The firm Gelati-Banking (GB) is considering a project with the following characteristics. Sales will be $100 MM for sure in the first year and grow 10% in the second year; thereafter, the long-term growth rate is 3%. Gross Profit Margin (Gross Profit over Sales) will be 20%. Depreciation will be $10 MM each year for the next two years. Working Capital held for the project will have to be 10% of sales. Additional CAPX each year will be $11MM in year 1 and $12 MM in year 2. All cash flows defined here are deterministic and will go on indefinitely. Interest rates are as follows: 3-month t-bill is 3%, the 2-year treasury is 4% and the long bond (30-year) is trading at 5% per year. The Corporate Tax Rate is 40%. What would the investment need to be for this project to be breakeven (ignoring depreciation effects of the investment)? Assume that 1) Everything grows at 3% per year from year 2 onwards to infinity; and 2) The cash flow stream that goes from time 0 on indefinitely is similar in nature to a long term treasury bond.

for the Number 3, I am just checking the answer and I have no idea as of the net cash flow, how comes these answers?

14.20

15.33

15.79

16.26

16.75

1. You are considering a project which generates $10,000 in 6 months and $20,000 in one year and will run you $26,000 today. You know these cash flows are exact. You also have the Treasury yield curve from the Wall Street Journal in front of you and see that the 6month T-bill is trading at a 4% CBE discount rate and the one-year T-bond (which pays coupons in 6-months and one-year) is trading at par (100) with a yield of 6%. (Rates are CBE). Should you invest in this project? First I solve the one-year spot rate s: 100 = 3/1.04 + 1.03/(1+s) s = 0.0606 NPV = -26,000 + 10,000/1.04 + 20,000/1.0606 = 2472.64 > 0 Invest in this project 2. You are doing some bookkeeping concerning a mortgage you took out 10 years ago, $500,000 used to finance a home. You presume it is a 30-year mortgage. You are trying to determine the interest rate (mortgage equivalent yield) on the loan. You know that the monthly payments are $4,023.11. So, you assume therefore that the interest rate on the loan is 9% and call your mortgage broker to check this out. Looking at your numbers, he tells you that you have two things incorrect. First, this was a weird mortgage that did not start with a 30-year maturity. Second, the 9%, it turns out, was purely coincidental. He also tells you that the actual interest paid thus far is 8.78% less than that shown in your calculations based on the 9% interest rate and a $500,000 loan - that is the interest paid is .9122 times the figure calculated from your mortgage calculation. From this information, can you determine the actual terms of the mortgage: rate and maturity? Interest rate on the loan: 8.5%; Maturity: 25 years First, assuming 9% interest rate on a 30-year mortgage, I can use Excel to calculate how much interest I have paid in the past 10 years. Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Total monthly payment 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 Interest payment 3750.00 3747.95 3745.89 3743.81 3741.71 3739.60 3737.48 3735.34 3733.18 3731.00 3728.81 3726.60 3724.38 3722.14 3719.88 3717.61 3715.32 3713.01 3710.68 3708.34 3705.98 3703.60 3701.20 3698.79 3696.36 3693.91 3691.44 3688.95 Principle payment 273.11 275.16 277.22 279.30 281.40 283.51 285.63 287.77 289.93 292.11 294.30 296.51 298.73 300.97 303.23 305.50 307.79 310.10 312.43 314.77 