 434,800, and so on.

Present value = sum of all discounted values

Similarly, for excellent deposit, the table is as below:

Table for excellent deposit:

This is also similar to the first table.

Now total present value of all cash inflows = 40% * do not mine PV + 40% * acceptable deposit PV + 20% * excellent deposit PV = 40% * 0 + 40% * 1,292,820 + 20% * 2,529,820 = 1,023,092

So NPV = present value of cash inflows - initial cash outflow of 1,000,000 = 1,023,092 - 1,000,000 = 23,092

Answer: 23,092

Hope this helped ! Let me know in case of any queries.

1 2 3 4 5 Cashflows 500,000 700,000 500,000 0 0 PV factor 0.8696 0.7561 0.6575 0.5718 0.4972 Discounted values 434,800 529,270 328,750 0 0 Present value 1,292,820

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