Principles of Finance ACST603
Tutorial 6, Week 6 Capital budgetting using the NPV, IRR and payback period evaluation techniques
Homework questions.
A young lady is trying to decide if she should attend university or not.
The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The hard work studying at school in her childhood should be classified as:
The lady's hard work studying and attending school during her childhood is a sunk cost since there's nothing she can do to get that time back. It's in the past, it's spent, she should forget about it. Her decision to attend university should ignore this sunk cost because regardless of her decision, this cost can't be recouped. Only the incremental benefits and costs should be included in her decision. Economists were the first to discover the importance of marginal changes, and the period is known as the Marginalist Revolution.
A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.
What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?
The opportunity to meet a desirable future spouse should be classified as:
The higher chance of meeting a clever spouse is a positive side effect that should be included in the decision to go to university. It's not a sunk cost since the chance of meeting a clever young man depends on her decision to go to university or not. Also, it's not an opportunity cost since it's actually a benefit from going to university.
It's funny how the word 'opportunity' in the last sentence of the question makes people sub-consciously think opportunity cost, even though it is clearly not a cost.
A man is thinking about taking a day off from his casual painting job to relax.
He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.
But he's thinking about the hours that he could work today (in the future) which are:
The hours that he could work in the future are an opportunity cost of his decision to take a day off and relax, assuming that working is the 'next best alternative' to relaxing. The hours that he could spend working are not a sunk cost yet because they are in the future, they are an incremental cost of staying home to relax.
A man has taken a day off from his casual painting job to relax.
It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:
The hours that he took off from work are now a sunk cost because they are in the past and there is nothing that he can do to get them back, he should forget about them. As the saying goes, "don't cry over spilt milk".
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -100 |
| 1 | 0 |
| 2 | 121 |
###\begin{aligned} NPV &= C_0 + \frac{C_2}{(1+r)^2} \\ &= -100 + \frac{121}{(1+0.1)^2} \\ &= -100 + 100 \\ &= 0 \\ \end{aligned}###
What is the Internal Rate of Return (IRR) of the project detailed in the table below?
Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -100 |
| 1 | 0 |
| 2 | 121 |
###\begin{aligned} 0 &= C_0 + \frac{C_2}{(1+r_\text{IRR})^2} \\ &= -100 + \frac{121}{(1+r_\text{IRR})^2} \\ \end{aligned}###
###(1+r_\text{IRR})^2 = \frac{121}{100} ######\begin{aligned} r_\text{IRR} &= \left( \frac{121}{100} \right)^{1/2} - 1 \\ &= 0.1 \\ \end{aligned}###
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
By definition, the Internal Rate of Return (IRR) is the particular required return that makes the project's Net Present Value (NPV) equal to zero.
###\begin{aligned} NPV &= C_0 + \frac{C_1}{(1+r_\text{required})^1} + \frac{C_2}{(1+r_\text{required})^2} + ... + \frac{C_T}{(1+r_\text{required})^T} \\ 0 &= C_0 + \frac{C_1}{(1+r_{irr})^1} + \frac{C_2}{(1+r_{irr})^2} + ... + \frac{C_T}{(1+r_{irr})^T} \\ \end{aligned} ###
Therefore if the NPV is zero then the IRR must be equal to the required return.
The required return of a project is 10%, given as an effective annual rate.
What is the payback period of the project in years?
Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -100 |
| 1 | 11 |
| 2 | 121 |
Table method:
| Payback Period Calculation | ||
| Time (yrs) |
Cash flow ($) |
Cumulative cash flow ($) |
| 0 | -100 | -100 |
| 1 | 11 | -89 |
| 2 | 121 | 32 |
The payback period ##T_\text{payback}## is then the time at which the first positive cumulative cash flow occurs, less the cumulative cash flow divided by the single cash flow in that period:
###\begin{aligned} T_\text{payback} &= \left( \begin{array}{c} \text{time of} \\ \text{first positive} \\ \text{cumulative} \\ \text{cash flow} \\ \end{array} \right) - \frac{ \left( \begin{array}{c} \text{first positive} \\ \text{cumulative} \\ \text{cash flow} \\ \end{array} \right) }{ \left( \begin{array}{c} \text{cash flow over} \\ \text{that period} \\ \end{array} \right) } \\ &= 2 - \frac{32}{121} \\ &= 2 - \frac{32}{121} \\ &= 2 - 0.26446281 \\ &= 1.73553719 \text{ yrs} \\ \end{aligned}###
Quick method: A table might be overkill for this simple project, the payback period clearly occurs sometime during the second year (between t=1 and 2), so
###\begin{aligned} T_\text{payback} &= 2 - \frac{-100 + 11 + 121}{121} \\ &= 2 - \frac{32}{121} \\ &= 1.73553719 \text{ yrs} \\ \end{aligned}###
A project has the following cash flows:
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -400 |
| 1 | 0 |
| 2 | 500 |
What is the payback period of the project in years?
Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2.
To find the payback period,
###\begin{aligned} T_\text{payback} &= \left( \begin{array}{c} \text{time of} \\ \text{first positive} \\ \text{cumulative} \\ \text{cash flow} \\ \end{array} \right) - \frac{ \left( \begin{array}{c} \text{first positive} \\ \text{cumulative} \\ \text{cash flow} \\ \end{array} \right) }{ \left( \begin{array}{c} \text{cash flow over} \\ \text{that period} \\ \end{array} \right) } \\ &= 2 - \frac{(-400+500)}{500} \\ &= 2 - \frac{100}{500} \\ &= 1.8 \\ \end{aligned} ###
The below graph shows a project's net present value (NPV) against its annual discount rate.
For what discount rate or range of discount rates would you accept and commence the project?
All answer choices are given as approximations from reading off the graph.
Projects add to the firm's asset value if their net present value (NPV) of cash flows is positive, which in this case occurs between the discount rates of zero to five percent. The positive NPV can be seen on the graph where the blue line is above above zero on the vertical y-axis which represents the NPV.
The below graph shows a project's net present value (NPV) against its annual discount rate.
Which of the following statements is NOT correct?
The project's payback period is not infinite, it must be a finite amount of years because when the discount rate is zero, the NPV is $20m as can be seen from the graph. Therefore the sum of the cash flows is positive, so the project must eventually pay itself off.
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).
How much can you consume at each time?
Let ##C_t## be consumption at time t and ##V_t## be wealth at time t.
Common sense method:
We initially have ##V_0## wealth in the bank. Then we consume or spend ##C_0## a moment later, still at time zero. The amount left in the bank accrues interest so it grows over the next year by the interest rate. To find this future value we multiply by ##(1+r)^1##. At time one, everything that's left in the bank is consumed ##(C_1)## with nothing left over at the end.
###(V_0 -C_0)(1+r)^1 - C_1 = 0 ###| Formula Building Steps | ||
| Time | Event | Formula |
| 0 | Starting wealth | ##V_0## |
| 0 | Consume | ##V_0 - C_0## |
| 1 | Lend to bank for one year | ##(V_0 - C_0)(1+r)^1## |
| 1 | Consume all so there's nothing left | ##(V_0 - C_0)(1+r)^1 - C_1 = 0## |
The question stated that consumption at t=0 and t=1 are equal, so ##C_0 = C_1 ##. So we can solve simultaneously and substitute numbers (k represents thousands),
###(V_0 -C_0)(1+r)^1 - C_1 = 0 ### ###(V_0 -C_0)(1+r)^1 - C_\color{red}{0} = 0 ### ###(100k -C_0)(1+0.1)^1 - C_0 = 0 ### ###100k(1+0.1)^1 -C_0(1+0.1)^1 - C_0 = 0 ### ###C_0\left(1+(1+0.1)^1\right) = 100k(1+0.1)^1 ### ###\begin{aligned} C_0 &= \frac{100k(1+0.1)^1}{1+(1+0.1)^1} \\ &= \frac{100,000 \times 1.1}{2.1} \\ &= 52,380.9524 \\ \end{aligned}### ###C_1 = C_0 = 52,380.9524###Present value method:
This method is easier to formulate. Since all wealth will be consumed, the present value of the positive wealth and negative consumption must equal zero.
###V_0 -C_0 - \frac{C_1}{(1+r)^1} +\frac{V_1}{(1+r)^1} = 0 ###The question stated that consumption at t=0 and t=1 are equal, so ##C_0 = C_1 ##. Also ##V_1 = 0## since there's no wealth left over at the end.
