Partiel 2022 corpo
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: MALEKATOR
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.75 Ko KB
Mis en ligne Uploaded: 15/12/2024 - 15:49:18
Uploadeur Uploader: MALEKATOR (Profil)
Téléchargements Downloads: 4
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4406962
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.75 Ko KB
Mis en ligne Uploaded: 15/12/2024 - 15:49:18
Uploadeur Uploader: MALEKATOR (Profil)
Téléchargements Downloads: 4
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4406962
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
What is the present value of the following stream of cash-flows? ¬5,000 every year over the next 10 years (first payment in one year) + ¬10,000 every year over the following 10 years The annual interest rate remains at 3% over the next 5 years and will be equal to 7% in the following next 15 years. To reduce your calculations, you can pick the relevant values in the following table: PV=5000/0.03*(1-(1/1.03^5))+1/1.03^5*5000/0.07(1-(1/1.07^5))+1/1.03^5*1.07^5 * 10000/0.07 * (1-((1/1.07^10))=83779 ---------------------------------------------------------------------------------- A company plans to acquire a machine and to use it over the next 12 years. You are given the following information: - Initial payment: ¬50,000 to be paid now - Maintenance costs of ¬5,000 in exactly 4 years, 8 years and 12 years. - The machine will be sold for ¬10,000 in exactly 12 years. In 12 years, the company will have to purchase a new machine at the same price, bear the same costs and timing of maintenance and will be able to sell it at the same price (¬10,000) 12 years later (that is in 24 years). The company uses a 7% annual discount rate. What is the equivalent annual cost of a machine over a 24-year period? Round your answer to the nearest integer number. 50000+ 5000/1.07^4+ 5000/1.07^8+ 5000/1.07^12- 10000/1.07^12=54504 EAC= (54504*0.07) / (1- 1 / 1.07^12)= 6 862 ------------------------------------------------------------------------------------- You want to invest your wealth in Alpha and Beta through a portfolio P who presents the lowest risk. Alpha and Beta present the following characteristics: " Alpha: 3 times over 4, return is -2%; in the remaining cases, it is +10% " Beta: 1 times over 4, return is -4%; in the remaining cases, it is +6% The covariance of the returns between Alpha and Beta is -0.00225. Which are the weights and what is the level of risk for P? Solution: By the standard formula, we can compute the expected return of Alpha = 1% and of Beta = 3.5% After that come the variances: 0.0027 for Alpha and 0.001875 for Beta; then the standard deviations: 0.05196 for Alpha and 0.0433 for Beta. Knowing the value of the covariance, we deduce that the correlation is exactly -1. It is therefore possible to build a riskless portfolio. Let us call x the weight invested in Alpha; the variance of P is given by: x² 0.0027 + (1 x)² 0.001875 + 2 x (1 x) 0.0519 0.0433 Solving to get 0 leads to x = 0.5 ---------------------------------------------------------------------------------------- You intend to build a portfolio invested in the assets X, Y and the Treasury Bill. - X has an expected return of 9% and a standard deviation of 0.5 - Y has an expected return of 7% and a standard deviation of 0.3 The Treasury Bill provides a return of 3%. Thirty percent of your wealth will go in the Treasury Bill, the remaining has to be shared between X and Y, targeting a return of 6.4% If the correlation between the returns of X and Y is 1.2, what is the standard deviation of your portfolio? Solution: Let us call w the weight invested in X. We can write: w 9% + (1 0.3 - w) 7% + 0.3 3% = 6.4% We deduce that w = 0.3 and 0.4 is invested in Y. The variance of the portfolio is: 0.3² 0.5² + 0.4² 0.3² + 2 0.3 0.4 cov(X,Y) But cov(X,Y) = 1.2 0.5 0.3 Putting this value in previous formula, we find that the variance of the portfolio = 0.0801 and its standard deviation is 28.3% --------------------------------------------------------------------------- Your firm has a debt-equity ratio of .60. Your cost of equity is 11% and your after-tax cost of debt is 7%. a) What will your cost of equity be if the target capital structure becomes a 50/50 mix of debt and equity assuming that the risk on debt is unchanged? (1 point) Your answer : cost of equity = 12% D/E=0.6 -> D+E / E =1.6 -> E/E+D=1/1.6=0.625 WACC=0.625(11%)+0.375(7%)=9.5% THE WACC being constant, the change in the capital structure implies that rE satisfies 0.5(rE)+0.5(7%)=9.5%. rE= 6%/0.5%=12%. b) if we consider a change in the risk of debt, does the previous answer over-estimate or underestimate the true cost of equity? (1 point) Ï It overestimates it Ï It underestimates it Brief explanation in one sentence: If there is a change in the risk of debt following the increase in the D/E ratio (from 0.6 to 1), this change will be positive. As a result, rD would go up, and rE would be lower than 12%. As a result, the previous answer would overestimate the true cost of equity. -------------------------------------------------------------------- An investment is available that pays a tax-free 7%. The corporate tax rate is 40%. Ignoring risk, what is the pre-tax return on taxable bonds? rB(1-t)=7% and so rB= 7%/1-0.4=11.67% ------------------------------------------------------------------- EDHEC Company has a cost of equity of 11.9 percent and a pre-tax cost of debt of 9 percent. The weighted average cost of capital is 11 percent. What is the firm's debt-equity ratio based on Modigli
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Compatible OS 3.0 et ultérieurs.
