Corporate Finance Outline

 
CORPORATE FINANCE
WANG
SPRING 2014
 
 
 
A. Valuation of a Going Concern
I. Discounting Future Returns to Present Value
            I. Capitalizing or Capitalization
                        i. Formula: A = P (1 + r)t
II. Discounting a Single Future Payment to Present Value: The process of finding the present value of a series of future payments.
      i. Formula: P = A / (1 + r)t
ii. Discount Rate = The interest rate used to calculate the present value.
      iii. Lower discount rate more conservative.
III. Annuity/Discounting to Present Value a Series of Future Payments (Equal) = A series of equal annual amounts for a specified number of years.
i. Do not need to know the alternate formula. Just know divide & conquer grocery basket approach & look at Table 11-3 (PV of an Annuity Table).
            V. Relationship Between Discounting & Capitalizing
i. Capitalize & Capitalizing used when future equal payments are expected to continue in perpetuity.
ii. Discount & Discounting used with finite set of future payments.
iii. Discounting an even perpetual stream
            a. Great Disappearing Trick & an infinite series
                        1. A/(1+r) + A/(1+r)2 + … + A/(1+r)¥
            VI. Interest Rate and Present Value have an Inverse Relationship
i. At lower interest rates, one must deposit more money now in a savings account to have some fixed amount in the future.
            VII. Yield
i. Yield is defined as the rate of return that will be earned by a lender if the full amount of interest and principal that the borrower has agreed to pay are paid on schedule.
            a. In other words, a promised rate of return.
b. e.g. 10 year bond and an annual interest payment of $100 on an investment of $900. The current yield would be 11 percent.
c. However, “yield” means “yield to maturity” (true yield) which involves the issue of compound interest. The yield of the bond would actually be 11.72 percent, not 11 percent.
d. Remember, yield reflects the promised rate of return, not the expected rate of return.
            VIII. Why is the Interest Rate Positive?
i. The real interest rate is positive because it is the nominal (actual) rate minus the rate of anticipated inflation where there are default risk and resale volatility risk. The number should be at least zero or else people would be hoarding.
ii. Has to compensate for inflation rate & present consumption is “worth more” psychologically than future consumption where people must be paid to defer gratification.
            IX. Taking Tax Into Consideration
                        i. When capitalizing, adjusting for tax: there are two possible approaches:
                                    a. Suboptimal: simply ignore taxes and use the pre-tax savings account rate.
b. Better Approach: Take after-tax returns on investment opportunity and take after-tax rate on savings account.
                                    c. If you want to play it safe, always use after-tax returns and after-tax rate.
                                                1. Ex. Look at Problem 10.
                        ii. You should always discount after-tax return(s).
                                    a. Take after-tax returns on investment opportunity and use after-tax rate on savings account.
1. Ex. Look at Problem 10 & Look at Problem 11, don’t forget to find the real rate of inflation by subtracting the nominal rate by the inflation rate (anticipated inflation).
II. The Factor of Expected Returns
            I. The composition of “returns”
                        i. Few income producing assets last forever; assets must be replaced or else it wears out.
                        ii. The net inflow of cash is sometimes called “cash flow.”
                        iii. Accountant’s method of calculating the annual earnings of a firm: straight-line depreciation
                                    a. Divide the cost of building by life of the building.
1. Viewed as either (1) the annual decline in the value of the building or (2) an amortization, i.e., the averaging out of the original cost of the building.
(a) Remember that amortization is taking the cost of the income producing asset gradually over its useful life of income production.
            b. Then subtract the earnings by the depreciation.
            c. Then take the result and divide it by the capital rate
            d. Ex. Look at Problem 14.
            e. Issues with using the accounting depreciation
1. Blum & Katz: normal accounting depreciation fails to take into account the time lag between disinvestment and reinvestment.
2. Accounting earnings overstates the amount of annual earnings that needs to be set aside to provide for future replacement because money has a time value.
3. Therefore, undervaluation of the returns available for distribution and therefore undervaluation of the firm. Accounting depreciation is irrelevant except impact on taxes.
iv. Interest-bearing sinking fund approach: annual charge should be the amount that, annually deposited at a compound rate of interest equal to the capitalization rate, would grow to the total cost at the end of a set amount of years.
            a. Can be calculated using the reverse annuity table. We are not responsible for knowing this.
b. Taking the result using the figure from the reverse annuity table, subtract the cash flow by the result in order to find the proper annual earnings of the firm.
c. Then take the proper annual earnings of the firm and divide it by the capitalization rate in order to find the capitalized value of the firm.
d. Ex. Look at Problem 14.
v. How do you accurately value the enterprise without using the interest-bearing sinking fund approach?
            a. Method 1: The Bathtub Approach
                        1. Focus on the actual cash inflows & outflows (actual cash receipts & disbursements)
2. Subtract the P.V. of all cash inflows by the P.V. of future cash outflows ($500,000 every 10 years)
(a) Imagine a bathtub where you are putting the P.V. of all cash inflows inside of the tub and draining the P.V. of all future cash outflows.
                                    (b) Find the P.V. of inflows of net net rent by dividing the net net rent by the cap rate.
                                    (c) Find the P.V. of outflows by using the divide and conquer grocery basket method.
                                                (i) outflow/(1 + rate)year replaced + outflow (1 + rate)2nd year replaced + ….. +
                                                     outflow/(1+rate)¥
                                                (ii) How do you calculate the value of the infinite series of quotients?
                                                (iii) Great Disappearing Trick:
                                                            (1) Set “X” equal to infinite series
(2) Multiply both sides (of equation) by denominator of first quotient in infinite series.
(3) Subtract the first equation from second equation.
(4) Keep solving the rest of the equation, see Problem 15.
                                    (d) Finally subtract the P.V. of inflows by the P.V. of outflows.
            b. Method 2: Quick and Dirty Method – Treating Firm as Wasting Assets
1. Just find the P.V. of yearly cash inflow for the number of years before building becomes waste. Ignore the years afterwards.
                                    (a) To find the P.V., just use Table 11-3’s figure and multiply it by the yearly inflow.
                                    (b) Fairly close result. What accounts for the different results between both methods?
(i) The excess is in large part the value of the land, which depends on where you are.
vi. Positive investment is investment in new income-producing assets, as opposed to replacement of existing assets.
vii. When discounting future net returns, there is no reason to distinguish between amounts retained for investment in new projects from amounts retained to replace existing assets.
            a. Replacement of existing assets is an outflow.
            b. Don’t double-count. Double-counting is counting the replacement of building as inflow.
c. In other words, the act of investment by the firm involves an actual cash outflow. These funds are lost to the firm and only benefit by