Instructions: The Company has one asset. The asset has a three-year life and two possible payoffs each year: 1) $750 with a probability of 40%, and 2) $100 with a probability of 60%. The company depreciates assets using the straight-line method. Assume the states between years are independent, an interest rate of 6%, and state 1 is realized in year 1. Show the balance sheet, income statement, and residual income / goodwill analysis for year 1.
IBelieve this is the right answer, but I'm not totally sure goodwill was calculated correctly.
Year 0 1
Balance Sheet
Cash $0.00 $750.00
Investment(Book Value) $962.28 $641.52
Total Assets $962.28 $1,391.52
Net Worth
Invest Capital $962.28 $962.28
Retained Earnings $0.00 $429.24
Total Net Worth $962.28 $1,391.52
Income Statement
Actual cash flows $750.00
Depreciation $320.76
Interest Income $0.00
Net Income $429.24
Residual Income Analysis- Year 1
Expected interest income $45.00
Depreciation $320.76
Actual if good state $750.00
Good state Net Income $474.24
Expected Interest Income $45.00
Depreciation $320.76
Actual if bad state $100.00
Bad state Net Income ($175.76)
Expected Income $214.24
Return on Net Worth $83.49
Expected abnormal earnings $130.75
Goodwill $118.86
Valuation
BV 1391.522868
Gw $118.86
PA 1510.383953
I think this is right up to expected income. Don't you have to add the Good State x .60 and the bad state x .40 to arrive at expected income? And you take the present value of goodwill in the valuation.
To calculate the balance sheet, income statement, and residual income/goodwill analysis for year 1, we need some additional information. Specifically, we need to know the initial cost of the asset and the depreciation expenses for the first year.
Let's assume the initial cost of the asset is $1,000, and the straight-line depreciation method is used. This means that the asset's value decreases by the same amount each year over its three-year life. Since the asset has a three-year life, the annual depreciation expense would be $1,000 divided by 3, which is $333.33 per year.
Now, let's calculate the balance sheet for year 1:
1. Assets:
- Cash: $0 (assuming no other cash or asset)
- Asset (net of accumulated depreciation): $1,000 - $333.33 = $666.67
2. Liabilities:
- No information is given about liabilities, so we assume there are no liabilities.
3. Equity:
- Retained earnings (beginning of year): $0 (assuming the company has just started)
- Net income: To calculate the net income, we need to determine the revenue and expenses for year 1.
To calculate the revenue for year 1, we need to consider the probability of each payoff and their respective amounts. Since state 1 is realized in year 1, there are two possibilities:
- $750 with a probability of 40%: $750 * 0.40 = $300
- $100 with a probability of 60%: $100 * 0.60 = $60
Adding these two possibilities together, the revenue for year 1 is $300 + $60 = $360.
The expenses for year 1 consist of the depreciation expense, which we already calculated as $333.33.
So, the net income for year 1 would be:
Net Income = Revenue - Expenses
Net Income = $360 - $333.33
Net Income = $26.67
Now, let's calculate the residual income/goodwill for year 1.
Residual Income = Net Income - (Equity * Required Rate of Return)
Given that the interest rate is 6% and the equity (retained earnings) is $0, the residual income for year 1 would be:
Residual Income = $26.67 - ($0 * 6%)
Residual Income = $26.67
Since the equity (retained earnings) is $0, there is no goodwill to calculate.
To summarize the analysis for year 1:
- Balance Sheet:
- Assets: Cash $0, Asset $666.67
- Liabilities: None
- Equity: Retained earnings $0
- Income Statement:
- Revenue: $360
- Expenses: Depreciation $333.33
- Net Income: $26.67
- Residual Income/Goodwill Analysis:
- Residual Income: $26.67
- Goodwill: Not applicable (equity is zero)