Computation of Intrinsic value: Exercise
Let us assume Sky Limited intends to pay a $1 dividend per share next year and
it is expected that this would increase by 5% per year thereafter. Let us further
assume the required rate of return on Sky Limited’s stock is 10%. Currently, XYZ
Company stock is trading at $10 per share. Further, assume that during the next
few years Sky Limited’s dividends will increase rapidly and then grow at a stable
rate. Next year's dividend is still expected to be $1 per share, but dividends will
increase annually by 7%, then 10%, then 12%, and then steadily increase by 5%
after that.
Compute the intrinsic value and fair value of Sky Limited’s stock.
Answer
Intrinsic value = D1/(K-g)
The intrinsic value of the stock = Dividend per share / (Required Rate of Return
-The growth rate of Dividends) = $1.00/(.10-.05) = $20.
The current fair value of the stock
D1 = $1.00
k = 10%
g1 (dividend growth rate, year 1) = 7%
g2 (dividend growth rate, year 2) = 10%
g3 (dividend growth rate, year 3) = 12%
gn (dividend growth rate thereafter) = 5%
Since we know the dividend growth rate, we can calculate the actual dividends
for those years:
D1 = $1.00
D2 = $1.00 * 1.07 = $1.07
D3 = $1.07 * 1.10 = $1.18
D4 = $1.18 * 1.12 = $1.32
We now calculate the present value of each dividend during the unusual growth
period:
$1.00 / (1.10) = $0.91
$1.07 / (1.10)2 = $0.88
$1.18 / (1.10)3 = $0.89
$1.32 / (1.10)4 = $0.90
10% is the required return
Now, we value the dividends occurring in the stable growth period, starting by
calculating the fifth year's dividend:
D5 = $1.32*(1.05) = $1.39
5% is the stable growth rate of dividends.
We then apply the stable-growth Gordon Growth Model formula to these
dividends to determine their value in the fifth year:
$1.39 / (0.10-0.05) = $27.80
10% is the required return and 5% is the growth rate.
The present value of these stable growth period dividends is then calculated:
$27.80 / (1.10)5 = $17.26
Finally, we can add the present values of Sky Limited’s future dividends to arrive
at the current intrinsic value of Sky Limited stock:
[$0.91+$0.88+$0.89+$0.90+$17.26] = $20.84.
The multistage growth model also indicates that Sky Limited stock is
undervalued (a $20.84 intrinsic value, compared with a $10 trading price).
Residual method of valuation
This method is used to assess the Market Value of land, or land and buildings,
where there is potential for the land to be put to a higher value use. For instance:
a) farmland being sold for residential, commercial, or industrial development; b)
existing buildings that could be cleared and the land redeveloped for another
use; and c) existing buildings that could be converted to another, more valuable
use.
The method is sometimes known as the ‘development method’. Development
in this context refers to the highest and best use, in terms of value, that is
physically possible, legally permissible, and economically viable.
Exercise
From the following information compute the Gross Residual Value:
Market rent
$ 2,000 per sq. ft. per year
The building costs $
1,000 per sq. ft.
Development period
2 years
Letting cost
10% of the first year’s rent
Sale Fee
1% of development value
Professional Fees
3% of all costs
Interest on borrowed money 14%
Market capitalisation rate
10%
Developer’s profit
20% of the construction cost
Additional Information:
Consent has been given to construct a building on a land area of 6,000 sq. ft.
with a gross build area of 6,500 sq. ft.
Find the Residual Value.
Particulars
Annual Rent 6500 sq. ft*$2000
$ 1,30,00,000
Capitalized at 10% *1,30,00,000
$ 13,00,00,000
Letting fees at 10% * 1,30,00,000
$.13,00,000
Sale fee at 1%* 13,00,00,000
$ 13,00,000
Total fees
$ 26,00,000
Capitalized Rent – Total Fees
$ 12,74,00,000
Net Development Value
Construction costs
$65,00,000
Fees at 3% of all costs 65,00,000*0.03
$ 1,95,000
Interest at 14% *Construction costs + Fees
14%* ($. 65,00,000 + Rs. 1,95,000)
$. 9,37,300
Costs before profit
Profit on costs at 25%
Total cost (6500000+195000+937300)
$ 76,32,300
Gross Residual Value (Gross Development
Value – Net Development Value
(127400000-7632300)
$11,97,67,700
Estimating Cash Flow
A supermarket is deciding whether to install a sushi vending machine. The
vending machine costs $250,000 in year 0 and has a salvage value of $0 at the
end of 5 years. Ignoring taxes, what are the cash flows of this project?
Particulars
Sales
Operating
Expenses
Depreciation
Pre-tax profit
After-tax
profit (if the
tax rate is 0%)
Year
0
Year 1
Year2
Year 3
Year 4
Year 5
250,000
200,000
300,000
200,000
300,000
200,000
250,000
200,000
250,000
200,000
50,000
0
0
50,000
50,000
50,000
50,000
50,000
50,000
50,000
0
0
50,000
0
0
Answer
Particulars
Investment
Sales
Operating
Expenses
Cash Flows
Year 0
-250,000
Year 1
Year2
Year 3
Year 4
Year 5
250,000 300,000
200,000 200,000
300,000 250,000
200,000 200,000
250,000
200,000
50,000
100,000 50,000
50,000
100,000
The formula for calculating Cash Flows.
Total Cash Flow = Cash Flow from Investment in Plant and Equipment + Cash
Flow from Investments in Working Capital + Cash Flow from Operations.
Working Capital = Investments in Inventory and Accounts Receivable.
It is to be noted that cash flow is measured by the change in working capital
rather than the level of working capital.
Cash Flow from Operations = Revenues – Cash Expenses – Tax Paid
= After Tax Profit + Depreciation
= (Revenues – Cash Expenses) x (1- Tax Rate) + (Depreciation x Tax Rate).
Exercise-2
A project generates revenues of $1,000, cash expenses of $600, and
depreciation charges of $200 in a particular year. The firm's tax rate is 35%.
What is the firm's net income?
Answer
Profit Before Taxes = revenues - cash expenses - depreciation = (1000-6000200) =$200
Taxes = profit before taxes * tax rate = (200 *0.35) = $70
Profit After Taxes = profit before taxes - taxes = (200-70) = $130
Cash Flow from Operations
First Method
Revenues - Cash expenses - Taxes paid = $1000 - $600 - $70 = $330
Second Method
After-tax profit + Depreciation = $130 + $200 = $330
Third Method
(Revenues - Cash expenses) x (1 - Tax rate) + (Depreciation x tax rate) = ($1000
- $600) x (1 - .35) + ($200 x .35) = $330