Solving simultaneously and substituting numbers (k represents thousands),
###100k -C_0 - \frac{C_0}{(1+0.1)^1} +\frac{0}{(1+0.1)^1} = 0 ### ###C_0\left(1+ \frac{1}{(1+0.1)^1}\right) = 100k ### ###\begin{aligned} C_0 &= \frac{100k}{\left(1+ \frac{1}{(1+0.1)^1}\right)} \\ &= 52,380.9524 = C_1 \\ \end{aligned}###Future value method:
Similarly to the present value method, this method is easy to formulate. Since all wealth will be consumed, the future value of the positive wealth and negative consumption must equal zero.
###V_0(1+r)^1 -C_0(1+r)^1 - C_1 = 0 ###The question stated that consumption at t=0 and t=1 are equal, so ##C_0 = C_1 ##.
Solving simultaneously and substituting numbers (k represents thousands),
###100k(1+0.1)^1 -C_0(1+0.1)^1 - C_0 = 0 ### ###C_0\left(1+ \frac{1}{(1+0.1)^1}\right) = 100k ### ###C_0 = 52,380.9524 = C_1 ###You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).
How much can you consume at each time?
Let ##C_t## be consumption at time t and ##V_t## be wealth at time t.
Common sense method:
We have ##V_0## in the bank then we consume ##C_0## of that at time zero. The amount left in the bank accrues interest over the year so we grow it by ##(1+r)^1##. Again at time one we consume ##C_1##, and the amount remaining in the bank accrues more interest. At time two we consume ##C_2## and the amount left after this is ##V_2##.
###\left( (V_0 -C_0)(1+r)^1 - C_1 \right)(1+r)^1-C_2 = V_2 ###| Formula Building Steps | ||
| Time | Event | Formula |
| 0 | Starting wealth | ##V_0## |
| 0 | Consume | ##V_0 - C_0## |
| 1 | Lend to bank for one year | ##(V_0 - C_0)(1+r)^1## |
| 1 | Consume more | ##(V_0 - C_0)(1+r)^1 - C_1## |
| 2 | Lend to bank for another year | ##((V_0 - C_0)(1+r)^1 - C_1)(1+r)^1## |
| 2 | Consume again but leave some wealth aside | ##((V_0 - C_0)(1+r)^1 - C_1)(1+r)^1 - C_2 = V_2## |
The question stated that consumption at t=0,1 and 2 are equal, so ##C_0 = C_1 = C_2##.
Solving simultaneously and substituting numbers (k represents thousands),
###\left( (V_0 -C_0)(1+r)^1 - C_1 \right)(1+r)^1-C_2 = V_2 ### ###\left( (100k -C_0)(1+0.1)^1 - C_0 \right)(1+0.1)^1-C_0 = 50k ### ###\begin{aligned} C_0 &= \dfrac{100k(1+0.1)^2 - 50k }{1+(1+0.1)^1 + (1+0.1)^2} \\ &= 21,450.1511 = C_1 = C_2 \\ \end{aligned}###Present value method:
###V_0 -C_0 - \frac{C_1}{(1+r)^1} -\frac{C_2}{(1+r)^2}- \frac{V_2}{(1+r)^2}= 0 ###Also, consumption at t=0, 1 and 2 are all equal, so
###C_0 = C_1 = C_2 ###Solving simultaneously and substituting numbers (k represents thousands),
###100k -C_0 - \frac{C_0}{(1+r)^1} -\frac{C_0}{(1+r)^2} - \frac{50k}{(1+r)^2}= 0 ### ###C_0\left(1+ \frac{1}{(1+0.1)^1} + \frac{1}{(1+0.1)^2}\right) = 100k - \frac{50k}{(1+0.1)^2} ### ###\begin{aligned} C_0 &= \frac{100k - \dfrac{50k}{(1+0.1)^2}}{\left(1+ \dfrac{1}{(1+0.1)^1} + \dfrac{1}{(1+0.1)^2}\right)} \\ &= 21,450.1511 = C_1 = C_2 \\ \end{aligned}###You're considering a business project which costs $11m now and is expected to pay a single cash flow of $11m in one year. So you pay $11m now, then one year later you receive $11m.
Assume that the initial $11m cost is funded using the your firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about the net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
If the project is accepted, then the market value of the firm's assets will fall by $1m, since the net present value (NPV) of the project is -$1m. It's true that the firm's cash assets will fall by $11m when it buys into the project, but the positive $11m that will be received in one year adds a $10m present value to the market value of assets, giving an NPV of -$1m.
