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# NPV /WAAC ?

Hello

I come from a technical background, PhD in Engineering not MBA. I have a few questions about the NPV and I appreciate it if someone can clarify the following.

1- Can someone please explain what is expected from advanced degree candidates to know about NPV during a case interview? every time I look it up or come across a case using NPV, they use a different approximation/method to calculate the NPV. It is becoming very confusing to me.

A Few NPV equations that I came accross are:

NPV = -Initial Investment + (Future Value of Money/Discount Rate)

NPV = Future Value of Money / Discount Rate

(usually Future Value of Money = Revenues - ongoing costs) - I think not sure!

- How you would interpret an NPV value?

2- There is a case in which we determine the following(the first half is all about determining the R and C as follows:

- Revenues  = 928 M\$

- Costs = 574M \$

- Profits  = R -C = 354M \$

Then there is this given which I totally did not understand (no clairification as to what it means):

- Time value of money: 6 year lag for receipt of revenue

to Determine the NPV they used WAAC (I have no idea what is this):

Using the “Rule of 72,” we know that 72/rate of return means the number of years to double our money. With a six year lag and a 12% WACC, we know that all future cash flows must be halved

\$354/2 = \$177M in present value (NPV)

clearly the 12% is 72/6 (lag years)

Can someone please explain what is WAAC? Why NPV is halved?

Hello

I come from a technical background, PhD in Engineering not MBA. I have a few questions about the NPV and I appreciate it if someone can clarify the following.

1- Can someone please explain what is expected from advanced degree candidates to know about NPV during a case interview? every time I look it up or come across a case using NPV, they use a different approximation/method to calculate the NPV. It is becoming very confusing to me.

A Few NPV equations that I came accross are:

NPV = -Initial Investment + (Future Value of Money/Discount Rate)

NPV = Future Value of Money / Discount Rate

(usually Future Value of Money = Revenues - ongoing costs) - I think not sure!

- How you would interpret an NPV value?

2- There is a case in which we determine the following(the first half is all about determining the R and C as follows:

- Revenues  = 928 M\$

- Costs = 574M \$

- Profits  = R -C = 354M \$

Then there is this given which I totally did not understand (no clairification as to what it means):

- Time value of money: 6 year lag for receipt of revenue

to Determine the NPV they used WAAC (I have no idea what is this):

Using the “Rule of 72,” we know that 72/rate of return means the number of years to double our money. With a six year lag and a 12% WACC, we know that all future cash flows must be halved

\$354/2 = \$177M in present value (NPV)

clearly the 12% is 72/6 (lag years)

Can someone please explain what is WAAC? Why NPV is halved?

(edited)

• Date ascending
• Date descending

Hi there,

Several questions ;) Let me go one by one.

1) NPV

The correct NPV formula closer to what you reported is:

NPV = -Initial Investment + (FCF/Discount Rate)

Where FCF= Free cash flow of the project generated in one year (I guess that’s what you mean by Future Value of Money). Note that this formula assumes that (i) every year you will generate the same FCF and (ii) you will generate FCF forever with that project.

2) RULE OF 72

With the Rule of 72 you can calculate the time to double for a variable. The formula is:

Time to double = 72/r

Where r=discount rate*100 (so if the discount rate is say 15%, r=15).

3) WACC

From a theoretical point of view, the discount rate is normally approximated with the WACC of the company (Weighted Average Cost of Capital), which can be computed as follows:

WACC = Re x E/V + Rd x (1 - corporate tax rate) x D/V.

where:

Re= Cost of Equity

Rd= Cost of Debt

E= Equity

D= Debt

V= Total Value (E+D)

In practical terms, this is normally assumed to be 5% or 10% for simplicity in a case.

4) CASE QUESTION

I guess what they meant was that profits, not revenues, are going to be received in 6 years.

Given the WACC is 12%, if you apply the rule of 72 using the WACC as the discount rate, you will find that the returns of the project will double indeed in exactly 6 years (72/12=6 – see formula above).

So this means that if you have X in year zero and grow by 12% per year, this will be worth 2X in 6 years. Given in this case you have 354M in 6 years, 354M = 2X, so X (value today of that return) is 177M.

---

For more information on the other variables, you can refer to the following answer that goes more into detail:

https://www.preplounge.com/en/consulting-forum/case-net-present-value-calculations-325

Hope this helps,

Francesco

Hi there,

Several questions ;) Let me go one by one.

1) NPV

The correct NPV formula closer to what you reported is:

NPV = -Initial Investment + (FCF/Discount Rate)

Where FCF= Free cash flow of the project generated in one year (I guess that’s what you mean by Future Value of Money). Note that this formula assumes that (i) every year you will generate the same FCF and (ii) you will generate FCF forever with that project.

2) RULE OF 72

With the Rule of 72 you can calculate the time to double for a variable. The formula is:

Time to double = 72/r

Where r=discount rate*100 (so if the discount rate is say 15%, r=15).

3) WACC

From a theoretical point of view, the discount rate is normally approximated with the WACC of the company (Weighted Average Cost of Capital), which can be computed as follows:

WACC = Re x E/V + Rd x (1 - corporate tax rate) x D/V.

where:

Re= Cost of Equity

Rd= Cost of Debt

E= Equity

D= Debt

V= Total Value (E+D)

In practical terms, this is normally assumed to be 5% or 10% for simplicity in a case.

4) CASE QUESTION

I guess what they meant was that profits, not revenues, are going to be received in 6 years.

Given the WACC is 12%, if you apply the rule of 72 using the WACC as the discount rate, you will find that the returns of the project will double indeed in exactly 6 years (72/12=6 – see formula above).

So this means that if you have X in year zero and grow by 12% per year, this will be worth 2X in 6 years. Given in this case you have 354M in 6 years, 354M = 2X, so X (value today of that return) is 177M.

