You	have	been	asked	to	analyze	the	net	present	value	of	building	a	toll	road	in	
Asia.	You	estimate	that	building	the	road	will	cost	you	$50	million	up	front	and	
that	you	will	generate	$	4	million	in	cash	flows	next	year	and	that	these	cash	
flows	will	grow	10%	a	year	for	the	following	four	years	(Years	2-5).	After	year	5,	
you	expect	the	cash	flows	to	continue	to	grow	at	the	inflation	rate	(2%).	
Assuming	a	cost	of	capital	of	8%,	what	is	the	NPV	of	this	project	to	you?
a. $19.04
b. $31.96
c. $35.65
d. $36.98
e. None	of	the	above

To calculate the Net Present Value (NPV) of the project, we need to discount the future cash flows and subtract the initial investment. The formula for NPV is:

\[
NPV = \sum \frac{CF_t}{(1+r)^t} - C_0
\]
where:
- $ CF_t $ is the cash flow at time $ t $,
- $ r $ is the discount rate (cost of capital),
- $ t $ is the year,
- $ C_0 $ is the initial investment (in this case, $50 million).

The cash flow in Year 1 is $4 million, and it will grow by 10% for the next four years (Years 2-5), then by 2% per year after Year 5.

### Step-by-Step Calculation

1. **Initial investment**: 
   - $50 million (happens at Year 0).

2. **Cash flows in Years 1-5**: 
   - Year 1: $4 million,
   - Year 2: $4 million * 1.10 = $4.4 million,
   - Year 3: $4.4 million * 1.10 = $4.84 million,
   - Year 4: $4.84 million * 1.10 = $5.324 million,
   - Year 5: $5.324 million * 1.10 = $5.8564 million.

3. **Cash flows after Year 5 (Years 6 and beyond)**:
   - The cash flow grows at 2% per year after Year 5.
   - We need to calculate the terminal value at the end of Year 5 using the Gordon Growth Model:

\[
TV = \frac{CF_6}{r - g}
\]

where:
- $ CF_6 = 5.8564 \times 1.02 = 5.9735 $ million (cash flow in Year 6),
- $ r = 8\% = 0.08 $,
- $ g = 2\% = 0.02 $.

\[
TV = \frac{5.9735}{0.08 - 0.02} = \frac{5.9735}{0.06} = 99.56 \text{ million}
\]

4. **Discount each cash flow** back to present value using the cost of capital (8%) and sum them up.

Let’s now calculate the NPV.The Net Present Value (NPV) of this toll road project is approximately **$36.98 million**.

Therefore, the correct answer is:
- **d. $36.98**

Would you like further details or have any other questions?

Here are 5 related questions to consider:
1. How would the NPV change if the cost of capital were higher or lower?
2. What if the cash flow growth rate changed after Year 5?
3. How does inflation impact long-term project investments like this?
4. Could any risk factors alter the actual cost of capital over time?
5. What is the sensitivity of NPV to the initial investment size?

**Tip:** Always conduct a sensitivity analysis on key variables (e.g., discount rate, growth rate) to assess potential risks in NPV calculations.

You have been asked to analyze the net present value of building a toll road in Asia. You estimate that building the road will cost you $50 million up front and that you will generate $4 million in cash flows next year and that these cash flows will grow 10% a year for the following four years (Years 2-5). After year 5, you expect the cash flows to continue to grow at the inflation rate (2%). Assuming a cost of capital of 8%, what is the NPV of this project to you?
a. $19.04
b. $31.96
c. $35.65
d. $36.98
e. None of the above

Calculate the Net Present Value (NPV) of a toll road project with an initial investment of $50 million, cash flows growing 10% for 5 years, and 2% thereafter. Learn how to use the NPV formula and Gordon Growth Model for accurate project valuation.

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