For the NPV:
###\begin{aligned} V_0 &= C_0 + \dfrac{C_1}{(1+r)^1} \\ &= -11m + \dfrac{11m}{(1+0.1)^1} \\ &= -11m + 10m \\ &= -1m \\ \end{aligned}###The project's NPV is negative so it should be rejected.
For the IRR:
###V_0 = C_0 + \dfrac{C_1}{(1+r)^1} ### ###0 = -11m + \dfrac{11m}{(1+r_{IRR})^1} ### ###\begin{aligned} r_{IRR} &= \dfrac{11m}{11m} - 1 \\ &= 0 \\ \end{aligned}###The project's IRR is less than the cost of capital (10%) so again, the project should be rejected.
A firm is considering a business project which costs $10m now and is expected to pay a single cash flow of $12.1m in two years.
Assume that the initial $10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
If the project is accepted then there will be a gain of $2.1m since the $10m cash spent on the project will turn into $12.1m cash 2 years later. This gives a 10% pa internal rate of return (IRR). The calculation is detailed at the end.
However, if the project is rejected then the $10m cash not spent on the project will sit in the bank and will also increase at 10% pa which is the bank interest rate, so that the cash at bank will be worth $12.1m in 2 years. Hence, the project will not make the firm worth $2.1m more if it is accepted.
The fact that the project is zero NPV and has an IRR equal to the required return indicates that the project is not very good, but not bad either. The firm's managers would be indifferent to accepting or rejecting it.
To show that the NPV of accepting the project is zero:
###\begin{aligned}NPV &= -V_0 + \dfrac{V_2}{(1+r_\text{required return})^2} \\ &= -10m + \dfrac{12.1m}{(1+0.1)^2} = -10m + 10m = 0 \end{aligned}###To show that the project's IRR is equal to its required return (also known as the cost of capital):
###NPV = -V_0 + \dfrac{V_2}{(1+r_\text{required return})^2}### ###0 = -V_0 + \dfrac{V_2}{(1+r_\text{IRR})^2}### ###0 = -10m + \dfrac{12.1m}{(1+r_\text{IRR})^2}### ###(1+r_\text{IRR})^2 = \dfrac{12.1m}{10m}### ###1+r_\text{IRR} = \left( \dfrac{12.1m}{10m} \right)^{1/2}### ###\begin{aligned} r_\text{IRR} &= \left( \dfrac{12.1m}{10m} \right)^{1/2}-1 = 1.21^{(1/2)}-1 = 0.1 \\ \end{aligned}###Your neighbour asks you for a loan of $100 and offers to pay you back $120 in one year.
You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates.
Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs.
The Net Present Value (NPV) of lending to your neighbour is $9.09. Describe what you would do to actually receive a $9.09 cash flow right now with zero net cash flows in the future.
Right now (at t=0), borrow $109.09 from the bank and lend $100 of it to your neighbour now. This leaves us with a positive cash flow of $9.09 at t=0.
In on year (t=1), take the $120 from your neighbour and use it to pay back the bank the $120 owed ##\left(109.09\times(1+0.1)^1\right)##. This leaves us with a cash flow of zero at t=1.
To work out the amounts, use an arbitrage table.
| Arbitrage Table of Cash Flows | ||
| Instrument | Time 0 | Time 1 |
| Buy debt from (lend to) neighbour now, and wait for repayment in one year. | -100 | 120 |
| Sell debt to (borrow from) bank at 10% pa and pay it back in one year. | 109.09 Step 3 |
-120 Step 2 |
| Total | 9.09 Step 4 |
0 Step 1 |
The steps used to calculate the table's values are given here.
Step 1: All future cash flows need to total zero, that way only the initial (t=0) cash flow will be non-zero.
Step 2: The bank loan cash flow at time 1 must equal -120 so that total cash flows are zero. Since we're paying this $120 at the end, we must be borrowing using this bank loan.
Step 3: Since we're paying back 120 in one year, we must be borrowing the present value of that which is 109.09, calculated as follows: ###V_0 = -\dfrac{C_1}{(1+r)^1} = -\dfrac{-120}{(1+0.1)^1} = 109.09###
Step 4: Adding up the total cash flows at time zero, -100+109.09 = 9.09 which is the NPV of the arbitrage.