<<
What is the present value of the following stream of cash-flows? ¬5,000 every year over the next 10 years (first payment in one year) + ¬10,000 every year over the following 10 years The annual interest rate remains at 3% over the next 5 years and will be equal to 7% in the following next 15 years. To reduce your calculations, you can pick the relevant values in the following table: PV=5000/0.03*(1-(1/1.03^5))+1/1.03^5*5000/0.07(1-(1/1.07^5))+1/1.03^5*1.07^5 * 10000/0.07 * (1-((1/1.07^10))=83779 ---------------------------------------------------------------------------------- A company plans to acquire a machine and to use it over the next 12 years. You are given the following information: - Initial payment: ¬50,000 to be paid now - Maintenance costs of ¬5,000 in exactly 4 years, 8 years and 12 years. - The machine will be sold for ¬10,000 in exactly 12 years. In 12 years, the company will have to purchase a new machine at the same price, bear the same costs and timing of maintenance and will be able to sell it at the same price (¬10,000) 12 years later (that is in 24 years). The company uses a 7% annual discount rate. What is the equivalent annual cost of a machine over a 24-year period? Round your answer to the nearest integer number. 50000+ 5000/1.07^4+ 5000/1.07^8+ 5000/1.07^12- 10000/1.07^12=54504 EAC= (54504*0.07) / (1- 1 / 1.07^12)= 6 862 ------------------------------------------------------------------------------------- You want to invest your wealth in Alpha and Beta through a portfolio P who presents the lowest risk. Alpha and Beta present the following characteristics: " Alpha: 3 times over 4, return is -2%; in the remaining cases, it is +10% " Beta: 1 times over 4, return is -4%; in the remaining cases, it is +6% The covariance of the returns between Alpha and Beta is -0.00225. Which are the weights and what is the level of risk for P? Solution: By the standard formula, we can compute the expected return of Alpha = 1% and of Beta = 3.5% After that come the variances: 0.0027 for Alpha and 0.001875 for Beta; then the standard deviations: 0.05196 for Alpha and 0.0433 for Beta. Knowing the value of the covariance, we deduce that the correlation is exactly -1. It is therefore possible to build a riskless portfolio. Let us call x the weight invested in Alpha; the variance of P is given by: x² 0.0027 + (1 x)² 0.001875 + 2 x (1 x) 0.0519 0.0433 Solving to get 0 leads to x = 0.5 ---------------------------------------------------------------------------------------- You intend to build a portfolio invested in the assets X, Y and the Treasury Bill. - X has an expected return of 9% and a standard deviation of 0.5 - Y has an expected return of 7% and a standard deviation of 0.3 The Treasury Bill provides a return of 3%. Thirty percent of your wealth will go in the Treasury Bill, the remaining has to be shared between X and Y, targeting a return of 6.4% If the correlation between the returns of X and Y is 1.2, what is the standard deviation of your portfolio? Solution: Let us call w the weight invested in X. We can write: w 9% + (1 0.3 - w) 7% + 0.3 3% = 6.4% We deduce that w = 0.3 and 0.4 is invested in Y. The variance of the portfolio is: 0.3² 0.5² + 0.4² 0.3² + 2 0.3 0.4 cov(X,Y) But cov(X,Y) = 1.2 0.5 0.3 Putting this value in previous formula, we find that the variance of the portfolio = 0.0801 and its standard deviation is 28.3% --------------------------------------------------------------------------- Your firm has a debt-equity ratio of .60. Your cost of equity is 11% and your after-tax cost of debt is 7%. a) What will your cost of equity be if the target capital structure becomes a 50/50 mix of debt and equity assuming that the risk on debt is unchanged? (1 point) Your answer : cost of equity = 12% D/E=0.6 -> D+E / E =1.6 -> E/E+D=1/1.6=0.625 WACC=0.625(11%)+0.375(7%)=9.5% THE WACC being constant, the change in the capital structure implies that rE satisfies 0.5(rE)+0.5(7%)=9.5%. rE= 6%/0.5%=12%. b) if we consider a change in the risk of debt, does the previous answer over-estimate or underestimate the true cost of equity? (1 point) Ï It overestimates it Ï It underestimates it Brief explanation in one sentence: If there is a change in the risk of debt following the increase in the D/E ratio (from 0.6 to 1), this change will be positive. As a result, rD would go up, and rE would be lower than 12%. As a result, the previous answer would overestimate the true cost of equity. -------------------------------------------------------------------- An investment is available that pays a tax-free 7%. The corporate tax rate is 40%. Ignoring risk, what is the pre-tax return on taxable bonds? rB(1-t)=7% and so rB= 7%/1-0.4=11.67% ------------------------------------------------------------------- EDHEC Company has a cost of equity of 11.9 percent and a pre-tax cost of debt of 9 percent. The weighted average cost of capital is 11 percent. What is the firm's debt-equity ratio based on Modigli
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