...1.0 INTRODUCTION 1.1 Beam Deflections 1.2 Theory - Calculations DeflectionF formula for the load given above: A determination of flexural stress yields: When rectangular it is Where; δ = Deflection (mm) E = Coefficient of Elasticity L = Span (mm) I = Inertia Factor Mb = Moment of flexure (Nmm) F1 = Load occasioned by weight Wb = Resistance to flexure (mm3) of Load Device (N) σb = Flexural Stress (N/mm2) F = Load of occasioned by additional weight (N) 1.3 Objectives * To investigate the relationship between load, span, width, height and deflection of a beam placed on two bearers and affected by a concentrated load at the center. * To ascertain the coefficient of elasticity for steel brass and aluminium 2.0 METHODOLOGY 2.1 Procedure - Experiement 1A * Investigate the relationship between load and deflection. 1) Set the bearers so that a span of 600 mm is obtained. The interval between each groove on the shafts of the apparatus is 100 mm. 2) Place a test specimen with dimensions of 4 x 25 mm, on the bearers and mount the load device in the center of the test specimen. 3) Set the testing device so that the top of the gauge is centered on the upper plane of the load device. Lower the gauge so that its small hand is at about 10 and set the gauge to zero by twisting its outer ring. 4) Load the weights as shown in the table below and read off the deflection...
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...1-Turky Abdullah AL-Bussairi 2-Yasser Habib AL-Mutairi 3-Abdulrahamn Sa`ad AL-Huaifi 4-Abdulrahman hemdy AL-Harbi Abstract: We determined the elastic modulus, yield strength, tensile strength, modulus of toughens, elongation, reduction of area, as well as true stress and strain at rupture point for one specimen, aluminum,. We accomplished this by placing our specimen at a time into a universal testing machine (UTM), which, under computer control, slowly increased the tension force on each specimen, stretching each until failure. Purpose: The purpose of this experiment is to extract data on the material properties one specimen (aluminum), using a mechanically driven universal testing machine (UTM). The material properties include the following: the elastic modulus, 0.2% offset yield strength, ultimate tensile strength, modulus of rupture, modulus of resilience, as well as true strain and true stress at the point of rupture. Theory: Certain materials (those that are linear, homogeneous, elastic, and isotropic) can be described by their material properties. These properties include the modulus of elasticity, modulus of toughness, modulus of resilience, ultimate tensile strength, and yield strength. Once established by experimental means, these properties are then applied to all instances of that material undergoing the same type of stress, allowing one to design structural elements whose behavior can...
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...Problem 5-1 Current market price Given: Interest paid annually $1,000 par value 12 years to maturity Coupon rate of 8% Yield to maturity of 9% Using a financial calculator phone app PMT=80 FV=1000 I=9% N=12 Current market price=$928.39 Problem 5-2 Yield to Maturity Given: Interest paid annually $1,000 par value 12 years to maturity Coupon rate of 10% Current price=$850 Using a financial calculator phone app PV=-850 PMT=100 FV=1000 N=12 Yield to Maturity=12.48% Problem 5-6 Market Risk Premium Given: Risk Free Rate=3% Inflation=3% for two years Current Yield=6.3% Current Yield=rRF+IP+MRP 6.3%=3%+3%+MRP MRP=.3% Problem 5-7 Current Price of the Bond Given: Interest paid semiannually $1,000 par value 8 years to maturity Coupon rate of 10% Yield to maturity of 8.5% Using a financial calculator phone app PMT=100 FV=1000 I=8.5% N=8 Current market price=$1085.80 Problem 5-13 Yield to Maturity Given: 5 years to maturity Par value of $1000 Coupon Rate=8% Current Yield=8.21% Using Excel =RATE(5,80,-974.42144,1000) Yield to Maturity= 8.65% Question 6-6 If a company’s beta were to double, would its expected return double? No, the expected return will increase but since the beta is multiplied by the market risk premium it will not double as the beta does. Problem 6-1 Portfolio Beta Given: $35,000 in stock1 Beta1=.8 $40,000 in stock2 Beta2=1.4 Portfolio beta= (.46667)(.8)+(.53333)(1.4)=1.12 Problem 6-2 ...