---

For more information on the other variables, you can refer to the following answer that goes more into detail:

https://www.preplounge.com/en/consulting-forum/case-net-present-value-calculations-325

Hope this helps,

Francesco

Hi Anon,

1. Discount rate / WACC

This is the rate at which money changes its value per year. In common life we see this manifested in the form of interest "rate" on your mortgage, or inflation "rate" in the economy, etc. If you loan your friend \$100 today and ask them to return it back after 1 year with 10% interest, they will have to pay you back \$110. In this deal the 10% interest rate is the discount rate.

WACC [Weighted Average Cost of Capital] - for all intents and purposes is the blended discount rate for a business transaction. Just take it and forget it. You don't need to worry about the specifics - best to refer to Investopedia for that.

2. Rule of 72

This is a short-cut / hack to get to basic time-value-of-money calculations. If you invest \$1000 today in an index fund that gives you 10% per year returns - your \$1000 will double after Z years - where Z = 72/10 = ~7 years. The values will be as follows:

• Year 1: \$1000
• Year 2: \$1100
• Year 3: \$1210
• Year 4: \$1331
• Year 5: \$1464
• Year 6: \$1611
• Year 7: \$1772
• Year 8: \$1949 (7 years after year 1)

This also works from the future to the present. If you would be inheriting \$2000 in year 8 - it would be worth \$1000 in year 1 (assuming the same 10% discount rate).

3. NPV

In theory one can write:

NPV = sum of present values of all future cash flows

Lets break that down a bit:

• Cash flow in year 1 is the initial investment. Let it be X. Since X is in the present, its present value is also X. Also, since X is an investment/expenditure, lets denote it by -X.
• Cash flow in year 2 is C. The present value of C = C/(1 + discount rate). So if the assumed discount rate if 10%, the present value will be = C/1.1
• Cash flow in year 3 is C. The present value of C = C/(1 + discount rate)^2. The power is because the cash flow is 2 years in the future. So if the assumed discount rate if 10%, the present value will be = C/1.21

You will realise this is an infinite geometric progression starting from year 2. If you go through the infinite GP formula, you will realise that the sum of the present value of all the cash flows from year 2 onwards is = C/(discount rate)

Hence, the final formula will look like the following:

NPV = -X + C/r

4. 6-year lag

In the above example we saw that the investment in year 1 started bearing fruit from year 2 onwards. In reality, the projects may take longer than 1 year to setup (in this case 6 years). But, when the project does start bearing fruit - it will give C = 354M every year. Now going by the above concept we will have the following:

• Cash flow in year 1 is the initial investment. Let it be X.
• Cash flow in year 2/3/4/5/6 is zero (since the project is being setup)
• Cash flow in year 7 onwards is 354M. As we discussed above, you need to find the present value of this 354M. Given that discount rate is 12%, 354M in year 7 will be worth 354/(1+12%)^6 today. Which will be roughly half of 354M. This is also a demonstration of the rule of 72.

Hope this helps!

Hi Anon,

1. Discount rate / WACC

This is the rate at which money changes its value per year. In common life we see this manifested in the form of interest "rate" on your mortgage, or inflation "rate" in the economy, etc. If you loan your friend \$100 today and ask them to return it back after 1 year with 10% interest, they will have to pay you back \$110. In this deal the 10% interest rate is the discount rate.

WACC [Weighted Average Cost of Capital] - for all intents and purposes is the blended discount rate for a business transaction. Just take it and forget it. You don't need to worry about the specifics - best to refer to Investopedia for that.

2. Rule of 72

This is a short-cut / hack to get to basic time-value-of-money calculations. If you invest \$1000 today in an index fund that gives you 10% per year returns - your \$1000 will double after Z years - where Z = 72/10 = ~7 years. The values will be as follows:

• Year 1: \$1000
• Year 2: \$1100
• Year 3: \$1210
• Year 4: \$1331
• Year 5: \$1464
• Year 6: \$1611
• Year 7: \$1772
• Year 8: \$1949 (7 years after year 1)

This also works from the future to the present. If you would be inheriting \$2000 in year 8 - it would be worth \$1000 in year 1 (assuming the same 10% discount rate).

3. NPV

In theory one can write:

NPV = sum of present values of all future cash flows

Lets break that down a bit:

• Cash flow in year 1 is the initial investment. Let it be X. Since X is in the present, its present value is also X. Also, since X is an investment/expenditure, lets denote it by -X.
• Cash flow in year 2 is C. The present value of C = C/(1 + discount rate). So if the assumed discount rate if 10%, the present value will be = C/1.1
• Cash flow in year 3 is C. The present value of C = C/(1 + discount rate)^2. The power is because the cash flow is 2 years in the future. So if the assumed discount rate if 10%, the present value will be = C/1.21

You will realise this is an infinite geometric progression starting from year 2. If you go through the infinite GP formula, you will realise that the sum of the present value of all the cash flows from year 2 onwards is = C/(discount rate)

Hence, the final formula will look like the following:

NPV = -X + C/r

4. 6-year lag

In the above example we saw that the investment in year 1 started bearing fruit from year 2 onwards. In reality, the projects may take longer than 1 year to setup (in this case 6 years). But, when the project does start bearing fruit - it will give C = 354M every year. Now going by the above concept we will have the following:

• Cash flow in year 1 is the initial investment. Let it be X.
• Cash flow in year 2/3/4/5/6 is zero (since the project is being setup)
• Cash flow in year 7 onwards is 354M. As we discussed above, you need to find the present value of this 354M. Given that discount rate is 12%, 354M in year 7 will be worth 354/(1+12%)^6 today. Which will be roughly half of 354M. This is also a demonstration of the rule of 72.

Hope this helps!

(edited)

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