Question

You are thinking about starting a cafe. Opening requires an initial investment of $100,000 and a further investment of $50,000 one year from now. With 70% probability your cafe will be a great success and generate $60,000 in year 2 and FCF will grow at 2% per year after that. Otherwise, the cafe will be only ok and generate $10,000 in year 2 and FCF will not grow. What's the NPV of investing in the cafe if your required rate of return is 11%?

Answer 1

Given Information:

Initial investment = 100000, Investment in 1 year = 50000.

70% Probability of Earnings at year 2 =60000 and growth 2%

30% Probability of earnings at year 2 = 10000 and growth 0.

Required rate of return = 11%

1. Calculate the Value of Investment at 70% probability

Gordan gorowth formual is widely used to calculate the value if earnings are consitent with growth.

Since Earning start from year 2 so Gordan growth given Value at Year 1 as formula is:

P1 = Price at year 1, E2= Earnings at year 2, Ke= required return, g= growth

= 60000 / (0.11 - 0.02)

= 60000 / 0.09

Value at year 1 = 666,666.6667  

Now Find the Value at Now by discounting the above value.

Value today = 666666.6667 / (1.11)

Value today = 600,600.6006

2. Now calculate the Value as per 30% probability

Applying same concept as above. Here growth = 0

P1 = Price at year 1, E2= Earnings at year 2, Ke= required return, g= growth

= 10000 / (0.11)

= 90909.09091

Value at year 1 = 90909.09091

Now Find the Value at Now by discounting the above value.

Value today = 90909.09091 / (1.11)

Value today = 81,900.08190

3. Now using the Probabilty calculate the expected Present value of earnings

= (600600.6006 x 0.70)+(81900.08190 x 0.30)

= 420420.4204 + 24570.02457

Expected Presnt value of future earnings = 444990.4450

4. Calculate NPV

NPV = Present value of future earnings - Initinal investmend - Pv of additiona investment

= 444990.4450 - 100000 - (50000/(1.11)

=344990.4450 - 45045.045045

NPV of the project = + 299,945.40