Dr. P.V. Viswanath

pviswanath@pace.edu

Solutions to Final Exam

1. This is a 17-year growing annuity. The formula for the growing annuity is: PV=(1-(), where C is the first year profit, r is the interest rate, g is the growth rate,  and N is the number of periods. Plugging in the numbers, we get PV=($5,000,000/(0.07-0.03))*(1-(1.03/1.07)¹⁷) = =125,000,000*(1-0.523249) =$59,593,875.
   
   
2. 
   a. The company’s growth rate in earnings is proportional to its retention rate and the return it can get from its new investments. Thus, Earnings Growth Rate= Retention Rate*Return on New Investments. Substituting the appropriate values, we get (2.17/5.13)*14.7% = 6.22%.
   b. According to constant dividend method,  the value of the firm depends upon dividends for the next year, divided by the equity cost of capital adjusted by growth rate. Thus, P0= , where, P0 is current stock price per share, Div1 is the next dividend payment, RE is equity cost of capital, and g is expected dividend growth rate. For the constant payout ratio, the expected dividend growth is equal to the expected earnings growth; in this case, g=6.22%. Thus, P0=2.96/(0.118-0.0622) = $53.05.
   
   
3. Systematic risk/Diversifiable risks:
   1. The risk that your main production plan is shut down due to a tornado. Diversifiable risk
   2. The risk that the economy slows, decreasing demand for your firm’s products. Systematic risk.
   3. The risk that your best employees will be hired away. Diversifiable.
   4. The risk that the new product you expect your R&D division to produce will not materialize. Diversifiable risk.
      
      
4. 
   

   Year	0	1	2	3	4	5
   Sales	-	13000	22698	30326	36202	-
   Cost of goods sold	-	-6000	-9196	-10784	-11300	-
   Gross Profits	-	7000	13502	19542	24902	-
   SG&A	-	-2800	-2800	-2800	-2800	-
   R&D	-15000	-	-	-	-	-
   Depreciation	-	-2500	-2500	-2500	-	-
   EBIT	-15000	1700	8202	14242	22102	-
   Income Tax at 40%	6000	-680	-3281	-5697	-8841	-
   Unlevered Net Income	-9000	1020	4921	8545	13261	-

   Suppose that HomeNet Will have no incremental cash or inventory requirements, which implies that products will be shipped directly from contract manufacturer to customers.  Furthermore, assume that HomeNet will have no working capital requirements.
   Since there are no working capital requirements, free cash flow can be computed by taking unlevered net income, adding back depreciation and adjusting for capital expenditures and other cashflows.
   
   

   Year	0	1	2	3	4	5
   Unlevered Net Income	-9000	1020	4921	8545	13261	-
   Plus: Depreciation	-	2500	2500	2500	-	-
   Minus: Capital Expenditures	-7500	-	-	-	-	-
   Free Cash Flow	-16500	3520	7421	11045	13261
   Present Value (at 10%	-16500	3200	6133.06	8298.27	9057.44	-

   
   The NPV, thus, works out to $10,188.71 (in '000s). Hence the project is worth taking.
   
   
5. The price can be solved as P=C* *(1-)+, where C is the coupon in dollars, where P=$1100, y=6%, FV=$1000, assuming annual coupons. Solving, we find $1100=C*(1-)+, or C = $83.74. Hence the coupon rate is 83.74/1000=8.374%.
   
   
6. 
   
   
1. It would be difficult to make money off this pattern. Once the pattern is noticed by other traders, they will all want to capitalize on it. Hence they would buy on the second day in expectations of the rise on the third day. This would cause the price to rise on the second day itself. Finally, expectations of the second day rise would cause the entire increase to happen on the first day. Thus, knowledge of the pattern itself would tend to destroy the pattern and prevent the ability to make money off it.
2. Long-term bonds are more volatile. This is because changes in interest rates affect cash flows (coupon payments) over many periods. Furthermore, the discount factor for farther cash flows is affected much more in percentage terms for a given change in interest rates because the discounting function is nonlinear. However, the lower volatility of longer-term yields causes longer-term bond price volatility to be less than it would be otherwise. Nevertheless, longer-term bonds are, indeed, more volatile than shorter-term bonds.
3. The easiest way to do this is to regress asset returns on returns on a diversified index such as the S&P 500. The estimated slope coefficient is an estimate of the beta. There could be problems with such a beta particularly if not enough observations are available, but the estimated beta is, nevertheless a useful first-pass estimate.
4. Even if the space is currently not used, there is still an opportunity cost to the use of the space. This implict cost should be imputed to the space. If the project were not to be taken, then that space should be rented out, optimally.
5. This is true only if all earnings are paid out as earnings. Else, the dividends would differ from the earnings by the amount of the reinvested earnings. If these investments are positive NPV ones, then the true price would end up being greater than the price computed by simply discounting earnings.
   
   
7. 1. The most obvious inference would be that the bond with a larger spread was more risky.
   2. John Duensing notes that the spreads on investment-grade financials are higher than has historically been the case. He believes, therefore, that prices will rise when the spreads go back to their historical yields, investors in these bonds will have made a profit. He clearly doesn't believe that the higher spreads are due to higher risk.
   3. One evidence that Duensing is wrong is the fact that credit default swaps on financial bonds are pricing in a higher default rate than non-financials, thus suggesting that the market thinks that financial bonds are riskier than non-financials.
      

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