317.13 319.51 321.91 324.32 326.75 329.20 331.67 334.16 Principle outstanding before payment 500000.00 499726.89 499451.73 499174.51 498895.21 498613.81 498330.31 498044.67 497756.90 497466.97 497174.86 496880.56 496584.05 496285.32 495984.35 495681.13 495375.62 495067.83 494757.73 494445.30 494130.53 493813.40 493493.89 493171.99 492847.67 492520.91 492191.71 491860.04 Principle outstanding after payment 499726.89 499451.73 499174.51 498895.21 498613.81 498330.31 498044.67 497756.90 497466.97 497174.86 496880.56 496584.05 496285.32 495984.35 495681.13 495375.62 495067.83 494757.73 494445.30 494130.53 493813.40 493493.89 493171.99 492847.67 492520.91 492191.71 491860.04 491525.88 1 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 3686.44 3683.92 3681.38 3678.81 3676.23 3673.63 3671.01 3668.37 3665.71 3663.03 3660.32 3657.60 3654.86 3652.10 3649.32 3646.51 3643.69 3640.84 3637.98 3635.09 3632.18 3629.25 3626.29 3623.32 3620.32 3617.30 3614.25 3611.19 3608.10 3604.99 3601.85 3598.69 3595.51 3592.30 3589.07 3585.81 3582.53 3579.23 3575.90 3572.55 3569.17 3565.76 3562.33 3558.88 3555.39 3551.89 3548.35 3544.79 3541.20 3537.59 3533.95 3530.28 3526.58 3522.86 3519.11 3515.33 3511.52 3507.68 3503.82 3499.92 3496.00 3492.05 3488.06 3484.05 3480.01 3475.93 3471.83 3467.69 3463.53 3459.33 336.67 339.19 341.73 344.30 346.88 349.48 352.10 354.74 357.40 360.08 362.79 365.51 368.25 371.01 373.79 376.60 379.42 382.27 385.13 388.02 390.93 393.86 396.82 399.79 402.79 405.81 408.86 411.92 415.01 418.12 421.26 424.42 427.60 430.81 434.04 437.30 440.58 443.88 447.21 450.56 453.94 457.35 460.78 464.23 467.72 471.22 474.76 478.32 481.91 485.52 489.16 492.83 496.53 500.25 504.00 507.78 511.59 515.43 519.29 523.19 527.11 531.06 535.05 539.06 543.10 547.18 551.28 555.42 559.58 563.78 491525.88 491189.21 490850.02 490508.29 490163.99 489817.11 489467.63 489115.53 488760.78 488403.38 488043.29 487680.51 487315.00 486946.75 486575.74 486201.95 485825.36 485445.94 485063.67 484678.54 484290.52 483899.59 483505.72 483108.91 482709.11 482306.32 481900.51 481491.65 481079.73 480664.72 480246.59 479825.33 479400.91 478973.31 478542.50 478108.46 477671.16 477230.59 476786.71 476339.50 475888.93 475434.99 474977.64 474516.86 474052.63 473584.92 473113.69 472638.93 472160.62 471678.71 471193.19 470704.03 470211.20 469714.68 469214.43 468710.42 468202.64 467691.05 467175.62 466656.33 466133.14 465606.03 465074.97 464539.92 464000.86 463457.76 462910.58 462359.30 461803.88 461244.30 491189.21 490850.02 490508.29 490163.99 489817.11 489467.63 489115.53 488760.78 488403.38 488043.29 487680.51 487315.00 486946.75 486575.74 486201.95 485825.36 485445.94 485063.67 484678.54 484290.52 483899.59 483505.72 483108.91 482709.11 482306.32 481900.51 481491.65 481079.73 480664.72 480246.59 479825.33 479400.91 478973.31 478542.50 478108.46 477671.16 477230.59 476786.71 476339.50 475888.93 475434.99 474977.64 474516.86 474052.63 473584.92 473113.69 472638.93 472160.62 471678.71 471193.19 470704.03 470211.20 469714.68 469214.43 468710.42 468202.64 467691.05 467175.62 466656.33 466133.14 465606.03 465074.97 464539.92 464000.86 463457.76 462910.58 462359.30 461803.88 461244.30 460680.52 2 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 Total 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 4023.11 482773.20 3455.10 3450.84 3446.55 3442.23 3437.87 3433.48 3429.06 3424.60 3420.12 3415.59 3411.04 3406.45 3401.82 3397.16 3392.47 3387.74 3382.97 3378.17 3373.33 3368.46 3363.55 