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ADMS 3530 Final Review Session – Solutions Example 1: Multiple Cash Flows Answer B Detailed solution: 0 1 2 |-----------|-------------I $200 “Y” 2400 r = 4% FV2 = $3032.32 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) 200(1 + r)2 + Y(1 + r)1 + 2400 = 3032.32 200(1.04)2 + 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) 200 + Y/(1 + r)1 + 2400/(1 + r)2 = 3032.32/ (1 + r )2 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 PV1 to PV0 PV0 = $323.97 / (1.09)1 = $297.22 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)12 -1 = 25.82% Example 4: Mortgages Answer D 3530_Final_Tutorial_-_Solutions Updated.docx 1 The monthly interest rate is given by: (1 + im )12 = 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. Solution B 4-year Rate of Return = [30 x FVIFA(2%,8) + 1,040 – 1,015] / 1,015 = 27.8314% The annual rate of return is (1+27.8314%)1/4 – 1 = 6.3309% Example 6A: Stocks Answer D DIV1 DIV0 (1.25 ); DIV2 DIV0 (1.25 ) 2 ; DIV3 DIV0 (1.25 ) 3 ; DIV4 DIV0 (1.25) 3 (1.18 ). DIV5 DIV4 (1 g ) DIV0 (1.25 3 )(1.18 )(1 0.08) P4 rg rg 0.15 0.08 2.489 DIV0 35.56 DIV0 . 0.07 DIV0 (1.25 ) DIV0 (1.25 ) 2 DIV0 (1.25) 3 DIV0 (1.25 ) 3 (1.18 ) 35.56DIV0 P0 $60 1.15 1.15 2 1.15 3 1.15 4 1.15 4 DIV0 ( 25.2). DIV0 $60 $2.38 DIV1 $2.38 1.25 $2.975 $2.98. 25.2 3530_Final_Tutorial_-_Solutions Updated.docx 2 Example 7 Solution C Step 1: Determine the initial cash outflow. The payback is 2.25 years, so the cash flow will be: CF0 = -[CF1 + CF2 + 0.25(CF3)] = -[$500 + $300 + 0.25($400)] = -$900. Step 2: Calculate the IRR: CF0 = -900; CF1 = 500; CF2 = 300; CF3 = 400; CF4 = 600; and then solve for IRR = 33.49% ≈ 33.5% Example 7B Answer B Step 1: Determine the differential cash flows between Projects A and B Project A Project B ΔCFs Year Cash Flow Cash Flow A - B 0 -$2,000 -$1,500 -$500 1 700 300 400 2 700 500 200 3 1,000 800 200 4 1,000 1,100 -100 Step 2: Calculate the IRR of the differential cash flows CF0 = -500; CF1 = 400; CF2 = 200; CF3 = 200; CF4 = -100; and then solve for IRR = 26.67% Example 7C Answer C Choose the project that maximized your NPV NPVI = 2,781.65 NPVII = 1,922.12 Choose project I. Example 8 DCF Answer B Beg UCC Year 1 600,000 Year 2 510,000 CCA 90,000 153,000 CCA Tax Shield 31,500 53,550 End UCC 510,000 357,000 Example 9 Answer D From the PV CCA Tax Shield formula: PVCCATS = [(600,000 x .30 x .35)/(.12 + .30)] x [(1 + 0.5 x 0.12)/(1.12)] = 141,964 Example 10 Answer A After-tax CFO (excluding CCA) = 240,000 x (1 - 0.35) = 156,000 NPV = -600,000 + 156,000 x PVIFA(12%,4) + 141,964 = 15,791 3530_Final_Tutorial_-_Solutions Updated.docx 3 Example 11 Answer A PVCCATS will decrease by: [(50,000 x .30 x .35)/(.12 + .30)] x (1.12)-4 = 7,944 PV(CFO excluding CCATS) will increase by 50,000 x (1.12)-4 = 31,776 So, NPV will increase by 31,776 – 7,944 = 23,832 Example 12A Answer C 1) In the best-case scenario: The before-tax profit is = 12,000(1+10%)$21(1+5%) - 12,000(1+10%)$11(1-3%) - $44,000(1-1%) - $40,000 = $66,656. The after-tax profit = $66,656(1-34%) = $43,992.96. The operating cash flow = $43,992.96 + $40,000 = $83,992.96. The PV of the operating cash flow using an annuity factor of 12% for 2 years is = $141,952.39. The NPV is = $141,952.39 - $80,000 = $61,952.39. 