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Final

3530 Final Tutorial - Solutions.F11.pdf

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Department
Administrative Studies
Course
ADMS 3530
Professor
Lois King
Semester
Summer

Description
ADMS 3530 Final Review Session – Solutions Example 1: Multiple Cash Flows Answer B Detailed solution: 0 1 2 r = 4% |-----------|-------------I FV2= $3032.32 $200 “Y” 2400 You can use either Option a) FV formula and bring all cash flows to t=2 or Option b) PV formula and bring all cash flows to t=0 Option a) Bring all cash flows to t=2 (use FV or compound) 2 1 200(1 + r)2+ Y(1 + r) + 2400 = 3032.32 200(1.04) + Y (1.04) + 2400 = 3032.32 216.32 + Y(1.04) + 2400 = 3032.32 Y(1.04) = 3032.32 – 2400 – 216.32 Y(1.04) = 416 Y = 416 / (1.04) Y = $400 Option b) Bring all cash flows to t=0 (use PV and discount) 1 2 2 200 + Y/(1 + r) + 2400/(1 + r) = 3032.32/ (1 + r ) Y = $400.00 Example 2: Delayed Annuity Answer A Using your calculator: PMT = $100, I = 9, n= 4, Fv =0, COMP PV  PV = $323.97 at t=1 !! Bring PV 1o PV 0 PV = $323.97 / (1.09) = $297.22 0 Example 3: EAR Answer D Using your calculator: PMT = $1883.33, n = 12, PV = $20,000, FV=0, Comp “i”  i= 1.9322% EAR = (1+.019322) -1 = 25.82% Example 4: Mortgages Answer D 3530 Final Tutorial - Solutions.F11 1 The monthly interest rate is given by: (1 + im ) = 1 + EAR = (1 + 3125%)² = 1.076406, that is im = 0.5142% The monthly payment for the 20-year loan 320,000 = PMT x PVIFA(0.5142%,300) PMT = $2,095.22 Mortgage remaining at the end of 5 years  240 months remaining: Using your calculator: PMt = $2095.22, n=240, i=.5142, Fv=0, COMP PV  PV = 288,480.10 Example 5: Bonds Solution a) Current Yield = Annual Coupon Payment/ Bond Price Step 1: Find price of bond today (7 years remaining) Using your calculator: PMT = 70/2 = 35.00, n = 7 x 2 = 14, FV = 1000, i = 8/2 = 4%, COMP PV  PV = -947.18 -> Current Yield = $70/$947.18 = 7.39% Step 2: Find rate of return over holding period (3 years) b) Rate of Return = (Coupon Interest + Price Change) / Initial Price = [70 x 3 + (947.18 – 1000) ] / 1000 = [210 + (-52.82)] / 1000 = 15.718% (over 3 years) Step 3: Find annual rate of return EAR = (1 + .15718) 1/3-1 = 4.99% Example 6A: Stocks Answer D DIV 0 $2.00 ->Div1= 2.00 (1+g) 1 ->Div4= 2.00 (1+g) = 2 x (1 + 5%) = 2.43 and P 3 DIV /4(r – g) = 2.43 / (11% - 5%) = $40.52 Example 6B) Answer is $10.18 (try working it our yourself!) Example 7 Solution C Payback = 2 + $300/$500 = 2.6 years CF0 = -1000; CF1 = 400; CF2 = 300; CF3 = 500; CF4 = 400; I = 10 NPV = $260.43 ≈ $260; IRR = 21.22% 3530 Final Tutorial - Solutions.F11 2 Example 7: EAC Answer B You need to find EAC of $8,000 today, then calculate how much more per year you can spend on annual maintenance so you pay the equivalent of $4,000 per year total. EAC = PV[annual PMT] = $8,000 Using your calculator: I = 8, n=4, PV = $8,000, FV=0 , Comp PMT  PMT = $2,415.89 Thus, annual maintenance costs must be less than: $4,000 - $2,415.39 = $1,584.61 (B) When combined with the annuitized cost of the vehicle, any annual expense over $1,584.61 would place the total annual expense of the new vehicle over $4,000. Example 8 D
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