3358.60 429,922.52 568.01 572.27 576.56 580.88 585.24 589.63 594.05 598.51 602.99 607.52 612.07 616.66 621.29 625.95 630.64 635.37 640.14 644.94 649.78 654.65 659.56 664.51 52850.68 460680.52 460112.52 459540.25 458963.69 458382.81 457797.57 457207.94 456613.89 456015.39 455412.39 454804.88 454192.80 453576.14 452954.85 452328.90 451698.26 451062.89 450422.75 449777.81 449128.03 448473.38 447813.82 / 460112.52 459540.25 458963.69 458382.81 457797.57 457207.94 456613.89 456015.39 455412.39 454804.88 454192.80 453576.14 452954.85 452328.90 451698.26 451062.89 450422.75 449777.81 449128.03 448473.38 447813.82 447149.32 / As you can see from the table, the total interest payment that I have made in the past 10 years is $429,922.52, assuming 9% interest rate on a 30-year mortgage. Then, according my broker's description, I can calculate my actual interest payment, which is: 429,922.52 * 0.9122 = $392,175.32 Then, using Excel, I keep plugging in different interest rates into my formula until I get the total interest payment equals $392,175.32. Using this method, I figure out the interest rate on the loan is 8.5% and the monthly rate is 0.7083%. Then, I put monthly payment 4023.11 and monthly rate 0.7083% into the annuity formula and solve for the maturity, getting the maturity is 300 months, which is equivalent to 25 years. Therefore, I know this is a 25-year mortgage with 8.5% annul interest. 3. The firm Gelati-Banking (GB) is considering a project with the following characteristics. Sales will be $100 MM for sure in the first year and grow 10% in the second year; thereafter, the long-term growth rate is 3%. Gross Profit Margin (Gross Profit over Sales) will be 20%. Depreciation will be $10 MM each year for the next two years. Working Capital held for the project will have to be 10% of sales. Additional CAPX each year will be $11MM in year 1 and $12 MM in year 2. All cash flows defined here are deterministic and will go on indefinitely. Interest rates are as follows: 3-month tbill is 3%, the 2-year treasury is 4% and the long bond (30-year) is trading at 5% per year. The Corporate Tax Rate is 40%. What would the investment need to be for this project to be breakeven (ignoring depreciation effects of the investment)? Assume that 1) Everything grows at 3% per year from year 2 onwards to infinity; and 2) The cash flow stream that goes from time 0 on indefinitely is similar in nature to a long term treasury bond. Year 1 2 3 4 5 6 ... 3 Sales Profit Capital Expense Working Capital Change in WC Depreciation EBIT Taxes Net Cash flow 100.00 20.00 -11.00 -10.00 -10.00 -10.00 10.00 -4.00 5.00 110.00 22.00 -12.00 -11.00 -1.00 -10.00 12.00 -4.80 14.20 113.30 22.66 -12.36 -11.33 -0.33 -10.30 12.36 -4.94 15.33 116.70 23.34 -12.73 -11.67 -0.34 -10.61 12.73 -5.09 15.79 120.20 24.04 -13.11 -12.02 -0.35 -10.93 13.11 -5.25 16.26 123.81 24.76 -13.51 -12.38 -0.36 -11.26 13.51 -5.40 16.75 ... ... ... ... ... ... ... ... ... As we can see from the table, this project will provide a net cash flow of $5MM at the end of year 1, $14.2MM at the end of year 2, $15.33MM at the end of year 3. From year 3 onwards, the cash flow will grow at 3% annually, which is equivalent to a 3% growing perpetuity with the first annul payment to be $15.33MM. This project breakeven NPV > 0 5 14.2 NPV Investment 1.03 1.04 2 15.326 (0.05 0.03) 0 1.053 Investment 23.56% By contrast, Mr. Craig was not willing to pay $28 for a share of Maybelline at the time of IPO. Return = (30.6 - 28)/28 = 9.29%