Arbitrage tables are great since they show how to a create a positive arbitrage cash flow of the NPV right now ($9.09) with no risk and no capital required.
A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.
The net present value of making and commercialising the drug is $200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.
Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?
The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##ΔV = ΔD+ΔE##
Since the project has a positive NPV of $200m, the value of the firm's assets (V) must increase by $200m. Assuming that the debt can be fully paid off, this positive $200m NPV will all accrue to the equityholders since they have a residual claim on the firm's assets.
The project will be funded by issuing bonds which will add $600m to debt liabilities (D) and cash or equipment assets (V).
Therefore, ##ΔV=800m, ΔD = 600m, ΔE=200m##.
A mining firm has just discovered a new mine. So far the news has been kept a secret.
The net present value of digging the mine and selling the minerals is $250 million, but $500 million of new equity and $300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.
Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semi-strong form efficient.
The triangle symbol ##\Delta## is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##\Delta V = \Delta D+ \Delta E##
Since the project has a positive NPV of $250m, the value of the firm's assets (V) must increase by $250m. Assuming that the debt can be fully paid off, this positive $500m NPV will all accrue to the equity holders (E) since they have a residual claim on the firm's assets.
The project will be funded by issuing $500m of equity and $300m of bonds which will all be received in cash (an asset) and then spent on equipment (also an asset). This capital raising will cause assets (V) to rise by $800m, plus the $250m NPV as well, totaling $1,050m. Similarly, the increase in equity will be the sum of the capital raising and positive-NPV events, totaling $750m.
Therefore, ##\Delta V = 1,050m##, ##ΔD = 300m##, ##ΔE= 750##.
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
| Mutually Exclusive Projects | |||
| Project | Cost now ($) |
Sale price in one year ($) |
IRR (% pa) |
| Petrol station | 9,000,000 | 11,000,000 | 22.22 |
| Car wash | 800,000 | 1,100,000 | 37.50 |
| Car park | 70,000 | 110,000 | 57.14 |
Which project should the investor accept?
The best project appears to be the car park because it has the highest IRR. But the other important decision criteria is NPV which isn't calculated. The NPV's are:
###V_\text{0, Petrol station} = -9,000,000 + \dfrac{11,000,000}{(1+0.1)^1} = 1,000,000 ### ###V_\text{0, Car wash} = -800,000 + \dfrac{1,100,000}{(1+0.1)^1} = 200,000 ### ###V_\text{0, Car park} = -70,000 + \dfrac{110,000}{(1+0.1)^1} = 30,000 ###So while the car park has the highest IRR, it has the lowest NPV. The petrol station has the highest NPV, but lowest IRR.
Because the projects are mutually exclusive, only one project can be chosen. Rationally it's best to make the most money and choose the project with the highest NPV. After all, would you prefer to make $30,000 on the car park, or 1 millions of dollars on the petrol station?
An investor owns a whole level of an old office building which is currently worth $1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:
- Rented out to a tenant for one year at $0.1m paid immediately, and then sold for $0.99m in one year.
- Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for $2.4m when the refurbishment is finished in one year.
- Converted into residential apartments at a cost of $2m now, and then sold for $3.4m when the conversion is finished in one year.
All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).
| Mutually Exclusive Projects | |||
| Project | Cash flow now ($) |
Cash flow in one year ($) |
IRR (% pa) |
| Rent then sell as is | -900,000 | 990,000 | 10 |
| Refurbishment into modern offices | -2,000,000 | 2,400,000 | 20 |
| Conversion into residential apartments | -3,000,000 | 3,400,000 | 13.33 |
Which project should the investor accept?
Since the projects are mutually exclusive, the one with the highest NPV ##(V_0)## should be chosen.
###V_\text{0, Rent as is} = -900k + \dfrac{990k}{(1+0.1)^1} = 0### ###V_\text{0, Refurbish into offices} = -2m + \dfrac{2.4m}{(1+0.1)^1} = 0.1818m### ###V_\text{0, Convert to residential} = -3m + \dfrac{3.4m}{(1+0.1)^1} = 0.0909m###The refurbishment into modern offices has the highest NPV, so that's the best option. In this case it also has the highest IRR but that is a co-incidence. The best project is the one which makes the most wealth and that is best decided according to NPV.