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...Laboratory Experiment: Uniaxial Testing of Civil Engineering Materials Table of Contents Introduction 1 Procedure 1 Experimental 1 Analysis 1 Results 2 Conclusion 4 References 5 Introduction In this set of laboratory experiments, uniaxial tests were performed on two specimens: 1) a steel bar in tension, and 2) an aluminum bar in tension. The specific types of materials used in this experiment are grade 50 for the steel, and type 2017-T351 for the aluminum. The experimental procedure and analysis give a better insight to the behavior of different ductile materials under normal stresses. Through the analysis of the experimental data, various properties of the material can be found and these properties are used in the design of engineering structures which use these materials. Through the use of plots of the stress versus strain for each material, and tables providing material properties, the report will include the following objectives for all materials: • Describe the behavior in the elastic range by determining the moduli of elasticity, and yielding stresses. • Describe the behavior of the materials beyond yielding by determining plastic stresses, ultimate stresses, rupture stresses, and ductility as well as indicating the range of strain hardening and necking. • Compare computed values obtained from the test results to expected values found for steel and aluminum. Further...
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...The percentage yield acts as a guideline to tell the successfulness of the synthesis experiment. A low percentage yield enable d means that the conditions were not most favorable and could be better. The percentage yield of the synthesized aspirin obtained in this experiment is 13.8%, which is considered as relatively low. Some errors like random human errors and mechanism errors may have occurred. One of the sources of error might occur during the addition of ice water to the mixture for complete recrystallisation. There is a possibility that the ice water is not at its optimal temperature. The temperature of the ice water will increase because it is placed under room temperature for a period of time when waiting for the Erlenmeyer flask...
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...EXPERIMENT | Vanillin | Acetone | Vanillindeneacetone | Chemical formula | C8H803 | C3H60 | C11H1203 | Molecular weight | 152.25 g/mol | 58.08 g/mol | 192.21g/mol | Density (g/cm3) | 1.06 | 0.788 | | Amount used | | | | Total moles | | | | Theoretical yield | | | | Percentage yield | | | | TABLE 2: DATA FROM EXPERIMENT: REAGENTS | Sodium Hydroxide | Hydrochloric Acid | Chemical formula | NaOH | HCl | Molecular weight | 39.997 g/mol | 36.46 | Denisty | 2.13 | 1.18 | Amount used | 3mL | 7mL | Total moles | 0.i598 | 0.227 | TABLE 3 : IR SPECTRUM Peaks (cm-1) | Functional group | 3699.8 | OH group | 3267.6 | Alkene | 1634.79 | Aromatic | CALCULATIONS: Total moles of Vanillin = 0.5g/152.15 = 0.0033 moles of vanillin. Total moles of acetone = (4mL * 0.788)/ 158.08 = 0.0199 moles of Acetone. Theoretical yields: Vanillin = 0.5g * 1mole * 1mole * 192.21 = 0.632g 152.15 1mole 1mole Acetone = 4ml * 0.788 * 1mole * 1mole * 192.21 = 3.832g 1mole 158.08 1mole 1mole Therefore, vanillin is the limiting reagent. % yield = Actual yield *100 = 0.274 * 100 = 43.35% Theoretical yield 0.632 DISCUSSION: Vanillin also known as 4-hydroxy-3-methoxy benzene comes from an orchid (Vanilla planifola). Vanillin is extracted out of its seedpods composition of the extracts has roughly 200 different molecules with vanillin being the most abundant component...
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...Question 1 Which of the following is NOT a strong electrolyte? | | LiOH | | | CaCl2 | | | MgCO3 | | | NaC2H3O2 | | | Li2SO4 | 1 points Question 2 Which of the following compounds is soluble in water? | | CaS | | | MgCO3 | | | PbCl2 | | | BaSO4 | | | None of these compounds is soluble in water. | 1 points Question 3 Which of the following compounds is insoluble in water? | | Hg2I2 | | | MgSO4 | | | (NH4)2CO3 | | | BaS | | | All of these compounds are soluble in water. | 1 points Question 4 Give the net ionic equation for the reaction (if any) that occurs when aqueous solutions of Na2CO3 and HCl are mixed. | | 2 H+(aq) + CO32-(aq) H2CO3(s) | | | 2 Na+(aq) + CO32-(aq) + 2 H+(aq) + 2 Cl-(aq) H2CO3(s) + 2 NaCl(aq) | | | 2 H+(aq) + CO32-(aq) H2O(l) + CO2(g) | | | 2 Na+(aq) + CO32-(aq) + 2 H+(aq) + 2 Cl-(aq) H2CO3(s) + 2 Na+(aq) + 2 Cl-(aq) | | | No reaction occurs. | 1 points Question 5 Write balanced complete ionic and net ionic equations for the following reactions: AgNO3(aq) + NaCl(aq) --> AgCl(s) + NaNO3(aq) | | Ag+(aq) + NO3-(aq) + NaCl(aq) --> AgCl(s) + NaNO3(aq)Ag+(aq) + Cl-(aq) --> AgCl(s) | | | Ag+(aq) + NO3-(aq) + Na+(aq) + Cl-(aq) --> AgCl(s) + Na+(aq) + NO3-(aq)Ag+(aq) + Cl-(aq) + NO3-(aq) + Na+(aq)--> AgCl(s) | | | Ag+(aq) + NO3-(aq) + Na+(aq) + Cl-(aq) --> AgCl(s) + Na+(aq) + NO3-(aq)Ag+(aq) + Cl-(aq) --> AgCl(s) | | |...
