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Unformatted text preview: ivalent to: Internal growth rate = (NI / TAB) × b Since ROAB = NI / TAB 47 The internal growth rate equation is: Internal growth rate = ROAB × b 30. Since the company issued no new equity, shareholders’ equity increased by retained earnings. Retained earnings for the year were: Retained earnings = NI – Dividends Retained earnings = $95,000 – 68,000 Retained earnings = $27,000 So, the equity at the end of the year was: Ending equity = $183,000 + 27,000 Ending equity = $210,000 The ROE based on the end of period equity is: ROE = $95,000 / $210,000 ROE = 45.24% The plowback ratio is: Plowback ratio = Addition to retained earnings/NI Plowback ratio = $27,000 / $95,000 Plowback ratio = .2842 or 28.42% Using the equation presented in the text for the sustainable growth rate, we get: Sustainable growth rate = (ROE × b) / [1 – (ROE × b)] Sustainable growth rate = [.4524(.2842)] / [1 – .4524(.2842)] Sustainable growth rate = .1475 or 14.75% The ROE based on the beginning of period equity is ROE = $95,000 / $183,000 ROE = .5191 or 51.91% Using the shortened equation for the sustainable growth rate and the beginning of period ROE, we get: Sustainable growth rate = ROE × b Sustainable growth rate = .5191 × .2842 Sustainable growth rate = .1475 or 14.75% Using the shortened equation for the sustainable growth rate and the end of period ROE, we get: Sustainable growth rate = ROE × b 48 Sustainable growth rate = .4524 × .2842 Sustainable growth rate = .1286 or 12.86% Using the end of period ROE in the shortened sustainable growth rate results in a growth rate that is too low. This will always occur whenever the equity increases. If equity increases, the ROE based on end of period equity is lower than the ROE based on the beginning of period equity. The ROE (and sustainable growth rate) in the abbreviated equation is based on equity that did not exist when the net income was earned. 49 CHAPTER 4 DISCOUNTED CASH FLOW VALUATION
Answers to Concepts Review and Critical Thinking Questions 1. 2. 3. 4. 5. 6. 7. Assuming positive cash flows and interest rates, the future value increases and the present value decreases. Assuming positive cash flows and interest rates, the present value will fall and the future value will rise. The better deal is the one with equal installments. Yes, they should. APRs generally don’t provide the relevant rate. The only advantage is that they are easier to compute, but, with modern computing equipment, that advantage is not very important. A freshman does. The reason is that the freshman gets to use the money for much longer before interest starts to accrue. It’s a reflection of the time value of money. TMCC gets to use the $24,099 immediately. If TMCC uses it wisely, it will be worth more than $100,000 in thirty years. This will probably make the security less desirable. TMCC will only repurchase the security prior to maturity if it is to its advantage, i.e. interest rates decline. Given the drop in interest rates needed to make this viable for TMCC, it is unlikely the company will repurchase the security. This is an example of a “call” feature. Such features are discussed at length in a later chapter. The key considerations would be: (1) Is the rate of return implicit in the offer attractive relative to other, similar risk investments? and (2) How risky is the investment; i.e., how certain are we that we will actually get the $100,000? Thus, our answer does depend on who is making the promise to repay. The Treasury security would have a somewhat higher price because the Treasury is the strongest of all borrowers. 8. 9. 10. The price would be higher because, as time passes, the price of the security will tend to rise toward $100,000. This rise is just a reflection of the time value of money. As time passes, the time until receipt of the $100,000 grows shorter, and the present value rises. In 2019, the price will probably be higher for the same reason. We cannot be sure, however, because interest rates could be much higher, or TMCC financial position could deteriorate. Either event would tend to depress the security’s price. Solutions to Questions and Problems NOTE: All-end-of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. The simple interest per year is: $5,000 × .09 = $450 So, after 10 years, you will have: $450 × 10 = $4,500 in interest. The total balance will be $5,000 + 4,500 = $9,500 With compound interest, we use the future value formula: FV = PV(1 +r)t FV = $5,000(1.09)10 = $11,836.82 The difference is: $11,836.82 – 9,500 = $2,336.82 2. To find the FV of a lump sum, we use: FV = PV(1 + r)t a. b. c. d. FV = $1,000(1.06)10 = $1,790.85 FV = $1,000(1.09)10 = $2,367.36 20 FV = $1,000(1.06) = $3,...
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