Fin550Midterm_2013_VersionA-KEY.pdf

# 60 1 4130621 1 001 101 91883 c c tyler needs to make

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60 1 41,306.21 1 0.01 (1.01) 918.83 C C Tyler needs to make monthly deposits of \$918.83 in order to finance Project Mayhem for five years (the difference is just due to rounding).

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8 6. Suppose that instead of the Project ending, Tyler wanted to fund Project Mayhem forever (i.e. make payments every six months forever, starting 60 months from now with \$10,000, with the payments growing by 2% each six months forever) by making a single deposit into his savings account today. What is the minimum amount he would need to deposit today to fully fund the Project forever? (10 points) Here we have a growing perpetuity which starts at month 60 and pays every six months forever. Because we have a six month period, we need a six month rate. We can use the EPR formula and we know that the APR is 12% and it is compounded monthly. Thus, m=12. We now want a semi- annual period which is ½ of a year so y=½ . 1 1 my APR EPR m 1 2 12* 0.12 1 1 0.0615 12 EPR Thus our semi-annual rate is 0.0615, which is r. We also know that the cash flows will grow at a rate of 2% per six month period so g=0.02. Finally, the value for C should be the first cash flow so it will be \$10,000. With a growing perpetuity, the present value is simply C/(r-g) 10,000 240,963.86 0.0615 0.02 PV HOWEVER, we need to remember that the formula assumes that the first payment occurs at the END of the period. If month 60 is the END of a six-month period, then the present value of the above growing perpetuity is really located at month 54. We need to discount that back to today by

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