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...11.2 a. Determine the current value of the bond if present market conditions justify a 14 percent required rate of return. PV = CF^n / (1 +i) ^n PV = CF n / (1 + i)^4 PV = 70 / (1 + .14) ^4 PV = 70 / (1.14) ^4 PV = 70/ 1.14 + 70/ 1.30 + 70/ 1.48 + 70/ 1.69 PV = 61.40 + 53.85 + 47.30 + 41.42 = $203.97 PV of the par value = 1,000 PV = $203.97 + 1,000 = $1203.97 b. Now, suppose Twin Oaks' four-year bond had semiannual coupon payments. What would be its current value? (Assume a 7 percent semiannual required rate of return. However, the actual rate would be slightly less than 7 percent because a semiannual coupon bond is slightly less risky than an annual coupon bond). PV = 35/ (1+ i/2) ^n*2 PV = 35/ (1 + .7/2) ^4*2 PV = 35/ (1 +.035)^8 PV = 35/ 1.035 ^8 PV= $240.44 PV of the par value = $1,000 + $240.44 = $1,240.44 c. Assume that Twin Oaks' bond had a semiannual coupon but 20 years remaining to maturity. What is the current value under these conditions? (Again, assume a 7 percent semiannual required rate of return, although the actual rate would probably be greater than 7 percent because of increased price risk). PV= CFn/ (1 + i/2) ^n*2 PV= 35/ (1+.7/2) ^20*2 PV= 35/ (1.035)^40 PV= $746.26 PV = $1,000 + $746.26 PV of the par value = $1746.26 Week 6: Discussion 11.2 Assignment #3 Thank you for your questions. (A) 2(1.05)/(1.15-1.05) = $21 (B) 2(1.05)/(1.13-1.05) = $26.25 (C) 2(1.07)/(1.15-1.07) =...
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...ceEDHEC Business School Principles of Finance M1 - Business & Management Track Exam Monday 13 December 2010, 13h00 - 16h00. • The exam is closed book. Use only pocket calculators accepted by the school. • You should only write your answers in the space allocated to you after each question. • The blank sheets of paper in the back of each page will not be considered. You may therefore use them for your “rough answers”. • Show the approach you use to obtain the solution: Partial credit is given to answers that are numerically incorrect but that show correct understanding of the solution method. A wrong number without a good explanation will conversely not obtain any partial credit. • Please fill in below your: Candidate Name: ID. Number: Question 1. [15 points] Super-fun fund manages a risky portfolio with an expected rate of return of 18% and a standard deviation of 27%. The T-bill rate is 8%. Big Mike wishes to have a portfolio with total expected rate of return of 14%, by investing in the Super-fun portfolio a proportion w of his total investment and the rest in the T-bills. (a) What is the proportion w? [7 points] (b) What is the standard deviation on Big Mike’s portfolio? [8 points] 1 Question 2 . [40 points] Suppose that the return on the CAC 40 portfolio and the return on the Banji Fund portfolio are respectively: State Good Bad Probability Return on CAC 40 Return on Banji Fund 0.6 10% 20% 0.4 7% 2% (a) What is the expected return on the CAC 40...
