Answer:
NPV = $11,525.6
Probability the project has negative NPV: 30%
Explanation:
1. When there is no risk:
It is given that the initial British corporate tax rate on income earned by US firms is 40%.
The initial investment: $200,000
<em>The cash flow of Hoosier can be described as following: </em>
+) The addition to the cash flow includes:
- Pretax earnings: £300,000
+) The subtraction to the cash flow includes:
- Tax on income (40%): £300,000 x 40% = £120,000
=> The cash flow = 300,000 - 120,000 = £180,000 = 180,000 x $1,6 = $288,000
=> The Present value of the project after one year is:
<em>PV = Cash flow/ [(1 + required rate of return)^ 1 year]</em>
<em>= 288,000/ (1+0.18) = $244,068</em>
=> The Net Project Value is:
<em>NPV1 = ∑PV - Initial investment = 244,068 - 200,000 = $44,068</em>
2. Case 2: The British economy may weaken
The initial British corporate tax rate on income earned by US firms is 40%.
The initial investment: $200,000
<em>The cash flow of Hoosier can be described as following: </em>
+) The addition to the cash flow includes:
- Pretax earnings: £200,000
+) The subtraction to the cash flow includes:
- Tax on income (40%): £200,000 x 40% = £80,000
=> The cash flow = 200,000 - 80,000 = £120,000 = 120,000 x $1,6 = $192,000
=> The Present value of the project after one year is:
<em>PV = Cash flow/ [(1 + required rate of return)^ 1 year]</em>
<em>= 192,000/ (1+0.18) = $162,712</em>
=> The Net Project Value is:
<em>NPV 2= ∑PV - Initial investment = 162,712 - 200,000 = -$37,288</em>
<em />
3. Case 3: The British corporate tax rate on income earned by U.S. firms may increase from 40 to 50 percent
British corporate tax rate on income earned by US firms is 50%.
The initial investment: $200,000
<em>The cash flow of Hoosier can be described as following: </em>
+) The addition to the cash flow includes:
- Pretax earnings: £300,000
+) The subtraction to the cash flow includes:
- Tax on income (50%): £300,000 x 50% = £150,000
=> The cash flow = 300,000 - 150,000 = £150,000 = 150,000 x $1,6 = $240,000
=> The Present value of the project after one year is:
<em>PV = Cash flow/ [(1 + required rate of return)^ 1 year]</em>
<em>= 240,000/ (1+0.18) = $203,390</em>
=> The Net Project Value is:
<em>NPV3= ∑PV - Initial investment = 203,390 - 200,000 = $3,390</em>
The probability of the case there is no risk = 100% - probability of Case 2 - probability of case 3 = 100% - 30% - 20% = 50%
The expected value of the project’s net present value is:
<em>NPV = probability Case 1 x NPV1 + probability Case 2 x NPV2 + probabilityCase 3 x NPV3 </em>
= 50% x 44,068 + 30% x (-37,288) + 20% x 3,390= $11,525.6
<em>As only the NPV of case 2 are negative, so that the probability that the project will have a negative NPV = probability case 2 = 30%</em>
<em />
