Introductory Finance - Applewriters
I need help on 10.1 10.2 and 10.3.
9.1The Constant-Growth-Rate Discounted Dividend Model, as described equation 9.5 on page 247, says that:P0 = D1 / (k – g)A.rearrange the terms to solve for:i. G ii. D1.As an example, to solve for k, we would do the following:1. Multiply both sides by (k – g) to get: P0 (k – g) = D12. Divide both sides by P0 by to get: (k – g) = D1 / P03. Add g to both sides: k = D1 / P0 + g (8 marks)Given,P0 = D1 / (k – g)(k-g) * P0 = (k-g)* D1 / (k – g)k- g = D1/P0g = k – D1/P0 Given,P0 = D1 / (k – g)(k-g) * P0 = (k-g)* D1 / (k – g)K*P0- g*P0 = D19.2Notation: Let Pn = Price at time nDn = Dividend at time nYn = Earnings in period nr = retention ratio = (Yn– Dn) / Yn = 1 – Dn/ Yn = 1 – dividend payout ratioEn = Equity at the end of year nk = discount rateg = dividend growth rate = r x ROEROE = Yn / En-1 for all n>0.We will further assume that k and ROE are constant, and that r and g are constant after the first dividend is paid. A.Using the Discounted Dividend Model, calculate the price P0 if D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1 = 100 per share P0 = D1/(k-g) = 20/(0.15-0.12) = 666.67 B.What, then, will P5 be if:D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12? P5 = D6/(k-g) = 20/(0.15-0.12) = 666.67 C.If P5 = your result from part B, and assuming no dividends are paid until D6, what would be P0? P1? P2? P0 = P5/(1+k)^5 = 666.67/(1.15)^5 = 331.45P1 = P5/(1+k)^4 = 666.67/(1.15)^4 = 381.17P2 = P5/(1+k)^3 = 666.67/(1.15)^3 = 438.34 D.Again, assuming the facts from part B, what is the relationship between P2 and P1 (i.e., P2/P1)? Explain why this is the result.If we look at the formulae in part c, we can see the below relationship:P2/P1 = (1+k)This is because if no dividends are paid between the two periods, the only factor that remains is the discount factor. E.If k = ROE, we can show that the price P0 doesn’t depend on r. To see this, let g = r x ROE, and ROE = Yn / En-1, and since r = (Yn – Dn) / Yn , then D1 = (1 – r) x Y1 andP0=D1 / (k – g)P0=[(1 – r) x Y1]…
5.1Assume you have $1 million now, and you have just retired from your job. You expect to live for 20 years, and you want to have the same level of consumption (i.e., purchasing power) for each of these 20 years, after adjusting for inflation. You also wish to leave the purchasing power equivalent of $100,000 today to your kids at the end of the 20 years as a bequest (or to pay them to take care of you).You expect inflation to be 3% per year for the next 20 years, and nominal interest rates are expected to stay around 8% per year.A.Calculate the actual amount of consumption, in nominal dollars, using the stated assumptions.i.How much do you need for your kids?ii.If you plan to consume $1.03 in year 1, how much will you need to have to keep the same real consumption in year 2? In year 10? In year 20?iii.How much, in nominal dollars, will $1 of retirement funds earn in year 1? Year 2? Year 10? Year 20?iv.In an Excel spreadsheet (or in a manual table), calculate the following:a.annual investment earnings for each yearb.total savings after investment earnings for each yearc.subtract annual consumption from total savings each yeard.by trial and error, or with the Goal Seek command, determine the amount of consumption that will give you exactly $100,000, in today’s purchasing power, at the end of 20 yearsHint: You will need to make your annual consumption column dependent on the inflation rate, your investment earnings will grow at the nominal rate, and the bequest of $100,000 will grow at the inflation rate.B.Do the calculation again using real rates, and setting inflation to equal 0. If you set up your Excel spreadsheet carefully, you should be able to set the inflation rate to equal 0 and enter the real rate of return as the investment earning rate.i.What is the amount of real consumption in year 1? In year 2? In year 10? In year 20?ii.Show that this is consistent with your calculation using nominal rates.iii.How much, in real dollars, does that leave for your…
9.1The Constant-Growth-Rate Discounted Dividend Model, as described equation 9.5 on page 247, says that:P0 = D1 / (k – g)A.rearrange the terms to solve for:i. G ii. D1.As an example, to solve for k, we would do the following:1. Multiply both sides by (k – g) to get: P0 (k – g) = D12. Divide both sides by P0 by to get: (k – g) = D1 / P03. Add g to both sides: k = D1 / P0 + g (8 marks) 9.2Notation: Let Pn = Price at time nDn = Dividend at time nYn = Earnings in period nr = retention ratio = (Yn– Dn) / Yn = 1 – Dn/ Yn = 1 – dividend payout ratioEn = Equity at the end of year nk = discount rateg = dividend growth rate = r x ROEROE = Yn / En-1 for all n>0.We will further assume that k and ROE are constant, and that r and g are constant after the first dividend is paid. A.Using the Discounted Dividend Model, calculate the price P0 if D1 = 20, k = .15, g = r x ROE = .8 x .15 = .12, and Y1 = 100 per share B.What, then, will P5 be if:D6 = 20, k = .15, and g = r x ROE = .8 x .15 = .12? C.If P5 = your result from part B, and assuming no dividends are paid until D6, what would be P0? P1? P2? D.Again, assuming the facts from part B, what is the relationship between P2 and P1 (i.e., P2/P1)? Explain why this is the result. E.If k = ROE, we can show that the price P0 doesn’t depend on r. To see this, let g = r x ROE, and ROE = Yn / En-1, and since r = (Yn – Dn) / Yn , then D1 = (1 – r) x Y1 andP0=D1 / (k – g)P0=[(1 – r) x Y1] / (k – g)P0=[(1 – r) x Y1] / (k – g), but, since k = ROE = Y1 / E0P0=[(1 – r) x Y1] / (ROE– r x ROE)P0=[(1 – r) x Y1] / (Y1 / E0 – r x Y1 / E0)P0=[(1 – r) x Y1] / (1 – r) x Y1 / E0), and cancelling (1 – r)P0=Y1 / (Y1/E0) = Y1 x (E0 / Y1) = E0 So, you see that r is not in the final expression for P0, indicating that r (i.e., retention ration or, equivalently, dividend policy) doesn’t matter if k = ROE.Check that changing r from .8 to .6 does not change your answer in part A of this question by re-calculating your result using r = .6. (10 marks)