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...Calculation of cost of debt by using IRR method : Formula : B0=I*t=1n11+rd t +M*11+2dn=I*PVIFA r d,n+M*PVIFrd,n B0=Value of the bond at time zero I= annual interest paid in dollars n=number of years to maturity m=par value in dollars rd=required return on bond B0=$956 Coupon Rate =13.5% I= coupon payment=13.5%*1000 = 135 Year to maturity =n=25 years Par value =1000 A trial –and – error technique: At the first consider rd=7.58%equal to method one and B0=$956 I= coupon payment=$135 1)The first try: 956=135*t=1251(1+7.58%)t +1000*(1(1+7.58%)25) 956= 135*(PVIFArd,n) +1000*(PVIFArd,n) From table A-4 and A -2 (Appendix A) r=7.58%, n=25 PVIFArd,n=11.164 1000*(1(1+7.58%)25)=1000*0.161=161 135*11.164=1507.1 956≠1507.1+22.3 2)Another try rd=0.10 956=135*t=1251(1+10%)t +1000*(1(1+10%)25) PVIFArd,,n=9.077 135*9.077=1225.4 1000(1(1+10%)25)=0.092 PVIFrd,n=0.092 ,1000*0.092=92 956 ≠ 1225.4 +92 3)An other try: rd:=12% PVIFArdn=7.843 PVIFrdn=0.059 135×7.843=1058.9 1000×0.059=59 956≠1058.9+59 4) An other try: rd=%14 PVIFArdn=6.873 PVIFrdn=0.038 135×6.873=927.9 1000×0.038=38 927.9+38=965.9 956≠965.9 5)An other try: rd=%14.2 PVIFArdn=6.791 PVIFrdn=0.036 135×6.791=916.8 1000×0.036=36 916.8+36=952.6 956≠952.8 6)An other try: rd=%14.15 PVIFArdn=6.810 PVIFrdn=0.037 135×6.81=919.3 1000×0.037=37 919.3+37 = 956.3 959=956.3 rd=%14.15= cost of debt=correct...
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...coupon Paid Annually -5 years to maturity / Market yield 0 | 1 | 2 | 3 | 4 | 5 | | 40 | 40 | 40 | 40 | 40 | | | | | | 1000 | Calculator Solution N=5 Bond Terminology Face Value or Par Value- Amount to be repaid at end of loan Coupon- Stated interest payment made on bond Coupon Rate- The annual coupon/ Face Value of Bond Maturity- Specific Date the bond principle must be repaid Time to Maturity- the number of years until maturity Yield to Maturity- Return to bond holder if they hold the bond to maturity, Market driven rate, I/Y on your calculator Current Yield= (Annual coupon$/Current bond price) *100 Bond Par Value | 1,000.00 | FV | 1,000 | Years to Maturity | 5.00 | N | 5 | Coupon Rate | 6.0% Paid Annually | PMT | 60.00 | Yield to Maturity | 6.8% | I/Y | 6.80 | Current Price | ???? | CPT PV | | Par Value | 1,000.00 | FV | 1,000 | Years to Maturity | 5.00 | N | 10 | Coupon Rate | 6.0% Paid Semiannually | PMT | 30.00 | Yield to Maturity | 6.8% | I/Y | 3.40 | Current Price | ???? | CPT PV | 966.57 | Bond Information $1,000 Face or Par Values 10 Years to Maturity 6.6% coupon rate/ Paid SEMIANNUALLY Market Yield to Maturity 6.2% N | 20 | I/Y | 3.1 | PMT | 33 | FV | 1000 | CPT PV | $1029.48 | Bond Price | 980.00 | N | 16 | Par Value | 1000.00 | PV | (980.00) | Coupon Rate | 6% PAID SEMIANNUALLY | PMT | 30.00 | Years to Maturity | 8 | FV | 1,000 | Yield to Maturity | ???? | CPT I/Y | 3.16119%*2=6.32...
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...CHAPTER 5 – Problems p. 210-211 5-1) Market price formula = INT*r*[1 -(1+rd)-n]/i + M*(1+rd)-n, where INT = par value M= maturity value r = coupon rate per coupon payment period rd= effective interest rate per coupon payment period n = number of coupon payments remaining Market price of bonds = 1000*.08 * (1 - 1.09-12)/.09 + 1000*1.09-12 Market price of bonds = $928.39 5-2) Value of the bond formula = 1nPar value*Coupon rate1+YTMt+Par value1+YTMn Time to maturity = 12 Par value = $1,000 Coupon rate = 10% Price of the bond = $850 Yield to maturity =12.475% 5-6) r = r* + IP + MRP 6.3 = 3 + 3 + MRP 6.3 – 6 = MRP 0.3 = MRP 5-7) N = 16 I/YR = 8.5/2 = 4.25 PMT = 50 FV = 1000 Excel Input: PV(0.0425,16,50,1000) = $1,085.80 5-13) N= 5 PMT = 80 FV = 1000 I/YR = ? Current yield = 8.21% Current yield = Annual interest/Current price 0.0821 = $80/PV PV = $80/0.0821 = $974.42. Excel Input : N = 5, PV = -974.42, PMT = 80, and FV = 1000. I/YR = YTM = 8.65% CHAPTER 6 – Questions p.257 6-6) If a company’s beta were to double, I would not expect the company’s return to double. The return would be expected to increase by an amount equal to the market risk premium times the change in beta. CHAPTER 6 – Problems p. 258-259 6-1) ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12 Bp = 1.12 6-2) Ri = rRF + (Rm – rRF) bi Ri = 6% + (13% - 6%) 0.7 Ri = 10.9 % 6-7) a. Ri = rRF + (Rm – rRF) bi Ri = 9% + (14% - 9%) 1.3 Ri...