2) In the worst-case scenario: The before-tax profit is = 12,000(1-10%)$21(1-5%) - 12,000(1-10%)$11(1+3%) - $44,000(1+1%) - $40,000 = $8,656. The after-tax profit = $8,656(1-34%) = $5,712.96. The operating cash flow = $5,712.96 + $40,000 = $45,712.96. The PV of the operating cash flow using an annuity factor of 12% for 2 years is = $77,257.23. The NPV is = $77,257.23 - $80,000 = -$2,742.77. 3) The difference in the NPVs = $61,952.39 – (-$2,742.77) ≈ $64,695. Example 12B Answer B Old price = $60/1.2 = $50. Therefore, variable costs per product = $50 × 0.7 = $35, which equals 58.33% of the new price. So the new accounting break-even revenue = $1 million / (1-0.5833) $2,400,000. 3530_Final_Tutorial_-_Solutions Updated.docx 4 Example 13A: Risk Answer C The equal probability is 1/3. The portfolio expected return = (1/3)(-4% + 2% + 5%) = 1%. The portfolio variance = (1/3)[(-4%-1%)2 + (2%-1%)2 + (5%-1%)2] = 14 percentages squared = 0.0014. Taking the square root of the portfolio variance, we find that the portfolio standard deviation is 3.74%. Example 13B: Risk Answer A Correlation Coefficient: j ,m Portfolio standard deviation P Cov(rj , rm ) jm = -0.016 / (.16 x.20) = -0.5 x12 12 x22 22 2 x1 x2 1, 2 1 2 , = 10.44% Example 14 CAPM Answer A Example 15 CAPM Answer C Example 16 CAPM Answer B Expected Return W = 6% + 2.0 x 9% = 24% < 25% => Buy W. Expected Return X = 6% + 1.6 x 9% = 20.4% > 19% => Do not buy X. Expected Return Y = 6% + 1.1 x 9% = 15.9% < 17% => Buy Y. Expected Return Z = 6% + 0.8 x 9% = 13.2% > 11% => Do not buy Z. Note: You should sell (short) X and Z because they are overpriced by the market Example 16B Answer A Project I: expected return = 0.06 + 2 × 0.09 = 0. 24 < IRR of 0.25. Project I plots above the SML and should be accepted. Project II: expected return = 0.06 + 1.1 × 0.09 = 0. 159 > IRR of 0.15. Project II plots below the SML and should be rejected. 3530_Final_Tutorial_-_Solutions Updated.docx 5 Example 17 WACC A. Answer D On your financial calculator: FV=1000, PV=-860, N=20, PMT=45; I=? 5.69% YTM=5.69 × 2 =11.38%. After-tax cost of debt = 11.38% × (1-35%) = 7.40%. B. Answer B By the CAPM: requity = 5.25% + 2 × 4.15% = 13.55%. C. Answer D The annual dividend paid on per preferred share is $100 × 5% = $5. So rpreferred = $5 / $63 = 7.94%. D. Answer C Price Shares (million) Market Value ($ million) Weights Costs WACC Equity 58 38 2,204 0.60 13.55% 11.22% Preferred Debt 63 860 14 0.7 882 0.24 7.94% Value 602 0.16 7.40% 3,688 Chap 20, 21 and 22 (consistent with the course outline) A) Answer: B B) Answer: C Cash conversion cycle = (inventory period + accounts receivable period) – accounts payable period C) Answer: D The implicit interest rate per month = $(1,000,000-960,000)/$960,000 = 4.1667% 12 The effective annual rate = (1+0.041667) -1=63.21% 3530_Final_Tutorial_-_Solutions Updated.docx 6 D) AnswerC E) 3530_Final_Tutorial_-_Solutions Updated.docx 7