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...years to maturity. The bonds were originally issued at par value. a. What was the original yield to maturity on the bonds? They were issued at par…so the YTM = Coupon rate: 7% b. If the current price of the bonds is $875, what is the yield to maturity of the bonds TODAY? 1000 FV .07(1000)÷2= PMT (15-7)*2 = N -875 PV I/Y = 4.623*2 = 9.25% c. If the yield to maturity computed in part b remains constant, what will be the price of the bonds three years from today? Leave everything the same, just change N to (8 – 3)*2 = 10 PV = $911.70 2. You are looking to invest some money and identify two $1,000 par bonds with the same risk, both with 12 years to maturity and paying semi-annual coupons. Each of the bonds has a required return of 7%, but one bond is priced at $839.42 and the other at $1,120.44. Compute the annual coupon rates for each bond. 1000 FV Only difference is price for second one 12*2 N -1120.44 PV 3.5 I/Y -839.42 PV PMT = 42.5*2 = 85 PMT = 25*2 = 50 C. Rate = 85/1000 = .085 = 8.5% C . Rate = 50/1000 = .05 = 5% 3. A $1,000 par bond has a 5% semi-annual coupon and 12 years to maturity. Bonds of similar risk are currently yielding 6.5%. a. What should be the current price of the bond? 1000 FV .05(1000)÷2= PMT 12*2 = N 6.5/2 = I/Y PV = $876.34 b. If the bond’s price five years from now is $1,105, what would be the yield to maturity for the bond at that time? Just change N again, to…(12-5)*2 = N -1105 PV...
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...The bonds have a yield to maturity of 9%. What is the current market price of these bonds? 0 1 2 3 4 5 6 7 8 9 10 11 n=12 PV 80 80 80 80 80 80 80 80 80 80 80 80 Par Vaule= $1,000.00 Coupon interest rate = 8% Par value = $1,000.00 Payment = Par value x coupon rate Payment = $1,000.00 x 0.08 Payment = $80.00 Yield to maturity = 9% The current market price of the Jackson Corporation's bonds are calculated as follows. =PV(Rate, Nper, Payment, FV, Type) =PV(9%,12,80,1000,0) [pic] The current market price of Jackson Corporation's bonds is $928.39. (5–3) Heath Foods’s bonds have 7 years remaining to maturity. The bonds have a face value of $1,000 and a yield to maturity of 8%. They pay interest annually and have a 9% coupon rate. What is their current yield? 0 1 2 3 4 5 6 n= 7 PV 90 90 90 90 90 90 90 Par Vaule= $1,000.00 Coupon interest rate = 9% Par value = $1,000.00 Payment = Par value x coupon rate Payment = $1,000.00 x 0.09 Payment = $90.00 Yield to maturity 8% The current yield for Heath Food's bond is calculated as follows. Current Yield=current payment/current price Current Yield = $90.00/Present Value =PV(Rate, Nper, Payment, FV, Type) =PV(8%,7,90,1000,0) [pic] Current Yield= $90.00/$1052.06 Current Yield= [pic] Current Yield = 8.55% Heath Food's bond current yield is 8.55% (5–5) A Treasury bond that matures in 10 years has a yield of 6%. A 10 year corporate...
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...dividends would be steady or will increase at a perpetual rate for years. But we know that due to the ups and downs of the economy it can be pretty tricky to forecast exactly what the dividends would be year from now. #3 Yes I was noticing in order to calculate the DDM there are three main inputs to have and I was missing at least one or tow to be able to calculate it. DPS(1) = Dividends expected to be received in one year Ks= requires rate of return for a specific investment G=growth rate in dividends in years from now at some point I found it tricky to come up with these components to calculate for DDM. As I searched on line there are more than one way to calculate DDM so it was a bit challenging. !!! #4 In bond investing, yield is the tool to measure the return of...
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